Error Correction in Optical Networks by Probabilistic Shaping and Symbol Rate Optimization

Abstract

To provide an optical transmitter and a transmission method for stochastic shaping and symbol rate optimization.SOLUTION: A transmitter portion 600 includes multiple distribution matchers 604, multiple FEC encoders 606, multiple symbol mappers 607, multiple Nyquist filtering elements 608, and multiple frequency shift elements 609 for respective parallel streams generated by a serial / parallel converter 603. For each of subcarriers 1 to n, the transmitter portion 600 may perform symbol mapping and Nyquist filtering before frequency shift keying (FS) is applied. The outputs of multiple processing paths respectively including binary data representing various codewords are combined by a single subcarrier multiplexer 605 using subcarrier multiplexing for transmission to an optical receiver over optical transmission.SELECTED DRAWING: Figure 6A

Description

Technical Field

[0001] The present disclosure generally relates to error correction in optical networks that perform both probabilistic shaping and symbol rate optimization, and more specifically to optical communication networks.

Background Art

[0002] Telecommunication systems, cable television systems, and data communication networks use optical networks to carry large amounts of information at high speeds between remote locations. In an optical network, information is carried through optical fibers in the form of optical signals. Optical networks may also include various network nodes such as amplifiers, dispersion compensators, multiplexer / demultiplexer filters, wavelength selective switches, couplers, etc. to perform various operations within the network.

[0003] Optical superchannels are emerging solutions for the transmission of optical signals at 400 Gb / s and 1 Tb / s per channel, and in the future, much higher data rates can be expected. A typical superchannel includes a set of subcarriers that are frequency multiplexed to form a single wavelength channel. The superchannel can then be transmitted through the optical network as a single channel between network endpoints. The subcarriers within the superchannel are tightly packed to achieve high spectral efficiency while enabling the superchannel to achieve an increase in data capacity. However, the reach of the optical signal is still potentially limited by the optical signal-to-noise Ratio (OSNR) level during transmission, even when using superchannels. In some systems, constellation shaping or symbol rate optimization is applied to optical signals, such as high-capacity optical signals modulated using advanced modulation formats, to extend the transmission reach of specific optical signals.

Summary of the Invention

[0004] In one aspect, an optical transmitter for probabilistic shaping and symbol rate optimization includes one or more matcher elements. Each matcher element assigns a respective probability to a symbol in an M-QAM constellation of a given M-QAM modulation format in the complex plane represented by the binary data received by that matcher element, according to the target probability distribution of the symbols, and is configured to output a respective shaped bit sequence corresponding to the binary data received by that matcher element. The optical transmitter further includes a single systematic error correction coder configured to add parity bits collectively to each of the shaped bit sequences across each of the shaped bit sequences, and output a first composite shaped bit sequence including data representing each of the shaped bit sequences and the collectively added parity bits. The optical transmitter further includes a plurality of mapping elements each configured to generate a respective codeword for each symbol represented in the received portion of the first composite shaped bit sequence, a first serial / parallel converter configured to supply each portion of the first composite shaped bit sequence to each of the plurality of mapping elements, and a multiplexer configured to combine the binary data representing each of the codewords generated by the plurality of mapping elements for transmission on an optical transmission line by subcarrier multiplexing.

[0005] In any of the disclosed embodiments, the one or more matcher elements may include two or more matcher elements, and the optical transmitter may further include a first parallel / serial converter configured to combine each of the shaped bit sequences output by the two or more matcher elements to generate binary data representing a second composite shaped bit sequence, and supply the binary data representing the second composite shaped bit sequence as an input to a single systematic error correction coder.

[0006] In any of the disclosed embodiments, the optical transmitter may further include a second serial / parallel converter configured to supply each portion of the binary data received by the optical transmitter to respective ones of two or more matcher elements in a parallel binary data stream, and a plurality of tap elements. Each tap element may be configured to tap one or more bits from respective ones of the parallel binary data streams and supply the one or more tapped bits to a first parallel / serial converter. The first parallel / serial converter may be further configured to supply the one or more tapped bits received from respective ones of the plurality of tap elements to a single systematic error correction coder as bits to be collectively added across each of the shaped bit sequences output by the two or more matcher elements. In some embodiments, the optical transmitter may further include a combining element. Each of the tap elements may be further configured to supply one or more tapped bits, and the combining element may be configured to integrate the tapped bits supplied by the tap elements into a first composite shaped bit sequence before supplying the first composite shaped bit sequence as an input to the first parallel / serial converter. Parity In some embodiments, the optical transmitter may further include a combining element. Each of the tap elements may be further configured to supply one or more tapped bits, and the combining element may be configured to integrate the tapped bits supplied by the tap elements into a first composite shaped bit sequence before supplying the first composite shaped bit sequence as an input to the first parallel / serial converter.

[0007] In any of the disclosed embodiments, the optical transmitter may further include a second serial / parallel converter configured to supply each portion of the serial binary data received by the optical transmitter to respective ones of two or more matcher elements in a parallel binary data stream, and before converting the serial binary data into a parallel binary data stream, tap one or more bits from the serial binary data received by the optical transmitter, and supply the one or more tapped bits to a single systematic error correction coder as bits to be collectively added across each of the shaped bit sequences output by the two or more matcher elements. ParityIt may further include tap elements configured to supply bits to a single systematic error correction coder as bits. In some embodiments, the optical transmitter may further include a combining element. The tap element may be further configured to supply one or more tapped bits to the combining element, and the combining element may be configured to integrate the tapped bits supplied by the tap element into the first composite shaped bit sequence before supplying the first composite shaped bit sequence as an input to the first serial / parallel converter.

[0008] In any of the disclosed embodiments, one or more matcher elements may include a single matcher element.

[0009] In any of the disclosed embodiments, a single systematic error correction coder may be communicatively coupled to a single matcher element, may be configured to receive from the single matcher element a shaped bit sequence corresponding to the binary data received by the single matcher element, and the first serial / parallel converter may be configured to apply symbol-wise interleaving to the first composite shaped bit sequence to supply each portion of the first composite shaped bit sequence to respective ones of a plurality of mapping elements.

[0010] In any of the disclosed embodiments, the optical transmitter may further include a bit-wise interleaving element configured to receive the first composite shaped bit sequence from a single matcher element, apply bit-wise interleaving to the first composite shaped bit sequence to generate binary data representing a second composite shaped bit sequence, and supply the binary data representing the second composite shaped bit sequence as an input to the single systematic error correction coder.

[0011] In some embodiments, an optical receiver that receives transmission from an optical transmitter on an optical transmission path may include a single error correction decoder configured to receive binary data representing a first composite shaping bit sequence, extract collectively added parity bits from the binary data representing the first composite shaping bit sequence, and output a third composite shaping bit sequence from which the collectively added parity bits have been extracted. In some embodiments, the optical receiver may include two or more de-matcher elements and a second serial / parallel converter configured to receive the third composite shaping bit sequence output by the single error correction decoder and supply each portion of the third composite shaping bit sequence to each of the two or more de-matcher elements. Each de-matcher element may be configured to receive each portion of the third composite shaping bit sequence and recover binary data representing information transmitted by the optical transmitter from each portion of the third composite shaping bit sequence. In some embodiments, the optical receiver may include a single de-matcher element configured to receive a second composite shaping bit sequence and recover binary data representing information transmitted by the optical transmitter from the second composite shaping bit sequence.

[0012] In another aspect, a method for error correction in an optical network by probabilistic shaping and symbol rate optimization includes receiving binary data to be transmitted as an optical signal, and for each of one or more matcher elements, assigning a respective probability to a symbol of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the received binary data supplied to that matcher element, according to the target probability distribution of the symbol, outputting, for each of one or more matcher elements, a respective shaped bit sequence corresponding to the portion of the received binary data supplied to that matcher element, collectively adding parity bits to each of the shaped bit sequences across each of the shaped bit sequences to generate a first composite shaped bit sequence including data representing each of the shaped bit sequences and the collectively added parity bits, supplying each portion of the first composite shaped bit sequence to each of a plurality of mapping elements, each mapping element generating a respective codeword for each symbol represented in each portion of the first composite shaped bit sequence supplied to that mapping element, and combining binary data representing each of the codewords generated by the plurality of mapping elements for transmission on an optical transmission line by subcarrier multiplexing.

[0013] In any of the disclosed embodiments, one or more matcher elements may include two or more matcher elements, and the method may further include combining each of the shaped bit sequences output by the two or more matcher elements to generate binary data representing a second composite shaped bit sequence. Collectively adding parity bits to each of the shaped bit sequences across each of the shaped bit sequences may include adding parity bits to the second composite shaped bit sequence.

[0014] In any of the disclosed embodiments, the method may further include receiving binary data representing a first complex-shaped bit sequence via an optical transmission path, extracting collectively added parity bits from the binary data representing the first complex-shaped bit sequence, outputting a third complex-shaped bit sequence from which the collectively added parity bits have been extracted, supplying each part of the third complex-shaped bit sequence to each of two or more dematcher elements, and recovering, by each of the two or more dematcher elements, binary data representing information received via the optical transmission path from each part of the third complex-shaped bit sequence.

[0015] In any of the disclosed embodiments, the method may further include supplying each part of the serial binary data received for transmission to each of two or more matcher elements in a parallel binary data stream, and tapping one or more bits from each of the parallel binary data streams. Collectively adding parity bits to each of the shaped bit sequences may further include adding, as additional parity bits, one or more tapped bits received from each of a plurality of tap elements to the second complex-shaped bit sequence.

[0016] In any of the disclosed embodiments, the method may further include supplying each part of the serial binary data received for transmission to each of two or more matcher elements in a parallel binary data stream, and tapping one or more bits from the received serial binary data before converting the serial binary data into a parallel binary data stream. Collectively adding parity bits to each of the shaped bit sequences may further include adding, as additional parity bits, one or more tapped bits from the received serial binary data to the second complex-shaped bit sequence.

[0017] In any of the disclosed embodiments, one or more matcher elements may include a single matcher element.

[0018] In any of the disclosed embodiments, the method may further include receiving binary data representing a first complex-shaped bit sequence via an optical transmission path, extracting collectively added parity bits from the binary data representing the first complex-shaped bit sequence, outputting a second complex-shaped bit sequence from which the collectively added parity bits have been extracted, supplying the second complex-shaped bit sequence to a single dematcher element, and recovering, by the single dematcher element, binary data representing information received via the optical transmission path from the second complex-shaped bit sequence.

[0019] In any of the disclosed embodiments, supplying each portion of the first complex-shaped bit sequence to each of a plurality of mapping elements may include applying symbol-wise interleaving to the first complex-shaped bit sequence.

[0020] In any of the disclosed embodiments, the method may further include receiving a first complex-shaped bit sequence from a single matcher element and applying bit-wise interleaving to the first complex-shaped bit sequence to generate binary data representing a second complex-shaped bit sequence. Collectively adding parity bits to each of the shaped bit sequences may include adding parity bits to the second complex-shaped bit sequence.

[0021] In any of the disclosed embodiments, the number of mapping elements may be equal to the number of subcarrier channels selected for symbol rate optimization and may depend on the characteristics of the transmission medium for the optical transmission path and the target reach of the transmission.

[0022] For a more complete understanding of the present invention and its features and advantages, reference is now made to the following description taken in conjunction with the accompanying drawings.

Brief Description of the Drawings

[0023]

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[0024] In the following description, for the purpose of assisting in the discussion of the disclosed subject matter, details are shown by way of example. It will be apparent to those skilled in the art that the disclosed embodiments are examples and do not include all possible embodiments.

[0025] Referring now to the drawings, FIG. 1 depicts an example of an optical transport network (OTN) 101, which may represent an optical communication system. The optical transport network 101 includes one or more optical fibers 106 for carrying one or more optical signals communicated by components of the optical transport network 101. Network elements of the optical transport network 101 that are connected by the fibers 106 may include one or more transmitters (Tx) 102, one or more multiplexers (MUX) 104, one or more optical amplifiers 108, one or more optical add / drop multiplexers (OADM) 110, one or more demultiplexers (DEMUX) 105, and one or more receivers (Rx) 112.

[0026] The optical transmission network 101 may be a point-to-point optical network having terminal nodes, a ring optical network, a mesh optical network, or any other suitable optical network, or a combination of optical networks. The optical transmission network 101 may be used in short-distance urban networks, long-distance inter-urban networks, or any other suitable network, or a combination of networks. The capacity of the optical transmission network 101 may include, for example, 100 Gbit / s, 400 Gbit / s, or 1 Tbit / s. The optical fiber 106 has thin strands of glass that can communicate signals over long distances with very low loss. The optical fiber 106 may have a suitable type of fiber selected from a variety of fibers for optical transmission. The optical fiber 106 may include, among others, any suitable type of fiber such as standard SMF (Single-Mode Fiber), E-LEAF (Enhanced Large Effective Area Fiber), or TW-RS (TrueWave Reduced Slope).

[0027] The optical transmission network 101 may include a device that transmits optical signals over the optical fiber 106. Information may be transmitted and received through the optical transmission network 101 by modulating one or more wavelengths of light so as to encode information thereon. In optical networking, the wavelength of light is sometimes also referred to as a "channel" contained in the optical signal. Each channel may carry a certain amount of information through the optical transmission network 101.

[0028] To increase the information capacity and transmission capabilities of the optical transmission network 101, multiple signals transmitted on multiple channels may be combined into a single wide-bandwidth optical signal. The process of communicating information on multiple channels is optically referred to as wavelength division multiplexing (WDM). Coarse wavelength division multiplexing (CWDM) typically refers to the multiplexing of wavelengths with a relatively small number of channels, fewer than 16 wavelengths, and widely spaced wavelengths with an interval greater than 20 nm, onto a fiber. Dense wavelength division multiplexing (DWDM) typically refers to the multiplexing of wavelengths with a relatively large number of channels, more than 40 wavelengths, and closely spaced wavelengths with an interval less than 0.8 nm, onto a fiber. WDM or other multi-wavelength multiplexing transmission techniques are employed in optical networks to increase the aggregate bandwidth per optical fiber. Without WDM, the bandwidth in an optical network may be limited to the bit rate of just one wavelength. With a wider bandwidth, an optical network can transmit a greater amount of information. The optical transmission network 101 may transmit different channels using WDM or some other suitable channel multiplexing technique and amplify the multi-channel signals.

[0029] In recent years, the progress of DWDM has made it possible to combine several optical carrier waves to generate a composite optical signal of the desired capacity. One such example of a multi-carrier optical signal is a superchannel, which is an example of high spectral efficiency (SE) that can achieve transmission rates of 100 Gb / s, 400 Gb / s, 1 Tb / s, or more. Thus, in a superchannel, the sub-carriers are densely packed and consume less optical spectrum than conventional DWDM. Another notable feature of a superchannel is that the sub-carriers within the superchannel travel from the same starting point to the same destination and are not added or dropped using an OADM during transmission. Techniques for achieving high spectral efficiency (SE) in an optical network may include the use of superchannels modulated using dual-polarization quadrature phase-shift keying (DP-QPSK) for long-haul transmission at data rates of 100 Gb / s or more. In certain embodiments, Nyquist Wavelength Division Multiplexing (N-WDM) may be used in a superchannel. In N-WDM, optical pulses having a substantially rectangular spectrum are packed together in the frequency domain with a bandwidth approaching the baud rate.

[0030] The optical transmission network 101 may include one or more optical transmitters (Tx) 102 that transmit optical signals through the optical transmission network 101 at specific wavelengths or channels. The transmitter 102 may have a system, device, or apparatus that converts an electrical signal into an optical signal and transmits the optical signal. For example, each of the transmitters 102 may receive an electrical signal, modulate the information contained in the electrical signal onto a beam of light generated by a laser at a specific wavelength, and have a laser and a modulator to transmit the beam carrying the signal across the optical transmission network 101. In some embodiments, the optical transmitter 102 may be used to determine the baud rate for transmitting data during optical modulation. An example of a transmitter 102 that applies different baud rates is an adaptive rate transponder. An example of a transmitter 102 that applies different modulation formats is a universally programmable transceiver. Furthermore, a Forward Error Correction (FEC) module may be included in the optical transmitter 102 or may be used with the optical transmitter 102. The FEC module may process the electrical signal carrying the information or data to be transmitted to include an error correction code. The FEC module in the transmitter 102 may also determine the baud rate for sending the data to be transmitted to the optical transmitter 102 for optical modulation.

[0031] The multiplexer 104 may be coupled to the transmitter 102 and may be a system, device, or system that combines the signals transmitted by the transmitter 102, for example, at each individual wavelength, into a WDM signal.

[0032] Optical amplifier 108 may amplify the multi-channel signals within optical transmission network 101. Optical amplifier 108 may be positioned before and after a specific length of fiber 106, which is referred to as "in-line amplification". Optical amplifier 108 may have a system, device, or apparatus for amplifying an optical signal. For example, optical amplifier 108 may have an optical repeater for amplifying an optical signal. This amplification may be performed together with optical-electric or electric-optical conversion. In some embodiments, optical amplifier 108 may have an optical fiber doped with a rare earth element to form an additional fiber amplification element. External energy may be applied in the form of a pump signal to excite the atoms of the additional portion of the optical fiber when the signal passes through the fiber. This amplifies the strength of the optical signal. As an example, optical amplifier 108 may have an Erbium-Doped Fiber Amplifier (EDFA). Any other suitable amplifier such as a Semiconductor Optical Amplifier (SOA) may also be used.

[0033] OADM 110 may be coupled to optical transmission network 101 via fiber 106. OADM 110 has an add / drop module. The add / drop module may include a system, device, or apparatus for adding and dropping optical signals (i.e., at individual wavelengths) from fiber 106. After passing through OADM 110, the optical signal may proceed directly along fiber 106 to a destination, or the signal may pass through one or more additional OADM 110s and optical amplifiers 108 before reaching the destination. In this way, OADM 110 enables the connection of different optical transmission network topologies such as different rings and different linear spans together.

[0034] In a particular embodiment of the optical transmission network 101, the OADM 110 may correspond to a Reconfigurable Optical Add-Drop Multiplexer (ROADM) that can add or drop individual or multiple wavelengths of a WDM signal. The individual or multiple wavelengths may be added or dropped in the optical domain, for example, using a Wavelength Selective Switch (WSS) (not shown in FIG. 1) that may be included in the ROADM.

[0035] Many existing optical networks operate at a signal rate of 10 Gigabits per second (Gbps) or 40 Gbps with a channel spacing of 50 Gigahertz (GHz) according to the ITU (International Telecommunications Union) standard wavelength grid, also known as a fixed grid spacing. This is compatible with the conventional implementation of an optical add / drop multiplexer (OADM) and the conventional implementation of the demultiplexer 105. However, as the data rate increases to 100 Gbps or more, the broader spectral requirements of such higher data rate signals often require widening the channel spacing. In conventional fixed grid networking systems that support signals of different rates, the entire network system typically has to operate at the coarsest channel spacing (100 GHz, 200 GHz, etc.) that can accommodate the maximum rate signal. This can lead to over-provisioning of channel spectra for lower rate signals and lower overall spectral utilization.

[0036] Thus, in certain embodiments, the optical transmission network 101 may employ components that are compatible with flexible grid optical networking that enables specifying a particular frequency slot for each channel. For example, each wavelength channel of WDM transmission may be allocated using at least one frequency slot. Thus, one frequency slot may be allocated to a wavelength channel with a low symbol rate, while multiple frequency slots may be allocated to a wavelength channel with a high symbol rate. Thus, in the optical transmission network 101, the ROADM 110 may have the ability to add or drop individual or multiple wavelengths of a WDM, DWDM, or superchannel signal carrying data channels to be added or dropped in the optical domain. In certain embodiments, the ROADM 110 may include or be coupled to a wavelength selective switch (WSS).

[0037] As shown in FIG. 1, the optical transmission network 101 may also include one or more demultiplexers 105 to one or more destinations of the network 101. The demultiplexer 105 may have a system, apparatus, or device that operates as a demultiplexer by splitting a single composite WDM signal into individual channels at each wavelength. For example, the optical transmission network 101 may transmit and carry a 40-channel DWDM signal. The demultiplexer 105 may split the signal, i.e., the 40-channel DWDM signal, into 40 separate signals according to 40 different channels. It will be understood that different numbers of channels or subcarriers may be transmitted and demultiplexed in the optical transmission network 101 in various embodiments.

[0038] In FIG. 1, the optical transmission network 101 may also include a receiver 112 coupled to the demultiplexer 105. Each receiver 112 may receive an optical signal transmitted at a specific wavelength or channel and process the optical signal to obtain (demodulate) the information (data) contained in the optical signal. Thus, the network 101 may include at least one receiver 112 for each channel of the network. As shown, the receiver 112 may demodulate the optical signal according to the baud rate used by the transmitter 102. In some embodiments, the receiver 112 may include or may be followed by a forward error correction (FEC) mode that uses an error correction code to check the integrity of the received data. The FEC module may also correct specific errors in the data based on the error correction code. The FEC module in the receiver 112 may demodulate the data at a specific baud rate defined for each channel at the transmitter 102 as described above.

[0039] Optical networks such as the optical transmission network 101 of FIG. 1 may use modulation techniques to carry information in optical signals over optical fibers. Such modulation schemes may include, among other examples of modulation techniques, Phase-Shift Keying (PSK), Frequency-Shift Keying (FSK), Amplitude-Shift Keying (ASK), and Quadrature Amplitude Modulation (QAM). In PSK, the information carried by the optical signal may be conveyed by modulating the phase of a reference signal known as the carrier wave, or simply the carrier. The information may be conveyed by modulating the phase of the signal itself using Binary Phase-Shift Keying (BPSK), quadrature phase-shift keying (QPSK), Multi-level Phase-Shift Keying (M-PSK), and Differential Phase-Shift Keying (DPSK). In QAM, the information carried by the optical signal may be conveyed by modulating both the amplitude and phase of the carrier wave. PSK may be regarded as part of QAM in which the amplitude of the carrier wave is kept constant.

[0040] PSK and QAM signals may be represented using a complex plane having a real axis and an imaginary axis on a constellation diagram. Points on the constellation diagram representing symbols carrying information may be positioned at uniform angular intervals around the origin of the diagram. The number of symbols to be modulated using PSK and QAM may be increased, thus increasing the information that can be carried. The number of signals may be given as a multiple of 2. When additional symbols are added, they may be arranged uniformly around the origin. PSK signals may include such an arrangement circularly on the constellation diagram, i.e., PSK signals have a constant power for all symbols. QAM signals may have the same angular arrangement as that of the PSK signals but may include different amplitude arrangements. QAM signals may have those symbols arranged around a plurality of circles, i.e., QAM signals include different powers for different symbols. This arrangement may reduce the risk of noise when the symbols are separated from each other as much as possible. Thus, the number of symbols “m” is used and may be represented as “m-PSK” or “M-QAM”.

[0041] Examples of PSK and QAM with different numbers of symbols may include binary PSK (BPSK or 2-PSK) using two phases at 0° and 180° (or in radians, 0 and π) on the constellation diagram, or quadrature PSK (QPSK, 4-PSK, or 4-QAM) using four phases at 0°, 90°, 180°, and 270° (or in radians, 0, π / 2, π, and 3π / 2). The phases in such signals may be offset. Each of the 2-PSK and 4-PSK signals may be arranged on the constellation diagram. Certain m-PSK signals may also be polarized using techniques such as differential phase-shift keying QPSK (DP-QPSK), where the separated m-PSK are multiplexed by orthogonally polarizing the signals. Also, M-QAM signals may be polarized using techniques such as differential polarization 16-QAM (DP-16-QAM), where the separated M-QAM signals are multiplexed by orthogonally polarizing the signals.

[0042] Polarization multiplexing technology, sometimes also referred to as Polarization Division Multiplexing (PDM), enables achieving a higher bit rate for information transmission. PDM transmission has the effect of simultaneously modulating information onto various polarization components of an optical signal associated with a channel, thereby nominally increasing the transmission rate by a multiple of the number of polarization components. The polarization of an optical signal can refer to the direction of oscillation of the optical signal. The term "polarization" generally may refer to the path traced by the tip of the electric field vector at a point in space, which is perpendicular to the propagation direction of the optical signal.

[0043] In certain embodiments, the optical transmission network 101 may transmit superchannels. In a superchannel, a plurality of subcarriers (or subchannels or channels) are densely packed in a fixed bandwidth band and may be transmitted at a very high data rate such as 400 Gb / s, 1 Tb / s, or higher. Further, the superchannel may be suitable for transmission over a very long distance, such as several hundred kilometers. A typical superchannel may have a set of subcarriers that are frequency multiplexed to form a single channel transmitted through the optical transmission network 101 as one entity. The subcarriers within a superchannel may be densely packed to achieve a high spectral efficiency.

[0044] In an optical network such as the optical transmission network 101 of FIG. 1, it is common to refer to a management plane, a control plane, and a transmission plane (sometimes called the physical layer). A central management host (see also FIG. 3) may exist in the management plane and may configure and supervise components of the control plane. The management plane includes ultimate control over all transmission plane and control plane entities (e.g., network entities). As an example, the management plane may consist of a central processing unit (e.g., the central management host) that includes one or more processing resources, a data storage component, and the like. The management plane may communicate electrically with elements of the control plane and also with one or more network elements of the transmission plane. The management plane may perform management functions for the entire system and may bring about cooperation among network elements, the control plane, and the transmission plane. As an example, the management plane may include an Element Management System (EMS) that treats those elements from the perspective of one or more network elements, a Network Management System (NMS) that treats many devices from the start point of the network, or an Operational Support System (OSS) that treats network-scale operations.

[0045] Without departing from the scope of the present disclosure, changes, additions, or deletions may be made to the optical transmission network 101. For example, the optical transmission network 101 may include more or fewer elements than those represented in FIG. 1. Also, even if represented as a point-to-point network as described above, the optical transmission network 101 may be any suitable network topology for transmitting optical signals, such as a ring, mesh, or hierarchical network topology.

[0046] During operation, the optical transmission network 101 represents a specific transmission capacity for data. As the demand for transmission capacity continues to increase, various methods may be adopted on the optical transmission network 101 to adapt to more transmission capacity. For example, advanced modulation formats such as 16-QAM or 64-QAM may be used to increase the transmission capacity for each wavelength channel. The advanced modulation format may be applied using the transmitter 102 and the receiver 112. However, the use of higher-order modulation formats may result in a reduction in the transmission reach of the optical signal (also simply referred to as "reach"). For example, reach may be determined by the bit error rate (BER) observable at the receiver 112, and thus the allowable value of OSNR.

[0047] Another strategy for increasing transmission capacity is the use of superchannels where multiple subcarriers (or subchannels or channels) are densely packed in a fixed bandwidth band and can be transmitted at very high data rates such as 400 Gb / s, 1 Tb / s, or higher. As described above, optical superchannels can correspond to a promising solution for signal transmission at data rates of 400 Gb / s and 1 Tb / s for each channel. However, as described above, superchannels are typically used in fixed grid network components. This may not be universally available. Also, the administration of superchannels may be associated with an additional layer of network management, which may be undesirable in a particular network. The use of superchannels typically enables an increase in transmission capacity, while superchannels typically do not extend the transmission reach of the optical signals using the optical transmission network 101.

[0048] During operation of the optical transmission network 101, constellation shaping may be applied to an optical signal, such as a high-capacity optical signal modulated using an advanced modulation format, to extend the transmission reach of the specific optical signal. In constellation shaping, data bits are mapped and encoded into an improved constellation that may exhibit improved noise tolerance or an increased OSNR. As a result of the improved noise tolerance, the reach of the optical signal to which constellation shaping is applied will be extended, which is desirable for optical communications using the optical transmission network 101. In a typical modulation format (e.g., QPSK or M-QAM), symbols exhibit a uniform distribution in the complex plane, as shown as uniformly distributed constellation points in a constellation diagram. When constellation shaping is applied to the modulation format, the distribution of symbols in the complex plane is changed to provide an improved mapping of noise tolerance. In some cases, the distribution of symbols may be a Gaussian or Gaussian-like distribution, shown as non-uniform constellation points in a constellation diagram (see also FIG. 2).

[0049] As described above, the transmitter 102 may be a universally programmable transceiver that applies different modulation formats, while the receiver 112 may include corresponding functions for demodulation. Thus, the transmitter 102 may be adapted to use constellation shaping and may be selectively programmed to apply constellation shaping on a per-channel basis, while the receiver 112 may correspondingly demodulate channels to which a particular type of constellation shaping has been applied. In various embodiments, the transmitter 102 and the receiver 112 may each include a respective mapping / demapping function, e.g., within a digital signal processing (DSP) module, to enable implementation of constellation shaping in the optical transmission network 101.

[0050] In one example, constellation shaping may include superposition mapping, as described by Equation (1).

Number

[0051] In Equation (1), y is an optical signal consisting of modulated symbols, y I and y Q are the in-phase (real) and quadrature (imaginary) components, N is the number of bits per symbol, b n is the encoded binary bit, h n is h n =α n e jθn is a weighted symbol mapping scheme given by, where α n is the amplitude factor, and θ n is the phase factor.

[0052] In this example, h n assigns specific amplitudes and phases to each symbol. By adjusting the amplitude factor α n and the phase factor θ n , different superposition mapping schemes can be implemented. For example, in superposition coding mapping using phase shift modulation (PSM), the amplitude factor α n is kept constant, and the phase factor θ n is uniformly distributed in the complex plane. Furthermore, different coding schemes such as superposition coding mapping using bit interleaved coded modulation may be applied before the superposition mapping. It is known that when the superposition mapping is used in a non-bijective (many-to-one) mapping, decoding and demapping at the receiver may involve iterative operations.

[0053] Other constellation shaping techniques include Iterative Polar Modulation (IPM) and Low - density Parity Check coded modulation along with probabilistic shaping. Probabilistic shaping (PS) based on M - QAM has been studied as a way to control spectral efficiency at a finer granularity and achieve improved performance closer to the Shannon capacity limit. In one example, PS - M - QAM may be implemented using Constant Composition Distribution Matching (CCDM). Performing probabilistic shaping based on M - QAM can improve the utilization of network resources. In some cases, the shaped profile follows a Maxwell - Boltzmann distribution. Using existing methods, the minimum entropy of probabilistic shaping based on M - QAM is 2 bits / symbol, which corresponds to QPSK. Here, entropy as an indicator of information is defined as the number of bits of information contained in each message or symbol when channel noise is not considered.

[0054] In the optical transmission network 101, constellation shaping may be made active / inactive as a procedure in network operation on a channel - by - channel basis for a given optical path. In this way, the available spectrum can be flexibly allocated with respect to bandwidth and constellation shaping to satisfy various traffic demands based on specific path information (distance, number / type of co - propagating channels, fiber type, and dispersion map), which may be economically favorable. Furthermore, constellation shaping using a general - purpose programmable transceiver in the optical transmission network 101 can bring about an improvement in reach together with the same electronic and optical components that are already available and installed, which may enable a rapid upgrade to implement constellation shaping.

[0055] As described above, entropy may be defined as the number of bits of information contained in each message or symbol. Entropy may be calculated using the following equation:

Equation

[0056] In Equation (2), X is a discrete random variable that can take on M symbols {x1, x2, ···, x M}, and P(X) is a probability mass function representing the probability of each assigned symbol. In the case of a uniform distribution, Equation 2 becomes as follows.

Equation

[0057] FIG. 2A shows selected elements of an embodiment of a uniform probability distribution diagram 200 corresponding to a constellation diagram in the complex plane for 16-QAM. In this example, for 16-QAM having a uniform distribution, there are 16 different symbols each having a probability of 1 / 16. The height of each column represents the probability value of the symbol at the corresponding position in the constellation diagram 200. In this example, the probability of each assigned symbol is 1 / 16, i.e., 0.0625. As will be described later, applying the probability P = 1 / 16 to the above Equation (2), applying M = 16 to the above Equation (3), or applying M = 16 to the above Equation (4) results in an entropy of 4 bits per symbol.

[0058] Referring now to FIG. 2B, there is shown a selected element of an embodiment of a probability distribution diagram 201 for constellation points in a probabilistically shaped 16-QAM constellation. In the probability distribution diagram 201, the probabilistically shaped 16-QAM constellation is shown to have a non-uniform probability distribution of constellation points as an example of constellation shaping disclosed herein. The height of each column represents the probability value of the symbol at the corresponding position in the constellation diagram for 16-QAM.

[0059] As represented in FIG. 2B, the probabilistic shaping is circularly symmetric and the probability depends on the symbol energy. For example, all symbols at the same first distance from the center of the constellation have the same probability. In the example shown, the probabilistic shaping is applied to the 16-QAM constellation to increase the relative probability of the four innermost symbols (when compared to the uniform distribution) and decrease the probability of the other symbols. As a result of the shaping, the eight symbols at the same second distance from the center of the constellation have the same energy and corresponding probability to each other. Both their energy and probability are smaller than those of the four innermost symbols. The four outermost symbols at the same third distance from the center of the constellation (shown as corner symbols in FIG. 2B in the probability distribution diagram 201) have the same energy and corresponding probability outside the body, and the probability is the smallest among those of the symbols in the constellation.

[0060] In the extreme case of probabilistic shaping for 16-QAM, the four innermost symbols each have a probability of 0.25, and all other symbols have a probability of zero. This extreme case represents the lowest possible entropy of 2 bits / symbol, which corresponds to the QPSK modulation format. In this case, as shown by the formula for calculating entropy above, the number of bits / symbol is smaller than that of uniform 16-QAM. Note that in the example shown in FIG. 2B, note that no symbol has a probability of zero. Therefore, the lowest possible entropy of 2 bits / symbol is not achieved in this example. Note that by controlling the probability, the actual data rate for transmitting the information encoded in the optical signal can also be controlled.

[0061] As described in more detail herein, methods and systems for error correction in optical transmission networks, such as optical transmission network 101 that implements both probabilistic shaping and symbol rate optimization, are disclosed. In such a network, a single systematic error correction encoder may be configured to collectively add parity bits across each of the shaped bit sequences associated with different subcarrier channels.

[0062] Referring now to FIG. 3, there is shown a block diagram of selected elements of an embodiment of a network management system 300 that implements a control plane function in an optical network, such as, for example, optical transmission network 101 (see FIG. 1). The control plane may include functions for network intelligence and control and may have an application that supports the ability to establish network services, including applications or modules for discovery, routing, path calculation, and signaling, as described in further detail. The control plane applications executed by network management system 300 may operate together to automatically establish services within the optical network. Discovery module 312 may discover local links that connect to neighbors. Routing module 310 may broadcast local link information to optical network nodes while populating database 304. When a service request from the optical network is received, path calculation engine 302 may be called to calculate a network path using database 304. This network path may then be supplied to signaling module 306 to establish the requested service.

[0063] As shown in FIG. 3, network management system 300 includes a processor 308 and a memory medium 320. Memory medium 320 may store executable instructions (i.e., executable code). The executable instructions may be executable by processor 308 having access to memory medium 320. Processor 308 may execute instructions that cause network management system 300 to perform the functions and operations described herein. For purposes of this disclosure, memory medium 320 may include a non-transitory computer-readable medium that stores data and instructions for at least a certain period of time. Memory medium 320 may include persistent and volatile media, fixed and removable media, and magnetic and semiconductor media. Memory medium 320 may include, without limitation, direct access storage devices (e.g., hard disks or floppy (registered trademark) disks), sequential access storage devices (e.g., tape disk drives), compact discs (CDs), random access memory (RAM), read-only memory (ROM), CD-ROMs, digital versatile discs (DVDs), electrically erasable programmable read-only memory (EEPROM), and flash memory, such as storage media, non-transitory media, or various combinations of the above. Memory medium 320 is operable to store instructions, data, or both. Memory medium 320 shown includes a set or sequence of instructions that may correspond to an executable computer program, namely, a path calculation engine 302, a signaling module 306, a discovery module 312, and a routing module 310.

[0064] Network interface 314 is also shown as being included with network management system 300 in FIG. 3. Network interface 314 may be a suitable system, apparatus, or device operable to function as an interface between processor 308 and network 330. Network interface 314 may enable network management system 300 to communicate over network 330 using a suitable transmission protocol or standard. In some embodiments, network interface 314 may be communicatively coupled to network storage resources via network 330. In some embodiments, network 330 represents at least a particular portion of optical transmission network 101. In a particular embodiment, network 330 may include at least a particular portion of a public network such as the Internet. Network 330 may be implemented using hardware, software, or various combinations thereof.

[0065] In a particular embodiment, the control plane may be configured to interact with a person (i.e., a user) and receive data regarding the signaling path. For example, the control plane may also include and / or be coupled to one or more input devices or output devices that assist in receiving data regarding the signaling path from the user and outputting results to the user. The one or more input and output devices (not shown in FIG. 3) may include, without limitation, a keyboard, mouse, touchpad, microphone, display, touch screen display, audio speaker, etc. Alternatively or additionally, the control plane may be configured to receive data regarding the signaling path from a device (not shown in FIG. 3), such as another computer device or network element, via network 330 for example.

[0066] As shown in FIG. 3, in some embodiments, the discovery module 312 may be configured to receive data regarding optical signal transmission paths in an optical network and may be involved in discovering links between neighbors and neighbors. That is, the discovery module 312 may transmit discovery messages according to a discovery protocol and may receive data regarding optical signal transmission paths. In some embodiments, the discovery module 312 may determine, among other things, without limitation, fiber type, fiber length, number and type of components, data rate, data modulation format, input power of the optical signal, number of signals carrying wavelengths (i.e., channels), channel spacing, traffic demand, and network topology and other characteristics.

[0067] As shown in FIG. 3, the routing module 310 may be involved in propagating link connectivity information to various nodes within an optical network such as the optical transmission network 101. In certain embodiments, the routing module 310 may populate the database 304 with resource information to assist with traffic engineering. Traffic engineering may include link bandwidth availability. Accordingly, the database 304 may be populated by the routing module 310 with information that can be used to determine the network topology of the optical network.

[0068] The path calculation engine 302 may be configured to use the information supplied to the database 304 by the routing module 310 to determine the transmission characteristics of the optical signal transmission path. The transmission characteristics of the optical signal transmission path may provide insights, inter alia, into how chromatic dispersion (CD), nonlinear (NL) effects, polarization mode dispersion (PMD) and polarization effects such as polarization dependent loss (PDL), as well as transmission degradation factors such as amplified spontaneous emission (ASE), may act on the optical signal within the optical signal transmission path. To determine the transmission characteristics of the optical signal transmission path, the path calculation engine 302 may consider the interaction between the transmission degradation factors. In various embodiments, the path calculation engine 302 may generate values for specific transmission degradation factors. The path calculation engine 302 may further store data describing the optical signal transmission path in the database 304.

[0069] In FIG. 3, the signaling module 306 may provide functions associated with setting up, modifying, and tearing down end-to-end network services in the optical transmission network 101. For example, when the ingress node of the optical network receives a service request, the control plane may use the signaling module 306 to request from the path calculation engine 302 a network path that can be optimized according to various criteria such as bandwidth, cost, etc. When the desired network path is identified, the signaling module 306 may then communicate with each node along the network path to establish the requested network service. In various embodiments, the signaling module 306 may also use a signaling protocol to propagate subsequent communications between the nodes along the network path.

[0070] During operation of the network management system 300, the routing engine 302, or other entity or module, may supply routing information associated with a given optical path, such as distance, the number and type of optical channels to be transmitted, fiber type, and dispersion map. For example, the signaling module 306, or other entity or module, may receive the routing information and determine whether to use constellation shaping and / or subcarrier multiplexing for either the type of modulation format or any of the optical channels transmitted over the optical path. To activate or deactivate constellation shaping, the signaling module 306 may send a first command to each transmitter for each of the optical channels. The signaling module 306 may then send a second command to each receiver corresponding to each transmitter to activate or deactivate constellation shaping. Transmitters and receivers having a general-purpose programmable transponder function may receive commands from the signaling module 306 and then activate or deactivate the transmission of optical channels using constellation shaping. Similarly, to activate or deactivate symbol rate optimization using subcarrier multiplexing, the signaling module 306 may send a first command to each transmitter for each of the optical channels. The signaling module 306 may then send a second command to each receiver corresponding to each transmitter to activate or deactivate symbol rate optimization using subcarrier multiplexing. Transmitters and receivers having a general-purpose programmable transponder function may receive commands from the signaling module 306 and then activate or deactivate the transmission of optical channels using subcarrier multiplexing. In at least some embodiments, the optical transmission network described herein may be configured to implement both constellation shaping and symbol rate optimization using subcarrier multiplexing for the same optical channel.

[0071] FIG. 4 is a schematic diagram representing selected elements of an example of an optical transmission system 400 configured to apply symbol-level probabilistic shaping to one or more WDM channels in an optical network. In the example shown, the transmission system 400 includes, on the transmitter side, binary data supplied to the optical transmission system 400 for transmission, a forward error correction (FEC) encoder 406, a symbol mapper 408, and an optical modulator 410, and includes an optical channel 412 having an appropriate transmission medium, and on the receiver side, includes elements similar to those of a conventional transmitter / receiver including a coherent receiver and DSP elements 414, a symbol demapper 416, and an FEC decoder 418. In some embodiments, the FEC encoder 406 may be a systematic error correction encoder.

[0072] To apply probabilistic shaping, the transmission system 400 also includes a distribution matcher 404 on the transmitter side and a distribution dematcher 420 on the receiver side. The matcher may ensure that the central constellation points have a higher probability of occurrence than the end constellations. For example, the distribution matcher 404 may be configured to control the probability of occurrence of specific constellation points on the transmitter side to shape the distribution of the constellation points, and the distribution dematcher 420 may be configured to reverse the probabilistic shaping process.

[0073] In the optical transmission system 400, the distribution matcher 404 receives the binary data 402 and generates data that is modified to achieve a specific probability profile, for example, based on a target probability distribution. Following the distribution matcher 404, the FEC encoder 406 and the symbol mapper 408 may add forward error correction encoding and mapping portions to each symbol of the binary data 402 (which now has probabilities shaped by the distribution matcher 404) before supplying the output to the optical modulator 410 for transmission over the optical channel 412. In the example shown, the coherent receiver and DSP 414 may use the demapper 414 to extract the modified and mapped portions of the binary data 402 that was supplied to the optical modulator 410 and transmitted over the optical channel 412. Thereafter, this binary data may be processed by the FEC decoder 418 and the distribution dematcher 420 to recover the originally received binary data, shown as recovered data 422.

[0074] In the optical transmission system 400, the coherent receiver and DSP element 414 may include any or all of an I / Q imbalance compensation element, a chromatic dispersion compensation element, an adaptive equalizer, a polarization demultiplexer, a frequency offset compensation element, a carrier phase recovery element, and / or a cycle slip compensation element.

[0075] In one example, probabilistic constellation shaping may be applied in a transponder configured to transmit an optical signal using 64-QAM. By applying probabilistic shaping, the spectral efficiency can vary from 64-QAM to QPSK (e.g., from 6 bits / symbol per polarization to 2 bits / symbol per polarization) with very fine adjustment. In some embodiments, the spectral efficiency may be changed in increments of less than 1 bit / symbol. For example, rather than the spectral efficiency being set exactly to a value of 6 or 5 bits / symbol, the spectral efficiency may be set, for example, to a value of 5.1, 5.5, or 5.9 bits / symbol. In some embodiments, using the distribution matcher 404 and the distribution dematcher 420, one transponder can cover the entire range of spectral efficiencies between 2 bits / symbol and 6 bits / symbol.

[0076] While probabilistic shaping is becoming more popular due to the potential for SNR performance gain by shaping and the ability to finely tune the spectral efficiency, this approach has been found to incur a large non-linear transmission penalty compared to uniform QAM. There is an optimal symbol rate that minimizes the non-linearity penalty in a fiber transmission system using subcarrier multiplexing, and it has been discovered that this optimal symbol rate depends on the characteristics of the transmission fiber being used and the transmission distance. In at least some embodiments, subcarrier modulation may be utilized together with probabilistic shaping to improve transmission performance. In one example, a probabilistically shaped signal having a baud rate of 64 Gbaud may be split across four subcarriers. In this example, the baud rate of each subcarrier may be about 16 Gbaud.

[0077] Nonlinear interactions between subcarriers of a multi-carrier channel may include, among other things, phenomena such as Cross Phase Modulation (XPM), Self-Phase Modulation (SPM), and four-wave mixing. Cross-phase modulation can occur when phase information, amplitude modulation, or both from one subcarrier are modulated onto adjacent subcarriers within a multi-carrier channel. Self-phase modulation can occur when a change in the refractive index (or the dependence of the refractive index on intensity) causes a phase shift within each subcarrier. In four-wave mixing (FWM), three wavelengths may interact to generate a fourth wavelength that may match the wavelength of a subcarrier, causing an undesirable change in peak power or other types of signal distortion in the affected subcarriers. Further, non-linear crosstalk may have an inter-subcarrier component. Nonlinear interactions occur during fiber transmission and may not depend on the degree of overlap of the subcarrier frequency bands, so Nyquist pulse shaping may not be effective in solving certain problems associated with non-linear crosstalk in multi-carrier channels. In some embodiments, by splitting a single high-symbol-rate channel into multiple low-symbol-rate subcarriers, the effects of SPM and / or XPN can be significantly reduced. However, FWM can increase as the number of subcarriers increases. Thus, an optimal number of subcarriers, and the corresponding optimal symbol rate, may exist such that the total penalty due to fiber non-linearity is minimized, which may enable an extension of the transmission reach.

[0078] FIG. 5 shows the relationship between the non-linearity penalty, the transmission fiber characteristics, and the optimal symbol rate for a particular fiber type. More specifically, FIG. 5 shows, for a standard single-mode fiber (SMF), the non-linear interference G ch versus the number of channels N NLIRepresents an example of a graph 500 to be plotted. More specifically, the x-axis indicates the number of channels in a given signal band, while the y-axis indicates the coefficients of various non-linearity measurements as the number of channels increases.

[0079] In the example of graph 500 shown in FIG. 5, the straight line 502 (GN) represents a Gaussian noise model. The GN model assumes the same non-linear interference regardless of the number of sub-carrier channels for simplicity, and alone, it cannot accurately predict the effect of sub-carrier multiplexing on non-linearity well enough to be particularly useful in performing symbol rate optimization. In graph 500, the curve 504 (SPM) represents the self-phase modulation effect, the curve 506 (XPM) represents the cross-phase modulation effect, and the curve 508 (FWM) represents the four-wave mixing effect, all of which contribute to non-linear interference. In this example, the curve 510 (EGN) represents enhanced Gaussian noise that can be used in some embodiments to estimate non-linear interference in specific sub-carrier channels. More specifically, the EGN model is a set of the SPM, XPM, and FWM models and represents the overall non-linear interference penalty as the number of sub-carrier channels increases. This set model is considered to be more accurate than the GN model alone and is more suitable for use in performing symbol rate optimization. Using the EGN model, non-linear interference can be minimized at a specific number of sub-carrier channels in a given bandwidth. This can correspond to the optimal symbol rate for a given baud rate such as 64G baud. For example, the total non-linear interference may be calculated and plotted using the ENG model, and then the minimum non-linear interference penalty may be identified as the point where the ENG curve 510 drops to its lowest point with respect to the y-axis. The point where the ENG curve 510 drops to its lowest point may correspond to the optimal number of sub-carriers as shown on the x-axis.

[0080] Preliminary studies have shown that as the number of subcarriers increases, the fiber input power also increases, thus improving the non - linear transmission performance. Furthermore, it has been shown that when the entropy is reduced and stronger shaping is introduced, the gain achieved when using the optimal number of subcarriers increases. The studies have also shown that the performance at the central subcarriers may degrade more than that at the outer subcarriers due to the increased cross - phase modulation effect from adjacent channels.

[0081] Probabilistic shaping with symbol rate optimization has been shown to result in increased SNR performance gain and minimal non - linear transmission penalty. That is, the introduction of Symbol Rate Optimization (SRO) can improve the transmission performance of probabilistically shaped signals. Approaches for implementing both probabilistic shaping and symbol rate optimization where each subcarrier is associated with a different shaping factor, different net data rate, and / or different error correction rate can be prohibitively complex to implement. In at least some embodiments, the optical transmission system described herein does not perform FEC encoding for each subcarrier. Instead, it may implement both probabilistic shaping and symbol rate optimization using subcarrier multiplexing, using an error correction technique that applies error correction across the bitstreams from all subcarriers to average the performance of the subcarrier channels using a systematic error correction encoder. As described in more detail below, such a system includes one or more matcher elements each configured to assign respective probabilities to symbols represented in the received binary data according to a target probability distribution and output respective shaped bit sequences, and a single systematic error correction encoder configured to output a composite shaped bit sequence including the shaped bit sequences and data representing the added parity bits added collectively across the shaped bit sequences.

[0082] FIG. 6A is a schematic diagram representing selected elements of a transmitter portion 600 of an optical transmission system configured to apply symbol rate optimization using probabilistic constellation shaping and sub-carrier multiplexing, according to some embodiments. For example, in addition to performing symbol rate optimization using sub-carrier multiplexing, the transmitter portion 600 may be configured to perform probabilistic shaping based on M-QAM. In the illustrated embodiments, at least some of the elements of the transmitter portion 600 of the optical transmission system are similar to the elements of the transmitter portion of the optical transmission system 400 shown in FIG. 4 above. The display of the transmitter portion 600 is schematic and not to scale. In various embodiments, the transmitter portion 600 may be implemented with more, fewer, or different elements than those shown in FIG. 6A. In some embodiments, the transmitter portion 600 may include a field programmable gate array (FPGA) that performs at least some of the functions described herein. In some embodiments, the transmitter portion 600 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, the transmitter portion 600 includes binary data 602 that is provided for transmission to a receiver portion of the optical transmission system. In at least some embodiments, the transmitter portion 600 shown in FIG. 6A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of the data 602 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0083] A single serial / parallel converter 603 divides incoming binary data 602 into n streams. Each stream is directed to a respective processing path for parallel processing. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and on the n sub-carrier channels, the information represented in the binary data 602 is conveyed from the transmitter portion 600 to the receiver portion. In the illustrated embodiment, the transmitter portion 600 includes a plurality of distribution matchers 604, one for each of the parallel streams generated by the serial / parallel converter 603, a plurality of FEC encoders 606, one for each of the parallel streams, a plurality of symbol mappers 607, one for each of the parallel streams, a plurality of Nyquist filtering elements 608, one for each of the parallel streams, and a plurality of frequency offset elements 609, one for each of the parallel streams. As shown in FIG. 6A, in at least some embodiments, for each sub-carrier 1-n, the transmitter portion 600 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. In the illustrated embodiment, the outputs of the plurality of processing paths, each containing binary data representing various codewords, are combined by a single sub-carrier multiplexer 605 using sub-carrier multiplexing for transmission over an optical link to an optical receiver. For example, the sub-carrier multiplexer 605 may be configured to combine the individual sub-carrier data output by the plurality of processing paths into either the real (I) or imaginary (Q) part of the optical signal to be transmitted.

[0084] In this example, it may be considered that all subcarriers have the same shaping factor and FEC rate (and thus carry the same net data rate) based on a common QAM modulation format implemented for all subcarrier channels. In the embodiment shown in FIG. 6A, there is one distribution matcher 604 per subcarrier. In at least some embodiments of the optical transmission system described herein, systematic FEC may be used to add parity bits according to probabilistic amplitude shaping (PAS), rather than to modify the incoming bit pattern generated by the distribution matcher. In contrast, when FEC encoding is implemented on a per-subcarrier channel basis, the required OSNR may be determined based on the worst subcarrier channel performance, in that the non-linear transmission penalty depends on the number of subcarrier channels.

[0085] FIG. 6B is a schematic diagram showing selected elements of a receiver portion 620 of an example optical transmission system configured to recover information from an optical signal received from the transmitter portion shown in FIG. 6A, according to some embodiments. In the illustrated embodiments, at least some of the elements of the receiver portion 620 of the optical transmission system are similar to the elements of the receiver portion of the optical transmission system 400 shown in FIG. 4. The display of the receiver portion 620 is schematic and not to scale. In various embodiments, the receiver portion 620 may be implemented with more, fewer, or different elements than those shown in FIG. 6B. In some embodiments, the receiver portion 620 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, the receiver portion 620 may include a digital signal processor (DSP), and the DSP may include (or have access to) a memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, the receiver portion 620 receives a digitized signal of the transmitted optical signal in a coherent receiver of the optical transmission system from an analog-to-digital converter. In at least some embodiments, the receiver portion 620 shown in FIG. 6B may represent one of two receiver portions of the optical transmission system. The two receiver portions are configured to receive binary data representing the real (I) part or the imaginary (Q) part of the optical signal received from the transmitter portion of the optical transmission system, respectively.

[0086] In the illustrated embodiment, the receiver portion 620 includes a single sub-carrier demultiplexer 629 that divides an incoming optical signal into n streams. Each stream is directed to a respective processing path for parallel processing. In some embodiments, the sub-carrier demultiplexer 629 may include an adaptive equalizer, a carrier phase recovery element, or other functional elements of the optical receiver (not shown in FIG. 6B). In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and on the n sub-carrier channels, information is received from the transmitter portion 600.

[0087] In the illustrated embodiment, the receiver portion 620 includes a plurality of symbol demappers 627, each of which is one for each of the parallel streams, a plurality of FEC decoders 626, each of which is one for each stream, and a plurality of distribution dematchers 624, each of which is one for each stream. A single parallel / serial converter 623 combines the outputs of the parallel processing paths to recover the transmitted information as data 622. For example, the parallel / serial converter 623 may be configured to combine the outputs of the parallel processing paths of the receiver portion 620 to recover data representing either the real (I) part or the imaginary (Q) part of the received optical signal.

[0088] As described above, when the optical transmission systems shown in FIGS. 6A and 6B use the same shaping factor and the same FEC rate for all sub-carrier channels, the transmission performance of the sub-carriers may be different, and the overall transmission performance of the system may be limited by the channel with the worst performance. In at least some embodiments, the optical transmission systems described herein may apply a kind of "FEC interleaving" among sub-carriers to average the performance of the sub-carriers and improve the overall performance of the system. For example, an FEC encoder called a "systematic FEC encoder" may apply systematic error correction coding across the bit stream for at least one sub-carrier generated by one or more distribution matchers so as to average the performance of the sub-carrier channels. The specific interleaving pattern applied by the systematic FEC encoder may depend on the performance of a particular sub-carrier channel such that there is interleaving between the sub-carrier channel with the worst performance and the sub-carrier channel with the best performance so as to effectively average the overall performance of the sub-carrier channels.

[0089] In at least some embodiments, the size of the block for the input to the FEC may be a multiple of (m - 1), where m is the bit level in the probabilistic amplitude shaping PAS. For example, 64QAM may correspond to an FEC rate c = (m - 1) / m, 8-PAS for both the I and Q channels, and m = 3 for both the I and Q channels, respectively. As described in more detail with reference to FIG. 12B, for any FEC rate, a portion of the incoming data bits may be used as parity bits. Systematic FEC may be performed on the incoming serial bit stream regardless of whether the transmitter portion of the optical transmission system includes one distribution matcher or a plurality of distribution matchers. In at least some embodiments, the symbol distribution of the sub-carrier channels may follow the distribution after the distribution matcher, which may be considered to be applicable when the input bit stream is random.

[0090] In at least some embodiments, the optical transmission systems described herein may assign probabilities symmetrically. In one example, probabilistic amplitude shaping may be performed by one or more distribution matchers, where the probabilistic amplitudes are labeled 10, 11, 01, or 00, and then the parity check bits added by the systematic FEC encoder determine the sign of the probability label as the most significant bit of the probability. In this example, the systematic FEC encoder does not change the probabilistic amplitude represented by the two least significant bits output by the distribution matcher. In some examples, the probability of each parity bit assigned by the systematic FEC having a value of '1' or '0' is expected to be 50% in the case of a random sequence of shaped bits. In this example, the labels

[0111] and

[0111] represent the same probability but have different signs.

[0091] Figure 7 depicts an example of the symbol probability distribution 700 of probabilistic constellation shaping for 8-ASK. In this example, there are four possible amplitudes represented by the two least significant bits, while the most significant bit represents the coded bit added by the FEC encoder at the transmitter. The height of each bar represents the probability of each amplitude, and the probability distribution is symmetric with respect to the coded bit values of '0' and '1'. For example, the height of bar 702 indicates the probability of symbol -7, which is the same as the height of bar 716 indicating the probability of symbol +7. Similarly, the height of bar 704 indicates the probability of symbol -5, the height of bar 714 indicates the probability of symbol +5, the height of bar 706 indicates the probability of symbol -3, the height of bar 712 indicates the probability of symbol +3, the height of bar 708 indicates the probability of symbol -1, and the height of bar 710 indicates the probability of symbol +1.

[0092] Referring now to FIG. 8, a block diagram of selected elements of an embodiment of a method 800 for error correction in an optical network that implements both probabilistic shaping and symbol rate optimization is presented in flowchart form, as described herein. Method 800 may be implemented using an optical transmission network 101. In some embodiments, the network management system 300 represented in FIG. 3 may be used to obtain routing information and send commands to an optical transmitter and an optical receiver to configure them for symbol rate optimization using probabilistic constellation shaping and subcarrier multiplexing, as described herein. It is noted that the particular operations described in method 800 may be optional or may be rearranged in different embodiments.

[0093] Method 800 may begin at 802 by receiving binary data in a single binary bit stream to be transmitted as an optical signal at an optical transmitter.

[0094] At 804, method 800 includes assigning probabilities to symbols of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the received binary data supplied to each of one or more matcher elements, according to the target probability distribution of the symbols. As will be described in more detail below, in some embodiments, the optical transmitter may include multiple matchers. In other embodiments, the optical transmitter may include only a single matcher element. Each of the matcher elements may be similar to one of the distribution matchers 404 represented in FIG. 4 or the distribution matcher 604 represented in FIG. 6A.

[0095] At 806, method 800 includes outputting, by each of the matcher elements, a respective shaped bit sequence corresponding to the portion of the received binary data supplied to that matcher element.

[0096] At 808, method 800 includes generating a composite shaped bit sequence that includes data representing each shaped bit sequence and parity bits collectively added to each shaped bit sequence by adding parity bits collectively across each shaped bit sequence. In at least some embodiments, a single systematic error correction encoder may be configured to add parity bits collectively across the shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence. For example, a single systematic FEC encoder may add parity bits as code bits applied across the shaped bit sequences output by each matcher element.

[0097] At 810, method 800 includes supplying each portion of the composite shaped bit sequence to respective ones of a plurality of mapping elements by a serial / parallel converter, where each mapping element is configured to generate a respective codeword for each symbol represented in each portion of the composite shaped bit sequence supplied to that mapping element.

[0098] At 812, method 800 includes combining binary data representing each codeword generated by the plurality of mapping elements by subcarrier multiplexing for transmission on an optical transmission path.

[0099] In at least some embodiments, the operations shown as 802 through 812 may be repeated periodically or continuously when a binary bit stream is received by an optical transmitter.

[0100] In some embodiments, the transmitter portion of the optical transmission system described herein may include a plurality of parallel distributed matchers. In some cases, the use of parallel distributed matchers may enable the data rate of each distributed matcher to be reduced compared to the data rate of the incoming serial bit stream.

[0101] FIG. 9A is a schematic diagram representing selected elements of a transmitter portion 900 of an optical transmission system configured to apply probabilistic constellation shaping and symbol rate optimization and including a plurality of distribution matchers, according to some embodiments. For example, the transmitter portion 900 may be configured to perform probabilistic shaping based on M-QAM in addition to performing symbol rate optimization using subcarrier multiplexing. In the illustrated embodiments, some (but not all) of the elements of the transmitter portion 900 of the optical transmission system may be similar to the elements of the transmitter portion of the optical transmission system 400 represented in FIG. 4 or the transmitter portion 600 represented in FIG. 6A. The display of the transmitter portion 900 is schematic and not to scale. In various embodiments, the transmitter portion 900 may be implemented with more, fewer, or different elements than those represented in FIG. 9A. In some embodiments, the transmitter portion 900 may include a field programmable gate array (FPGA) that performs at least some of the functions described herein. In some embodiments, the transmitter portion 900 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, the transmitter portion 900 includes binary data 902 that is provided for transmission to a receiver portion of the optical transmission system. In at least some embodiments, the transmitter portion 900 represented in FIG. 9A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of the data 902 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0102] In the illustrated embodiment, the transmitter portion 900 includes binary data 902 that is provided for transmission to the receiver portion of the optical transmission system. A first serial / parallel converter 903 divides the incoming binary data 902 into n streams. Each stream is first directed to respective processing paths for parallel processing. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and on the n sub-carrier channels, the information represented in the binary data 902 is carried from the transmitter portion 900 to the receiver portion.

[0103] In the illustrated embodiment, the transmitter portion 900 includes a plurality of distribution matchers 904, one for each of the parallel streams generated by the first serial / parallel converter 903. The transmitter portion 900 includes a parallel / serial converter 910 that combines the outputs of the plurality of distribution matchers 904. The outputs of the plurality of distribution matchers 904 each include a shaped bit sequence. The parallel / serial converter 910 supplies an intermediate composite shaped bit sequence to a systematic FEC encoder 906. The systematic FEC encoder 906 applies parity bits collectively across the intermediate composite shaped bit sequence as coded bits for each of the probabilities represented in the intermediate composite shaped bit sequence to generate a final composite shaped bit sequence. A second serial / parallel converter 912 divides the final composite shaped bit sequence into n streams for further processing in a parallel processing path. For example, the transmitter portion 900 includes a plurality of symbol mappers 907, one for each of the parallel streams, a plurality of Nyquist filtering elements 908, one for each of the parallel streams, and a plurality of frequency offset elements 909, one for each of the parallel streams. As shown in FIG. 9A, in at least some embodiments, for each subcarrier 1-n, the transmitter portion 900 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. In the illustrated embodiment, the outputs of the plurality of processing paths each containing binary data representing various codewords are combined by a single subcarrier multiplexer 905 using subcarrier multiplexing for transmission to an optical receiver over an optical transmission. For example, the subcarrier multiplexer 905 may be configured to combine the individual subcarrier data output by the plurality of processing paths into either the real (I) part or the imaginary (Q) part of the optical signal to be transmitted.

[0104] FIG. 9B is a schematic diagram showing a part 950 of elements of a transmitter portion of an example of the optical transmission system shown in FIG. 9A according to some embodiments. In one example, the shaped bit sequence output by the distribution matcher 904-n is shown as 951. The shaped bit sequence 951 contains four bits with a value of 0110. The shaped bit sequence 951 represents two probability amplitude bits for each of the two symbols. When reading from right to left, the first symbol contains the probability amplitude 10 which is the lower two bits, and the second symbol contains the probability amplitude 01 which is the upper two bits. The shaped bit sequence output by the distribution matcher 904-1 is shown as 952. The shaped bit sequence 902 contains four bits with a value of 1101. The shaped bit sequence 952 represents two probability amplitude bits for each of the two symbols. When reading from right to left, the third symbol contains the probability amplitude 01 which is the lower two bits, and the fourth symbol contains the probability amplitude 11 which is the upper two bits. The outputs of the two distribution matchers 904 are combined by a parallel / serial converter 910 to generate an intermediate composite shaped bit sequence shown as 953. In this example, the intermediate composite shaped bit sequence 953 contains eight bits of the shaped bit sequences 951 and 952. These bits are interleaved and reordered as 01111001 (among the upper four bits, the first and third bits from the most significant bit are from the second symbol 01, and the second and fourth bits are from the fourth symbol 11. Also, among the lower four bits, the first and third bits from the most significant bit are from the first symbol 10, and the second and fourth bits are from the third symbol 01.).

[0105] As described above, a single systematic error correction coder may be configured to add parity bits collectively across the shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence. For example, the systematic FEC coder 906 may add parity bits as coded bits applied across the shaped bit sequence output by each matcher element. In this example, the FEC coder 906 adds four parity bits 1011 as coded bits to the intermediate composite shaped bit sequence 953 to generate the final composite shaped bit sequence 954. These parity bits are added across each symbol represented in the intermediate composite shaped bit sequence 953 while alternating between the symbols output by the distribution matcher 904-n and the symbols output by the distribution matcher 904-1. More specifically, the individual parity bits are added to the first symbol, the third symbol, the second symbol, and the fourth symbol, respectively, from right (least significant) to left (most significant) in the final composite shaped bit sequence 954, and the final composite shaped bit sequence 954 is supplied as an input to the second serial / parallel converter 912. The individual bit streams output by the second serial / parallel converter 912 are a stream 955 including bits 001110 (the least significant 2 bits "10" are from the first symbol, and the bit "1" above it, i.e., the third bit from the least significant, is from the most significant bit "1" of the parity bits "1011". The most significant bit "0" is from the second most significant bit "0" of the parity bits "1011", and the subsequent 2 bits "01" are from the second symbol.), and a stream 956 including bits 111101 (the least significant 2 bits "01" are from the third symbol, and the bit "1" above it, i.e., the third bit from the least significant, is from the third most significant bit "1" of the parity bits "1011". The most significant bit "1" is from the least significant bit "1" of the parity bits "1011", and the subsequent 2 bits "11" are from the fourth symbol.).That is, for each group of three bits, the most significant bit represents the sign of each probability, and the remaining bits represent the amplitude of each probability.

[0106] It should be noted that in fact, the optical transmission system described herein may implement sub-carrier multiplexing with dozens (not hundreds or thousands) of sub-carrier channels. The transmitter portion and the receiver portion of such an optical transmission system may include more than two distribution matchers, distribution dematchers, and other components in parallel processing streams. In such a system, the sign bits may be assigned in a round-robin fashion across a number of sub-carrier channels to a particular shaped bit sequence, or a portion thereof.

[0107] FIG. 9C is a schematic diagram showing selected elements of a receiver portion 920 of an example optical transmission system configured to recover information from an optical signal received from the transmitter portion shown in FIG. 9A. In the illustrated embodiment, at least some of the elements of the receiver portion 920 of the optical transmission system are similar to the elements of the receiver portion of the optical transmission system 400 shown in FIG. 4 or the receiver portion 620 shown in FIG. 6B. The display of the receiver portion 920 is schematic and not to scale. In various embodiments, the receiver portion 920 may be implemented with more, fewer, or different elements than those shown in FIG. 9C. In some embodiments, the receiver portion 920 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, the receiver portion 920 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to implement at least some of the functions described herein. In the illustrated embodiment, the receiver portion 920 receives a digitized signal of a transmitted optical signal in a coherent receiver of the optical transmission system from an analog-to-digital converter. In at least some embodiments, the receiver portion 920 shown in FIG. 9C may represent one of two receiver portions of the optical transmission system. The two receiver portions are configured to receive binary data representing the real (I) part or the imaginary (Q) part of the optical signal received from the transmitter portion of the optical transmission system, respectively.

[0108] In the illustrated embodiments, the receiver portion 920 includes a single subcarrier demultiplexer 929 that divides an incoming optical signal into n streams. Each stream is first directed to respective processing paths for parallel processing. In some embodiments, the subcarrier demultiplexer 929 may include an adaptive equalizer, a carrier phase recovery element, or other functional elements of the optical receiver (not shown in FIG. 9C). In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n subcarrier channels, and on the n subcarrier channels, information is received from the transmitter portion 900.

[0109] In the illustrated embodiments, the receiver portion 920 includes a plurality of symbol demappers 927, one for each of the parallel streams. The receiver portion 920 includes a first parallel / serial converter 930 that combines the outputs of the plurality of symbol demappers 927 and supplies an intermediate composite output to a single FEC decoder 926. The single FEC decoder 926 extracts the parity bits collectively applied across the intermediate composite formatted bit sequence by the FEC encoder 906 as the coded bits of each probability represented in the intermediate composite formatted bit sequence at the transmitter portion 900. The serial / parallel converter 932 re-divides the output of the FEC decoder 926 into n streams for further processing in the parallel processing paths. For example, the receiver portion 920 includes a plurality of distributed dematchers 924, one for each stream. In the illustrated embodiments, a second parallel / serial converter 923 combines the outputs of the parallel processing paths to recover the transmitted information as data 922. For example, the second parallel / serial converter 923 may be configured to combine the outputs of the parallel processing paths of the receiver portion 920 to recover data representing either the real (I) part or the imaginary (Q) part of the received optical signal.

[0110] In at least some embodiments, some of the incoming data bits may be used as parity bits. For example, for subcarrier modulation, data bits that may be used as parity bits may be tapped out and supplied to the FEC encoder as additional parity bits. As will be described later with reference to FIGS. 10A and 11A, the tapping point may be located at any of several suitable positions in different embodiments. Further, the number of data bits tapped out may vary depending on the desired FEC rate.

[0111] FIG. 10A is a schematic diagram representing selected elements of a transmitter portion 1000 of an optical transmission system configured to apply probabilistic constellation shaping and symbol rate optimization and including a plurality of distribution matchers and tap elements for a plurality of binary streams. For example, transmitter portion 1000 may be configured to perform probabilistic shaping based on M-QAM in addition to performing symbol rate optimization using subcarrier multiplexing. In the illustrated embodiments, some (but not all) of the elements of transmitter portion 1000 of the optical transmission system may be similar to the elements of the transmitter portion of optical transmission system 400 represented in FIG. 4 or the transmitter portion 600 represented in FIG. 6A. The display of transmitter portion 1000 is schematic and not to scale. In various embodiments, transmitter portion 1000 may be implemented with more, fewer, or different elements than those represented in FIG. 10A. In some embodiments, transmitter portion 1000 may include a field programmable gate array (FPGA) that performs at least some of the functions described herein. In some embodiments, transmitter portion 1000 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, transmitter portion 1000 includes binary data 1002 that is provided for transmission to a receiver portion of the optical transmission system. In at least some embodiments, transmitter portion 1000 represented in FIG. 10A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of data 1002 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0112] The first serial / parallel converter 1003 divides the incoming binary data 1002 into n streams. Each stream is first directed to each processing path for parallel processing. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and on the n sub-carrier channels, the information represented in the binary data 1002 is carried from the transmitter portion 1000 to the receiver portion.

[0113] In the illustrated embodiment, the transmitter portion 1000 includes a plurality of distribution matchers 1004, one for each of the parallel streams generated by the first serial / parallel converter 1003. The transmitter portion 1000 includes a first parallel / serial converter 1010 that combines the outputs of the plurality of distribution matchers 1004. The outputs of the plurality of distribution matchers 1004 each include a shaped bit sequence. The first parallel / serial converter 1010 supplies an intermediate composite shaped bit sequence to a single systematic FEC encoder 1006. The single systematic FEC encoder 1006 applies parity bits collectively across the intermediate composite shaped bit sequence as coded bits for each of the probabilities represented in the intermediate composite shaped bit sequence to generate a final composite shaped bit sequence. In the illustrated embodiment, the transmitter portion 1000 also includes, for each of the n parallel streams output by the serial / parallel converter 1003, each tap configured to tap one or more bits from the binary data stream and supply the tapped bits, shown as tapped bits 1051 and 1052, to a second parallel / serial converter 1011. The second parallel / serial converter 1011 combines the tapped bits and may be configured to supply the combined tapped bits to the single systematic FEC encoder 1006. The single systematic FEC encoder 1006 applies them collectively across the intermediate composite shaped bit sequence as additional coded bits. The combined tapped bits, shown at 1055, may also be re-interleaved by a combining element prior to its input to the second serial / parallel converter 1012 at the output of the single systematic FEC encoder 1006.

[0114] In one example, the shaped bit sequence output by the distribution matcher 1004-n is shown as 1053. The shaped bit sequence 1053 contains 4 bits with a value of 0110. The shaped bit sequence 1053 represents two probability amplitude bits for each of the two symbols. When reading from right to left, the first symbol contains the probability amplitude 10 which is the lower 2 bits, and the second symbol contains the probability amplitude 01 which is the upper 2 bits. The shaped bit sequence output by the distribution matcher 1004-1 is shown as 1054. The shaped bit sequence 1054 contains 4 bits with a value of 1101. The shaped bit sequence 1054 represents two probability amplitude bits for each of the two symbols. When reading from right to left, the third symbol contains the probability amplitude 01 which is the lower 2 bits, and the fourth symbol contains the probability amplitude 11 which is the upper 2 bits. The outputs of the two distribution matchers 1004 are combined by the parallel / serial converter 1010 to generate an intermediate composite shaped bit sequence. In this example, the intermediate composite shaped bit sequence contains 8 bits of the shaped bit sequences 1053 and 1054. These bits are interleaved and reordered as 01111001 (among the upper 4 bits, the first and third bits from the most significant bit are from the second symbol 01, and the second and fourth bits are from the fourth symbol 11. Also, among the lower 4 bits, the first and third bits from the most significant bit are from the first symbol 10, and the second and fourth bits are from the third symbol 01.). As represented in 10A, this intermediate composite shaped bit sequence may be supplied as an input to the FEC encoder 1006 together with the combined tapped bits 1055.

[0115] As described above, the systematic error correction coder may be configured to add parity bits collectively across the shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence. For example, the systematic FEC coder 1006 may add parity bits as coded bits applied across the shaped bit sequences output by each matcher element. In the transmitter section 1000, the second serial / parallel converter 1012 re-splits the final combined shaped bit sequence in which the combined tapped bits 1055 are re-interleaved into n streams for further processing in parallel processing paths. In this example, the input to the upper processing path, shown as 1056, may include six bits with a value of 001110. This includes additional coded bits as each bit appended to the beginning of each 2-bit amplitude value (the least significant 2 bits "10" are from the first symbol, and the bit above it, i.e., the third bit from the least significant "1", is the additional coded bit. Further, the most significant bit "0" is also an additional coded bit, and the following 2 bits "01" are from the second symbol.). The input to the lower processing path, shown as 1057, may include six bits with a value of 111101. This includes additional coded bits as each bit appended to the beginning of each 2-bit amplitude value (the least significant 2 bits "01" are from the third symbol, and the bit above it, i.e., the third bit from the least significant "1", is the additional coded bit. The most significant bit "1" is also an additional coded bit, and the following 2 bits "11" are from the fourth symbol.).

[0116] In the illustrated embodiments, the transmitter portion 1000 includes a plurality of symbol mappers 1007, one for each of the parallel streams, a plurality of Nyquist filtering elements 1008, one for each of the parallel streams, and a plurality of frequency offset elements 1009, one for each of the parallel streams. As shown in FIG. 10A, in at least some embodiments, for each subcarrier 1-n, the transmitter portion 1000 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. In the illustrated embodiments, the outputs of a plurality of processing paths each containing binary data representing various codewords are combined by a single subcarrier multiplexer 1005 using subcarrier multiplexing for transmission over the optical link to an optical receiver. For example, the subcarrier multiplexer 1005 may be configured to combine the individual subcarrier data output by the plurality of processing paths into either the real (I) part or the imaginary (Q) part of the optical signal to be transmitted.

[0117] FIG. 10B is a schematic diagram representing selected elements of a receiver portion 1020 of an example optical transmission system configured to recover information from an optical signal received from the transmitter portion depicted in FIG. 10A, according to some embodiments. The display of the receiver portion 1020 is schematic and not to scale. In various embodiments, the receiver portion 1020 may be implemented with more, fewer, or different elements than those depicted in FIG. 10B. In some embodiments, the receiver portion 1020 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, the receiver portion 1020 may include a digital signal processor (DSP), which may include (or have access to) a memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the depicted embodiment, the receiver portion 1020 receives a digitized signal of the transmitted optical signal in a coherent receiver of the optical transmission system from an analog-to-digital converter. In at least some embodiments, the receiver portion 1020 depicted in FIG. 10B may represent one of two receiver portions of the optical transmission system. The two receiver portions are configured to receive binary data representing the real (I) part or the imaginary (Q) part of the optical signal received from the transmitter portion of the optical transmission system, respectively.

[0118] In the illustrated embodiments, at least some of the elements of the receiver portion 1020 are similar to the elements of the receiver portion of the optical transmission system illustrated in FIG. 4 or the receiver portion 620 illustrated in FIG. 6B. In the illustrated embodiments, the receiver portion 1020 includes a single subcarrier demultiplexer 1029 that divides an incoming optical signal into n streams. Each stream is first directed to respective processing paths for parallel processing. In some embodiments, the subcarrier demultiplexer 1029 may include an adaptive equalizer, a carrier phase recovery element, or other functional elements of the optical receiver (not shown in FIG. 10B). In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n subcarrier channels, and on the n subcarrier channels, information is received from the transmitter portion 1000.

[0119] In the illustrated embodiment, the receiver portion 1020 includes a plurality of symbol demappers 1027, one for each of the parallel streams. The receiver portion 1020 includes a first parallel / serial converter 1030 that combines the outputs of the plurality of symbol demappers 1027 and supplies an intermediate composite output to a single FEC decoder 1026. The single FEC decoder 1026 extracts, at the transmitter portion 1000, the parity bits collectively applied across the intermediate composite shaped bit sequence as the coded bits of each probability represented in the intermediate composite shaped bit sequence shown as 1058 by the FEC encoder 1006. The serial / parallel converter 1032 re - splits the output of the FEC decoder 1026 into n streams for further processing in a parallel processing path. For example, the receiver portion 1020 includes a plurality of distribution dematchers 1024, one for each stream. In the illustrated embodiment, the receiver portion 1020 includes a second serial / parallel converter 1034 that receives the extracted parity bits 1058 and splits them into data bits that are re - interleaved with the output of each one of the distribution dematchers 1024. For example, bit 1059 is combined with the output of distribution dematcher 1024 - 1 and bit 1060 is combined with the output of distribution dematcher 1024 - n. In the illustrated embodiment, the second parallel / serial converter 1023 combines the outputs of the parallel processing paths in which each of the extracted parity bits 1058 is re - interleaved so as to recover the transmitted information as data 1022. For example, the second parallel / serial converter 1023 may be configured to combine the outputs of the parallel processing paths of the receiver portion 1020 so as to recover data representing either the real (I) part or the imaginary (Q) part of the received optical signal.

[0120] FIG. 11A is a schematic diagram representing selected elements of a transmitter portion 1100 of an optical transmission system configured to apply probabilistic constellation shaping and symbol rate optimization and including one or more tap elements that result in multiple distribution matchers and a single binary stream. For example, transmitter portion 1100 may be configured to perform probabilistic shaping based on M-QAM in addition to performing symbol rate optimization using subcarrier multiplexing. In the illustrated embodiments, some (but not all) of the elements of transmitter portion 1100 of the optical transmission system may be similar to the elements of the transmitter portion of optical transmission system 400 represented in FIG. 4 or the transmitter portion 600 represented in FIG. 6A. The display of transmitter portion 1100 is schematic and not to scale. In various embodiments, transmitter portion 1100 may be implemented with more, fewer, or different elements than those represented in FIG. 11A. In some embodiments, transmitter portion 1100 may include a field programmable gate array (FPGA) that performs at least some of the functions described herein. In some embodiments, transmitter portion 1100 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, transmitter portion 1100 includes binary data 1102 that is supplied for transmission to a receiver portion of the optical transmission system. In at least some embodiments, transmitter portion 1100 represented in FIG. 11A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of data 1002 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0121] In the illustrated embodiments, the transmitter portion 1100 includes binary data 1102 that is to be provided for transmission to the receiver portion of the optical transmission system. A first serial / parallel converter 1103 divides the incoming binary data 1102 into n streams. Each stream is first directed to respective processing paths for parallel processing. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n subcarrier channels, and on the n subcarrier channels, the information represented in the binary data 1102 is conveyed from the transmitter portion 1100 to the receiver portion.

[0122] In the illustrated embodiments, the transmitter portion 1100 includes a plurality of distribution matchers 1104, one for each of the parallel streams generated by the first serial / parallel converter 1103. The transmitter portion 1100 includes a first parallel / serial converter 1110 that combines the outputs of the plurality of distribution matchers 1104. The outputs of the plurality of distribution matchers 1104 each include a respective shaped bit sequence. The first parallel / serial converter 1110 supplies an intermediate combined shaped bit sequence to a single systematic FEC encoder 1106. The single systematic FEC encoder 1106 applies parity bits collectively across the intermediate combined shaped bit sequence as respective coded bits of each probability represented in the intermediate combined shaped bit sequence to generate a final combined shaped bit sequence. In the illustrated embodiments, the transmitter portion 1100 also includes a tap element configured to tap one or more bits from the input binary data stream 1102 and supply the tapped bits, shown as tapped bits 1151, to the single systematic FEC encoder 1106. The single systematic encoder FEC encoder 1106 applies them collectively across the intermediate combined shaped bit sequence as additional coded bits. As shown in FIG. 11A, the combined tapped bits 1151 may also be re-interleaved by a combining element at the output of the single systematic FEC encoder 1106, prior to its input to the second serial / parallel converter 1112.

[0123] In one example, the shaped bit sequence output by the distribution matcher 1104-n is shown as 1152. The shaped bit sequence 1152 contains four bits with a value of 0110. The shaped bit sequence 1152 represents two probability amplitude bits for each of the two symbols. When reading from right to left, the first symbol contains the probability amplitude 10 which is the lower two bits, and the second symbol contains the probability amplitude 01 which is the upper two bits. The shaped bit sequence output by the distribution matcher 1104-1 is shown as 1153. The shaped bit sequence 1153 contains four bits with a value of 1101. The shaped bit sequence 1153 represents two probability amplitude bits for each of the two symbols. When reading from right to left, the third symbol contains the probability amplitude 01 which is the lower two bits, and the fourth symbol contains the probability amplitude 11 which is the upper two bits. The outputs of the two distribution matchers 1104 are combined by the parallel / serial converter 1110 to generate an intermediate composite shaped bit sequence. In this example, the intermediate composite shaped bit sequence contains eight bits of the shaped bit sequences 1152 and 1153, and together with the tapped bit 1151, may be supplied as an input to the FEC encoder 1106.

[0124] As described above, the systematic error correction coder may be configured to add parity bits collectively across the shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence. For example, the systematic FEC coder 1106 may add parity bits as coded bits applied across the shaped bit sequence output by each matcher element to generate a final composite shaped bit sequence. In various embodiments, the FEC coder 1106 may utilize a minimum FEC rate or may implement a configurable FEC rate. Examples of FEC coders that utilize a minimum FEC rate and / or a configurable FEC rate are shown in FIG. 12B and are described in detail below. In the transmitter section 1100, the second serial / parallel converter 1112 re-divides the final composite shaped bit sequence in which the tapped bits 1151 are re-interleaved into n streams for further processing in parallel processing paths. In this example, the input to the upper processing path, shown as 1154, may include six bits with a value of 001110. This includes additional coded bits as each bit appended to the beginning of each 2-bit amplitude value (the least significant 2 bits "10" are from the first symbol, and the bit above it, i.e., the third bit from the least significant bit "1", is the additional coded bit. Further, the most significant bit "0" is also an additional coded bit, and the following 2 bits "01" are from the second symbol.). The input to the lower processing path, shown as 1155, may include six bits with a value of 111101. This includes additional coded bits as each bit appended to the beginning of each 2-bit amplitude value (the least significant 2 bits "01" are from the third symbol, and the bit above it, i.e., the third bit from the least significant bit "1", is the additional coded bit. The most significant bit "1" is also an additional coded bit, and the following 2 bits "11" are from the fourth symbol.).

[0125] In the illustrated embodiments, the transmitter portion 1100 includes a plurality of symbol mappers 1107, each for one of the parallel streams, a plurality of Nyquist filtering elements 1108, each for one of the parallel streams, and a plurality of frequency offset elements 1109, each for one of the parallel streams. As shown in FIG. 11A, in at least some embodiments, for each subcarrier 1 - n, the transmitter portion 1100 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. In the illustrated embodiments, the outputs of a plurality of processing paths, each containing binary data representing various codewords, are combined by a single subcarrier multiplexer 1105 using subcarrier multiplexing for transmission over the optical link to an optical receiver. For example, the subcarrier multiplexer 1105 may be configured to combine the individual subcarrier data output by the plurality of processing paths into either the real (I) or imaginary (Q) part of the optical signal to be transmitted.

[0126] FIG. 11B is a schematic diagram representing selected elements of a receiver portion 1120 of an example optical transmission system configured to recover information from an optical signal received from the transmitter portion represented in FIG. 11A, according to some embodiments. In the represented embodiments, at least some of the elements of the receiver portion 1120 are similar to the elements of the receiver portion of the optical transmission system represented in FIG. 4 or the receiver portion 620 represented in FIG. 6B. The representation of the receiver portion 1120 is schematic and not to scale. In various embodiments, the receiver portion 1120 may be implemented with more, fewer, or different elements than those represented in FIG. 11B. In some embodiments, the receiver portion 1120 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, the receiver portion 1120 may include a digital signal processor (DSP), and the DSP may include (or have access to) a memory storing instructions executable by the DSP to implement at least some of the functions described herein. In the represented embodiments, the receiver portion 1120 receives the digitized signal of the transmitted optical signal in a coherent receiver of the optical transmission system from an analog-to-digital converter. In at least some embodiments, the receiver portion 1120 represented in FIG. 11B may represent one of two receiver portions of the optical transmission system. The two receiver portions are configured to receive binary data representing the real (I) part or the imaginary (Q) part of the optical signal received from the transmitter portion of the optical transmission system, respectively.

[0127] In the illustrated embodiment, the receiver portion 1120 includes a single sub-carrier demultiplexer 1129 that divides an incoming optical signal into n streams. Each stream is first directed to respective processing paths for parallel processing. In some embodiments, the sub-carrier demultiplexer 1129 may include an adaptive equalizer, a carrier phase recovery element, or other functional elements of the optical receiver (not shown in FIG. 11B). In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and on the n sub-carrier channels, information is received from the transmitter portion 1100.

[0128] In the illustrated embodiment, the receiver portion 1120 includes a plurality of symbol demappers 1127, one for each of the parallel streams. The receiver portion 1120 includes a first parallel / serial converter 1130 that combines the outputs of the plurality of symbol demappers 1127 and supplies an intermediate composite output to a single FEC decoder 1126. The single FEC decoder 1126 extracts the parity bits that were collectively applied across the intermediate composite shaped bit sequence by the FEC encoder 1106, as each of the probability sign bits represented in the intermediate composite shaped bit sequence, shown as the extracted parity bits 1156 at the transmitter portion 1100. The serial / parallel converter 1132 re - splits the output of the FEC decoder 1126 into n streams for further processing in the parallel processing path. For example, the receiver portion 1120 includes a plurality of distribution dematchers 1124, one for each stream. In this example, bit 1158 is combined with the output of distribution dematcher 1124 - 1, and bit 1157 is combined with the output of distribution dematcher 1024 - n. A second parallel / serial converter 1123 combines the outputs of the parallel processing path to recover the transmitted information as data 1122. In the illustrated embodiment, the extracted parity bits 1156 are re - interleaved with the output of the second parallel / serial converter 1123 as additional bits of the recovered information shown as data 1122. For example, the recovered information may include data representing either the real (I) part or the imaginary (Q) part of the received optical signal.

[0129] FIG. 12A is a schematic diagram representing selected elements of a transmitter portion 1200 of an optical transmission system configured to apply probabilistic constellation shaping and symbol rate optimization and including a single distribution matcher, according to some embodiments. For example, transmitter portion 1200 may be configured to perform probabilistic shaping based on M-QAM in addition to performing symbol rate optimization using subcarrier multiplexing. In the illustrated embodiments, some (but not all) of the elements of transmitter portion 1200 of the optical transmission system may be similar to elements of the transmitter portion of optical transmission system 400 represented in FIG. 4 or transmitter portion 600 represented in FIG. 6A. The display of transmitter portion 1200 is schematic and not to scale. In various embodiments, transmitter portion 1200 may be implemented with more, fewer, or different elements than those represented in FIG. 12A. In some embodiments, transmitter portion 1200 may include a field programmable gate array (FPGA) that performs at least some of the functions described herein. In some embodiments, transmitter portion 1200 may include a digital signal processor (DSP), which may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, transmitter portion 1200 includes binary data 1202 supplied for transmission to a receiver portion of the optical transmission system. In at least some embodiments, transmitter portion 1200 represented in FIG. 12A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of data 1202 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0130] The transmitter section 1200 includes binary data 1202 that is supplied for transmission to the receiver section of the optical transmission system. In the illustrated embodiment, the incoming binary data 1202 is supplied as a single serial binary data stream to a single distribution matcher 1204. The output of the distribution matcher 1204 is a shaped bit sequence 1251, which is supplied to a single systematic FEC encoder 1206. The single systematic FEC encoder 1206 applies parity bits as coded bits over the probabilities represented in the shaped bit sequence 1251 to generate a final shaped bit sequence.

[0131] The serial / parallel converter 1212 divides the final shaped bit sequence into n streams. Each stream is directed to a respective processing path for further parallel processing. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n subcarrier channels, and over the n subcarrier channels, the information represented in the binary data 1202 is carried from the transmitter section 1200 to the receiver section. For example, the transmitter section 1200 includes a plurality of symbol mappers 1207, each of which is one for each of the parallel streams, a plurality of Nyquist filtering elements 1208, each of which is one for each of the parallel streams, and a plurality of frequency offset elements 1209, each of which is one for each of the parallel streams. As shown in FIG. 12A, in at least some embodiments, for each of the subcarriers 1 to n, the transmitter section 1200 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. In the illustrated embodiment, the outputs of the plurality of processing paths, each containing binary data representing various codewords, are combined by a single subcarrier multiplexer 1205 using subcarrier multiplexing for transmission to an optical receiver over the optical transmission. For example, the subcarrier multiplexer 1205 may be configured to combine the individual subcarrier data output by the plurality of processing paths into either the real (I) part or the imaginary (Q) part of the optical signal to be transmitted.

[0132] FIG. 12B is a schematic diagram showing further details regarding a portion 1220 of the elements of the transmitter portion 1200 shown in FIG. 12A, according to some embodiments. For example, portion 1220 includes binary data 1202, a single distribution matcher 1204, and a single systematic FEC encoder 1206. Portion 1220 further includes a code labeling element 1256 and a combining element 1254. The single systematic FEC encoder 1206 applies parity bits as code bits over the probabilities represented in the shaped bit sequence 1251 to generate a final shaped bit sequence. The single systematic FEC encoder 1206 includes a binary labeling element 1240 and a parity check matrix 1250. In some embodiments, the FEC encoder may implement a generator matrix [I|P], where I represents an identity matrix and P represents a parity matrix such as the parity check matrix 1250. The identity matrix I may be configured to simply copy the incoming data bit sequence, while the parity check matrix 1250 may be configured to add parity check bits to the incoming bit sequence, as described herein. In this example, any FEC rate controller 1236 shown in FIG. 12B may be absent, or may be disabled, or the FEC control input 1226 to the included FEC rate controller 1236 may indicate that the lowest FEC rate should be utilized.

[0133] In some embodiments, portion 1220 may be used in an optical transmission system where the distribution matcher implements probability amplitude shaping (PAS) and the FEC encoder implements the lowest FEC rate. In one example, the number of output amplitudes (block size) is n cis given by =4, and the bit level (symbol size) is given by m = 3, and as a result, an FEC rate c = (m - 1) / m = 2 / 3 is obtained. In this example, the number of input bits per block is 8, the number of output bits per block is 12, and 8 bits will be recovered by the FEC decoder in the receiver part of the optical transmission system. The size of the parity check matrix may be given as (m - 1)*n c x m*n c as may be given.

[0134] In this example, there are eight possible symbols represented using a 3-bit binary code. As seen in the example of the symmetric symbol probability distribution shown in FIG. 7, the leftmost bit of the three bits representing each symbol may represent a sign bit and take on a value of either '0' for negative values or '1' for positive values. On the other hand, the remaining two bits may represent the amplitude. In this example, the two bits representing the amplitude may collectively represent values of '1' (corresponding to the bit value 10), '3' (corresponding to the bit value 11), '5' (corresponding to the bit value 01), or '7' (corresponding to the bit value 00). In this example, the input binary data 1202 contains 8 bits with a value of 10111101 and is supplied as an input to the distribution matcher 1204.

[0135] The distribution matcher 1204 generates a shaped bit sequence 1251 according to a target probability distribution based on the input 1230 and the shaping control input 1234. In this example, the shaped bit sequence 1251 may correspond to a sequence of amplitudes of 1, 5, 1, 3 (from right to left). The binary labeling element 1240 may convert the elements of the amplitude sequence into their binary equivalents, and as a result, a shaped bit sequence 1242 of 11100110 is obtained. These 8 bits are fed as the shaped bit sequence 1244 to the parity check matrix 1250 without being changed. The parity check matrix 1250 adds, at 1252, 4 parity bits having values of 1, 1, 0, 1 from right to left. These parity bits represent sign bits of +1, +1, -1, and +1 respectively. The sign labeling element 1256 assigns these sign bits, shown as 1258, to the amplitude sequence. The combining element 1254 adds the sign bits to the amplitude sequence represented in the shaped bit sequence 1251, and as a result, a final 12-bit bit sequence 1260 representing values of 1, 5, -1, 3 from right to left is obtained.

[0136] In some embodiments, the portion 1220 may be used in an optical transmission system where the distribution matcher implements probability amplitude shaping (PAS) and the FEC encoder implements a configurable FEC rate. In such embodiments, the portion 1220 may also include or utilize an FEC rate controller 1236 and an additional path through the FEC encoder 1206 whose FEC rate is controllable. For example, the FEC rate may be controlled using an FEC control rate 1226 of r, where r represents the ratio of the number of parity bits to the block size n c In an example, the number of input bits per block is 10, the number of output bits per block is 12, and 10 bits will be recovered by the FEC decoder in the receiver portion of the optical transmission system. In this example, when the FEC rate control value r = 0.5, the number of output amplitudes (block size) is n cGiven by =4, the bit level (symbol size) is given by m = 3, and as a result, the FEC rate c = (m - 1 + r) / m = 5 / 6 is obtained. This is greater than the minimum FEC rate of 2 / 3. Based on the value of r, there are 10 input bits per block, but only 8 input bits are directed to the distribution matcher 1204, while the remaining 2 input bits bypass the distribution matcher 1204. For example, the number of bits selected to bypass the distribution matcher may be r * n c may be given by =2. In this example, the size of the parity check matrix is (m - 1 + r) * n c x m * n c may be given as

[0137] In this example, the input binary data 1202 contains 10 bits with a value of 1011110101. The two rightmost bits (value 01) are shown by the dotted line in Figure 12B as bypass bits 1228. These bits bypass the distribution matcher 1204 and are diverted directly to the FEC encoder 1206 and the code labeling element 1256. These bypass bits will be used as code bits and may be assigned an equal number of '0' and '1' code bit values. Note that the original values of these bits in the incoming binary data stream 1202 may be retained for subsequent recombination with the remaining 8 input bits. The remaining 8 bits are supplied as input to the distribution matcher 1204

[0138] In this example, the distribution matcher 1204 generates a shaped bit sequence 1251 according to a target probability distribution based on the input 1230 and the shaping control input 1234. Similar to the above example, the shaped bit sequence 1251 may correspond to a sequence of amplitudes of 1, 5, 1, 3 (from right to left). The binary labeling element 1240 may convert the elements of the amplitude sequence into their binary equivalents, and as a result, a shaped bit sequence 1242 of 11100110 is obtained. These 8 bits are combined with the bypass bits 1228 and supplied to the parity check matrix 1250 as a 10-bit shaped bit sequence 1244. The parity check matrix 1250 adds two parity bits having values of 1, 1 (from right to left) at 1252. These parity bits each represent a sign bit of +1. The sign labeling element 1256 concatenates these two sign bits 1252 and the two bypass bits 1228 (having values representing +1, -1 from right to left). The combining element 1254 that adds the sign bits shown as 1258 to the amplitude sequence represented in the shaped bit sequence 1251 results in a final bit sequence 1260 of 12 bits 011110101110. Among the 12 bits, the most significant (i.e., the leftmost), the fourth from the most significant, the seventh from the most significant, and the tenth from the most significant bits are the added sign bits. This 12-bit sequence represents values of 1, 5, 1, -3 from right to left. As described above, for 10 input bits and 12 output bits, the FEC rate is 10 / 12, i.e., 5 / 6, which is greater than the minimum FEC rate of 2 / 3. A higher FEC rate indicates that fewer parity bits are added, so the proportion of data bits representing useful information in the signal is higher compared to the case where the FEC rate is lower and more parity bits are added. In various embodiments, different numbers of bypass bits may be tapped to bypass the distribution matcher and control or adjust the FEC rate c.

[0139] FIG. 13A is a schematic diagram representing selected elements of a transmitter portion 1300 of an optical transmission system configured to apply probabilistic constellation shaping and symbol rate optimization and including a single distribution matcher and error correction rate control, according to some embodiments. For example, transmitter portion 1300 may be configured to perform probabilistic shaping based on M-QAM in addition to performing symbol rate optimization using subcarrier multiplexing. In the illustrated embodiments, some (but not all) of the elements of transmitter portion 1300 of the optical transmission system may be similar to elements of the transmitter portion of optical transmission system 400 represented in FIG. 4 or transmitter portion 600 represented in FIG. 6A. The display of transmitter portion 1300 is schematic and not to scale. In various embodiments, transmitter portion 1300 may be implemented with more, fewer, or different elements than those represented in FIG. 13A. In some embodiments, transmitter portion 1300 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, transmitter portion 1300 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, transmitter portion 1300 includes binary data 1302 that is provided for transmission to a receiver portion of the optical transmission system. In at least some embodiments, transmitter portion 1300 represented in FIG. 13A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of data 1202 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0140] The transmitter section 1300 includes binary data 1302 that is supplied for transmission to the receiver section of an optical transmission system. In the illustrated embodiment, the incoming binary data 1302 is supplied as a single serial binary data stream to a single distribution matcher 1304. The output of the distribution matcher 1304 is a shaped bit sequence 1351, which is supplied to a single systematic FEC encoder 1306. In one example, the number of possible amplitudes (block size) is given by n c = 4, the bit level (symbol size) is given by m = 3, and as a result, an FEC rate c = (m - 1) / m = 2 / 3 is obtained. In this example, the number of input bits per block is 8, the number of output bits per block is 12, and 8 bits will be recovered by the FEC decoder in the receiver section of the optical transmission system. In this example, the output of the distribution matcher 1304, shown as the shaped bit sequence 1351, contains 8 bits with a value of 10110010, where the number of bits is k(m - 1). The shaped bit sequence 1351 represents two probability amplitudes for each of the 4 symbols. When reading from right to left, the first symbol includes the probability amplitude 10, which is the lower 2 bits, the second symbol includes the probability amplitude 00, which is the 3rd and 4th bits from the least significant bit, the third symbol includes the probability amplitude 11, which is the 5th and 6th bits from the least significant bit, and the fourth symbol includes the probability amplitude 10, which is the 7th and 8th bits from the least significant bit, i.e., the upper 2 bits.

[0141] A single systematic FEC encoder 1306 applies k parity bits as coded bits over the probabilities represented in the shaped bit sequence 1351 to generate a final shaped bit sequence 1352. In this example, the FEC encoder 1306 adds four parity bits having a value of 1001 as coded bits to generate a final shaped bit sequence. In the illustrated embodiment, the serial / parallel converter 1312 divides the final shaped bit sequence into n streams. Each stream is directed to a respective processing path for further processing in parallel. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and over the n sub-carrier channels, the information represented in the binary data 1302 is carried from the transmitter portion 1300 to the receiver portion. In the illustrated embodiment, the serial / parallel converter 1312 is configured to apply a symbol-wise serial / parallel conversion. In this example, the input to the upper processing path, shown as 1353, includes six bits with a value of 011110. This includes additional coded bits as each bit appended to the beginning of the 2-bit amplitude values associated with the first and third symbols (the least significant 2 bits “10” are from the first symbol, and its upper, i.e., third bit from the least significant “1” is the additional coded bit. Further, the most significant bit “0” is also an additional coded bit, and the following 2 bits “11” are from the third symbol.). The input to the lower processing path, shown as 1354, includes six bits with a value of 110000. This includes additional coded bits as each bit appended to the beginning of the 2-bit amplitude values associated with the second and fourth symbols (the least significant 2 bits “00” are from the second symbol, and its upper, i.e., third bit from the least significant “0” is the additional coded bit. The most significant bit “1” is also an additional coded bit, and the following 2 bits “10” are from the fourth symbol.).

[0142] Similar to the transmitter portion 1200 shown in FIG. 12A, the transmitter portion 1300 includes a plurality of symbol mappers, a plurality of Nyquist filtering elements, and a plurality of frequency offset elements (not shown in FIG. 13A). For example, in at least some embodiments, for each subcarrier 1 to n, the transmitter portion 1300 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. In the illustrated embodiment, the outputs of a plurality of processing paths each containing binary data representing various codewords are combined by a single subcarrier multiplexer using subcarrier multiplexing for transmission to an optical receiver over an optical link (not shown in FIG. 13A). For example, the subcarrier multiplexer may be configured to combine the individual subcarrier data output by the plurality of processing paths into either the real (I) or imaginary (Q) part of the optical signal to be transmitted.

[0143] FIG. 13B is a schematic diagram representing selected elements of a receiver portion 1320 of an example optical transmission system configured to recover information from an optical signal received from the transmitter portion depicted in FIG. 13A, according to some embodiments. In the depicted embodiment, at least some of the elements of the receiver portion 1320 are similar to elements of the receiver portion of the optical transmission system depicted in FIG. 4 or the receiver portion 620 depicted in FIG. 6B. The display of the receiver portion 1320 is schematic and not to scale. In various embodiments, the receiver portion 1320 may be implemented with more, fewer, or different elements than those depicted in FIG. 13B. In some embodiments, the receiver portion 1320 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, the receiver portion 1320 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to implement at least some of the functions described herein. In the depicted embodiment, the receiver portion 1320 receives digitized signals of transmitted optical signals in a coherent receiver of the optical transmission system from an analog-to-digital converter. In at least some embodiments, the receiver portion 1320 depicted in FIG. 13B may represent one of two receiver portions of the optical transmission system. The two receiver portions are configured to receive binary data representing, respectively, the real (I) part or the imaginary (Q) part of an optical signal received from the transmitter portion of the optical transmission system.

[0144] In the illustrated embodiment, the receiver portion 1320 includes a single sub-carrier demultiplexer 1329 that divides an incoming optical signal into n streams. Each stream is first directed to respective processing paths for parallel processing. In some embodiments, the sub-carrier demultiplexer 1329 may include an adaptive equalizer, a carrier phase recovery element, or other functional elements of the optical receiver (not shown in FIG. 13B). In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and on the n sub-carrier channels, information is received from the transmitter portion 1300.

[0145] In the illustrated embodiment, the receiver portion 1320 includes a plurality of symbol demappers 1327, one for each of the parallel streams. The receiver portion 1320 includes a parallel / serial converter 1330 that uses symbol-wise parallel / serial conversion to combine the outputs of the plurality of symbol demappers 1327 and supply an intermediate composite output to a single FEC decoder 1326. The single FEC decoder 1326 extracts parity bits that were collectively applied across the intermediate composite shaped bit sequence by the FEC encoder 1306 as respective probability-coded bits represented in the intermediate composite shaped bit sequence at the transmitter portion 1300. The output of the FEC decoder 1326 is supplied to a single distribution dematcher 1324, and the single distribution dematcher 1324 recovers the transmitted information as data 1322. For example, the distribution dematcher 1324 may be configured to recover data representing either the real (I) part or the imaginary (Q) part of the received optical signal.

[0146] FIG. 14A is a schematic diagram representing selected elements of a transmitter portion 1400 of an optical transmission system configured to apply probabilistic constellation shaping and symbol rate optimization and including a single distribution matcher 1404 and a bitwise interleaver 1414, according to some embodiments. For example, the transmitter portion 1400 may be configured to perform probabilistic shaping based on M-QAM in addition to performing symbol rate optimization using subcarrier multiplexing. In the illustrated embodiments, some (but not all) of the elements of the transmitter portion 1400 of the optical transmission system may be similar to the elements of the transmitter portion of the optical transmission system 400 represented in FIG. 4 or the transmitter portion 600 represented in FIG. 6A. The display of the transmitter portion 1400 is schematic and not to scale. In various embodiments, the transmitter portion 1400 may be implemented with more, fewer, or different elements than those represented in FIG. 14A. In some embodiments, the transmitter portion 1400 may include a field programmable gate array (FPGA) that performs at least some of the functions described herein. In some embodiments, the transmitter portion 1400 may include a digital signal processor (DSP), which may include (or have access to) memory storing instructions executable by the DSP to perform at least some of the functions described herein. In the illustrated embodiments, the transmitter portion 1400 includes binary data 1402 that is supplied for transmission to a receiver portion of the optical transmission system. In at least some embodiments, the transmitter portion 1400 represented in FIG. 14A may represent one of two transmitter portions of the optical transmission system. Each of the two transmitter portions is configured to generate a real (I) or imaginary (Q) portion of the data 1402 for optical modulation that is converted to an analog signal by respective digital / analog converters (DACs).

[0147] The transmitter section 1400 includes binary data 1402 that is supplied for transmission to the receiver section of the optical transmission system. In the illustrated embodiment, the incoming binary data 1402 is supplied as a single serial binary data stream to a single distribution matcher 1404. The output of the distribution matcher 1404 is a shaped bit sequence 1451, which is supplied to a bitwise interleaver 1414. The output of the bitwise interleaver 1414, shown as 1452, is supplied to a single systematic FEC encoder 1406. In one example, the number of output amplitudes (block size) is given by n c = 4, the bit level (symbol size) is given by m = 3, and as a result, an FEC rate c = (m - 1) / m = 2 / 3 is obtained. In this example, the number of input bits per block is 8, the number of output bits per block is 12, and 8 bits will be recovered by the FEC decoder in the receiver section of the optical transmission system. In this example, the output of the distribution matcher 1404, shown as the shaped bit sequence 1451, contains 8 bits with a value of 10110010, where the number of bits is k(m - 1). The shaped bit sequence 1451 represents two probability amplitudes for each of the 4 symbols. When reading from right to left, the first symbol contains the probability amplitude 10, which is the lower 2 bits, the second symbol contains the probability amplitude 00, which is the 3rd and 4th bits from the least significant bit, the third symbol contains the probability amplitude 11, which is the 5th and 6th bits from the least significant bit, and the fourth symbol contains the probability amplitude 10, which is the 7th and 8th bits from the least significant bit, i.e., the upper 2 bits.

[0148] In this example, the bitwise interleaver 1414 receives the shaped bit sequence 1451, applies bitwise interleaving, and generates an intermediate shaped bit sequence 1452. The intermediate shaped bit sequence 1452 is 1 1Contains 8 bits with a value of 010100 (among the upper 4 bits, the 1st and 3rd bits from the most significant bit are from the 4th symbol 10, and the 2nd and 4th bits are from the 3rd symbol 11. Also, among the lower 4 bits, the 1st and 3rd bits from the most significant bit are from the 2nd symbol 00, and the 2nd and 4th bits are from the 1st symbol 10.).

[0149] A single systematic FEC encoder 1406 applies k parity bits as coded bits over the probabilities represented in the intermediate shaped bit sequence 1452 to generate a final shaped bit sequence 1453. In this example, the FEC encoder 1406 adds four parity bits having a value of 1011 as coded bits to generate a final shaped bit sequence. In the illustrated embodiment, the serial / parallel converter 1412 divides the final shaped bit sequence into n streams. Each stream is directed to each processing path for further parallel processing. In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n sub-carrier channels, and over the n sub-carrier channels, the information represented in the binary data 1402 is carried from the transmitter portion 1400 to the receiver portion. In this example, the input to the upper processing path, shown as 1454, includes six bits with a value of 011110. This includes additional coded bits as each bit appended to the beginning of the 2-bit amplitude values associated with the first and third symbols (the least significant 2 bits "10" are from the first symbol, and its upper, i.e., third bit from the least significant "1" is an additional coded bit. Further, the most significant bit "0" is also an additional coded bit, followed by the 2 bits "11" from the third symbol.). The input to the lower processing path, shown as 1455, includes six bits with a value of 110100. This includes additional coded bits as each bit appended to the beginning of the 2-bit amplitude values associated with the second and fourth symbols (the least significant 2 bits "00" are from the second symbol, and its upper, i.e., third bit from the least significant "1" is an additional coded bit. The most significant bit "1" is also an additional coded bit, followed by the 2 bits "10" from the fourth symbol.).Note that the shaped bit sequences 1353 and 1354 shown in FIG. 13A will contain the same bit values as the shaped bit sequences 1454 and 1455 shown in FIG. 14A when the values of the four parity bits added to the intermediate shaped bit sequence 1451 are the same as the values of the four parity bits added to the shaped bit sequence 1351 shown in FIG. 13A.

[0150] Similar to the transmitter portion 1200 shown in FIG. 12A, the transmitter portion 1400 includes a plurality of symbol mappers, a plurality of Nyquist filtering elements, and a plurality of frequency offset elements (not shown in FIG. 14A). As shown in FIG. 14A, in at least some embodiments, for each subcarrier 1 - n, the transmitter portion 1400 may perform symbol mapping and Nyquist filtering before frequency offset (FS) is applied. The outputs of a plurality of processing paths each containing binary data representing various codewords are combined by a single subcarrier multiplexer using subcarrier multiplexing for transmission over optical to an optical receiver (not shown in FIG. 14A). For example, the subcarrier multiplexer may be configured to combine the individual subcarrier data output by the plurality of processing paths into either the real (I) part or the imaginary (Q) part of the optical signal to be transmitted.

[0151] FIG. 14B is a schematic diagram representing selected elements of a receiver portion 1420 of an example optical transmission system configured to recover information from an optical signal received from the transmitter portion depicted in FIG. 14A, according to some embodiments. In the depicted embodiment, at least some of the elements of the receiver portion 1420 are similar to the elements of the receiver portion of the optical transmission system depicted in FIG. 4 or the receiver portion 620 depicted in FIG. 6B. The display of the receiver portion 1420 is schematic and not to scale. In various embodiments, the receiver portion 1420 may be implemented with more, fewer, or different elements than those depicted in FIG. 14B. In some embodiments, the receiver portion 1420 may include a field programmable gate array (FPGA) that executes at least some of the functions described herein. In some embodiments, the receiver portion 1420 may include a digital signal processor (DSP), and the DSP may include (or have access to) memory storing instructions executable by the DSP to implement at least some of the functions described herein. In the depicted embodiment, the receiver portion 1420 receives a digitized signal of the transmitted optical signal in a coherent receiver of the optical transmission system from an analog-to-digital converter. In at least some embodiments, the receiver portion 1420 depicted in FIG. 14B may represent one of two receiver portions of the optical transmission system. The two receiver portions are configured to receive binary data representing the real (I) part or the imaginary (Q) part of the optical signal received from the transmitter portion of the optical transmission system, respectively.

[0152] In the illustrated embodiment, the receiver portion 1420 includes a single subcarrier demultiplexer 1429 that divides an incoming optical signal into n streams. Each stream is first directed to respective processing paths for parallel processing. In some embodiments, the subcarrier demultiplexer 1429 may include an adaptive equalizer, a carrier phase recovery element, or other functional elements of the optical receiver (not shown in FIG. 14B). In at least some embodiments, there is a one-to-one mapping between the n parallel processing paths and the n subcarrier channels, and on the n subcarrier channels, information is received from the transmitter portion 1400.

[0153] In the illustrated embodiment, the receiver portion 1420 includes a plurality of symbol demappers 1427, one for each of the parallel streams. The receiver portion 1420 includes a parallel / serial converter 1430 that combines the outputs of the plurality of symbol demappers 1427 and supplies an intermediate composite output to a reverse bitwise interleaver 1434. The reverse bitwise interleaver 1434 reverses the effect of the bitwise interleaver 1414 in the transmitter portion 1400. The output of the reverse bitwise interleaver 1434 is supplied to a single FEC decoder 1426. The single FEC decoder 1426 extracts the parity bits applied by the FEC encoder 1406 in the transmitter portion 1400 as each probability-coded bit represented in the intermediate composite shaped bit sequence in the transmitter portion 1400. The output of the FEC decoder 1426 is supplied to a single distribution dematcher 1424, and the single distribution dematcher 1424 recovers the transmitted information as data 1422. For example, the distribution dematcher 1424 may be configured to recover data representing either the real (I) part or the imaginary (Q) part of the received optical signal.

[0154] FIG. 15A is a block diagram of selected elements of an embodiment of a method 1500 for error correction in an optical network that implements both probabilistic shaping and symbol rate optimization and includes a plurality of distribution matchers, represented in flowchart form. Method 1500 may be implemented using the optical transmission network 101. In some embodiments, the network management system 300 represented in FIG. 3 may be used to obtain routing information and send commands to optical transmitters and optical receivers to configure them for symbol rate optimization using probabilistic constellation shaping and subcarrier multiplexing as described herein. It is noted that the specific operations described in method 1500 may be optional or may be rearranged in different embodiments.

[0155] At 1502, method 1500 includes receiving, at an optical transmitter, binary data to be transmitted as an optical signal over a transmission path to an optical receiver.

[0156] At 1504, method 1500 includes, by each of a plurality of matcher elements, assigning respective probabilities to symbols of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the binary data received by that matcher element, according to the target probability distribution of that symbol. Each of the matcher elements may be similar to one of the distribution matchers 404 represented in FIG. 4 or the distribution matcher 604 represented in FIG. 6A.

[0157] At 1506, method 1500 includes, by each matcher element, outputting respective shaped bit sequences corresponding to portions of the binary data received by that matcher element, and combining the respective shaped bit sequences output by the matcher elements to generate an intermediate combined shaped bit sequence.

[0158] At 1508, method 1500 includes adding parity bits to an intermediate composite shaped bit sequence to generate a final composite representing each shaped bit sequence and the parity bits. In at least some embodiments, a single systematic error correction coder may be configured to add parity bits collectively across the shaped bit sequence represented in the intermediate composite shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence. For example, a single systematic FEC coder may add parity bits as coded bits applied across the shaped bit sequence represented in the intermediate composite shaped bit sequence.

[0159] At 1510, method 1500 may optionally include adding additional parity bits tapped from each parallel binary data stream input to two or more matcher elements (see FIGS. 10A and above) or tapped from serial binary data received for transmission prior to generating the parallel streams (see FIGS. 11A and above) to the final composite shaped bit sequence. For example, a single systematic FEC coder may also add additional parity bits as additional coded bits applied across the shaped bit sequence represented in the intermediate composite shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence.

[0160] At 1512, method 1500 includes supplying each portion of the final composite shaped bit sequence to each of a plurality of mapping elements. Each of the plurality of mapping elements is configured to generate respective codewords for each symbol represented in each portion of the final composite shaped bit sequence supplied to that mapping element. Method 1500 includes combining the binary data representing each codeword by subcarrier multiplexing for transmission to an optical receiver on an optical transmission path.

[0161] At 1514, method 1500 includes, at an optical receiver, demapping symbols in the received optical signal, extracting the added parity bits to generate a representation of an intermediate combined shaping bit sequence, demultiplexing the representation of the intermediate combined shaping bit sequence, and recovering binary data representing information received via an optical transmission path using a plurality of dematcher elements. In some embodiments, in addition to extracting the added parity bits, the FEC decoder of the optical receiver may also be configured to use the error correction code in the received optical signal to inspect the integrity of the received data and / or to correct certain errors in the data based on the error correction code.

[0162] FIG. 15B is a block diagram of selected elements of an embodiment of a method 1550 for error correction in an optical network that implements both probabilistic shaping and symbol rate optimization and includes a single distribution matcher, represented in flowchart form. Method 1550 may be implemented using an optical transmission network 101. In some embodiments, the network management system 300 represented in FIG. 3 may be used to obtain routing information and to send commands to optical transmitters and optical receivers to configure them for symbol rate optimization using probabilistic constellation shaping and subcarrier multiplexing as described herein. It is noted that the specific operations described in method 1550 may be optional or may be rearranged in different embodiments.

[0163] At 1552, method 1550 includes, at an optical transmitter, receiving binary data to be transmitted as an optical signal to an optical receiver over a transmission path.

[0164] In 1554, method 1550 includes assigning each probability to a symbol of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the received binary data by a single matcher element, according to the target probability distribution of that symbol. The single matcher element may be similar to one of the distribution matchers 404 represented in FIG. 4 or the distribution matcher 604 represented in FIG. 6A.

[0165] In 1556, method 1550 includes outputting a shaped bit sequence corresponding to the received binary data by a single matcher element.

[0166] In 1558, method 1550 may optionally include applying bitwise interleaving to the shaped bit sequence output by a single matcher element, as described above with reference to FIG. 13A.

[0167] In 1560, method 1550 includes adding parity bits to the shaped bit sequence to generate a composite shaped bit sequence that includes data representing the shaped bit sequence output by the matcher element, with or without any interleaving, and the added parity bits. In at least some embodiments, a single systematic error correction coder may be configured to add parity bits collectively across the shaped bit sequence without changing the amplitude of the symbols represented in the shaped bit sequence. For example, as described above with reference to FIGS. 13A and 14A, a single systematic FEC coder may add parity bits as coded bits applied across the probabilities represented in the shaped bit sequence output by a single matcher element.

[0168] In 1562, method 1550 includes supplying each portion of the complex-shaped bit sequence to each of a plurality of mapping elements, each configured to generate a respective codeword for each symbol represented in each portion of the complex-shaped bit sequence. Method 1550 may optionally include applying symbol-wise interleaving to the complex-shaped bit sequence as described above with reference to FIG. 14A.

[0169] In 1564, method 1550 includes combining the binary data representing each codeword by subcarrier multiplexing for transmission to an optical receiver over an optical transmission path.

[0170] In 1566, method 1550 includes, at an optical receiver, demapping the symbols in the received optical signal, extracting the added parity bits, generating a representation of the shaped bit sequence output by a single matcher element, and recovering the binary data representing the information received over the optical transmission path using a single dematcher element. Method 1550 may also include, at the optical receiver, reversing any symbol-wise or bit-wise interleaving performed at the optical transmitter, if applicable. In some embodiments, in addition to extracting the added parity bits, the FEC decoder of the optical receiver may also be configured to use the error correction code in the received optical signal to inspect the integrity of the received data and / or correct certain errors in the data based on the error correction code.

[0171] Note that, for simplicity, in some of the examples described herein, the number of input bits processed together as an input block is 8. In practice, the number of input bits processed together may be much larger. For example, in one embodiment, the number of input bits processed together may be 80. In this example, 40 parity check bits may be added for a 120-bit output block size. In other embodiments, the input block size may be 100 bits or more, and the number of parity check bits added depends on the desired FEC rate.

[0172] As described in detail herein, an optical transmission system implementing both symbol rate optimization using probabilistic shaping and subcarrier multiplexing may apply a kind of "FEC interleaving" between subcarriers to average the subcarrier performance and improve the overall system performance as compared to a system that applies FEC encoding on a subcarrier channel unit basis. For example, a systematic FEC encoder may apply systematic error correction encoding over a bit sequence collectively for all subcarriers generated by one or more distribution matchers to average the performance of the subcarrier channels. The systematic FEC encoder may apply parity bits by encoding the shaped bit sequence without changing the amplitude of each symbol represented in the shaped bit sequence. The ability to perform FEC encoding without changing the amplitude of each symbol may be essential for accurately implementing probabilistic shaping along with symbol rate optimization.

[0173] Although the subject matter of this application has been described in connection with exemplary embodiments, no claim is intended to be limited to the specific forms shown. In contrast, any claim of this disclosure is intended to cover alternatives, modifications, and equivalents that may be included within their spirit and scope.

[0174] In addition to the above embodiments, the following appendices are disclosed. (Appendix 1) An optical transmitter for probabilistic shaping and symbol rate optimization, one or more matcher elements, each of which assigns respective probabilities to symbols of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented by the binary data received by the matcher element, according to the target probability distribution of the symbols, and outputs respective shaped bit sequences corresponding to the binary data received by the matcher element, is configured such that, a single systematic error correction encoder configured to add parity bits collectively to the respective shaped bit sequences over the respective shaped bit sequences, and output a first composite shaped bit sequence including data representing the respective shaped bit sequences and the collectively added parity bits; a plurality of mapping elements, each configured to generate respective codewords for each symbol represented in the received portion of the first composite shaped bit sequence; a first serial / parallel converter configured to supply each portion of the first composite shaped bit sequence to each of the plurality of mapping elements; a multiplexer configured to combine binary data representing the respective codewords generated by the plurality of mapping elements for transmission on an optical transmission line by subcarrier multiplexing; and an optical transmitter having the same. (Appendix 2) The number of mapping elements is equal to the number of subcarrier channels selected for symbol rate optimization and depends on the characteristics of the transmission medium for the optical transmission line and the target reach of the transmission. The optical transmitter according to Appendix 1. (Appendix 3) The one or more matcher elements have two or more matcher elements, and the optical transmitter Generating binary data representing a second composite shaped bit sequence by combining each of the shaped bit sequences output by the two or more matcher elements, and further including a first parallel / serial converter configured to supply the binary data representing the second composite shaped bit sequence as an input to the single systematic error correction coder. The optical transmitter according to Supplementary Note 1. (Supplementary Note 4) A second serial / parallel converter configured to supply each part of the binary data received by the optical transmitter to each of the two or more matcher elements in a parallel binary data stream. A plurality of tap elements each configured to tap one or more bits from each of the parallel binary data streams and supply the one or more tapped bits to the first parallel / serial converter. Further comprising The first parallel / serial converter is further configured to supply the one or more tapped bits received from each of the plurality of tap elements to the single systematic error correction coder as bits to be collectively added across each of the shaped bit sequences output by the two or more matcher elements. Parity The optical transmitter according to Supplementary Note 3. The optical transmitter according to Supplementary Note 3. (Supplementary Note 5) The optical transmitter further includes a combining element. Each of the plurality of tap elements is further configured to supply the one or more tapped bits to the combining element. The combining element is configured to integrate the tapped bits supplied by the plurality of tap elements into the first composite shaped bit sequence before supplying the first composite shaped bit sequence as an input to the first serial / parallel converter. The optical transmitter according to Supplementary Note 4. (Supplementary Note 6) A second serial / parallel converter configured to supply each portion of the serial binary data received by the optical transmitter to respective ones of the two or more matcher elements in a parallel binary data stream. Before converting the serial binary data into the parallel binary data stream, one or more bits are tapped from the serial binary data received by the optical transmitter, and the one or more tapped bits are to be collectively added across the respective shaped bit sequences output by the two or more matcher elements. Parity A tap element configured to supply the bits to the single systematic error correction coder. The optical transmitter according to Appendix 3, further comprising the same. (Appendix 7) The optical transmitter further comprises a combining element. The tap element is further configured to supply the one or more tapped bits to the combining element. The combining element is configured to integrate the tapped bits supplied by the tap element into the first composite shaped bit sequence before supplying the first composite shaped bit sequence to the first serial / parallel converter as an input. The optical transmitter according to Appendix 6. (Appendix 8) The one or more matcher elements have a single matcher element. The optical transmitter according to Appendix 1. (Appendix 9) The single systematic error correction coder is communicatively coupled to the single matcher element and is configured to receive from the single matcher element a shaped bit sequence corresponding to the binary data received by the single matcher element. The first serial / parallel converter is configured to apply symbol-wise interleaving to the first composite shaped bit sequence to supply each portion of the first composite shaped bit sequence to respective ones of the plurality of mapping elements. The optical transmitter according to Supplementary Note 8. (Supplementary Note 10) Receiving the first complex-shaped bit sequence from the single matcher element, Applying bitwise interleaving to the first complex-shaped bit sequence to generate binary data representing a second complex-shaped bit sequence, Supplying the binary data representing the second complex-shaped bit sequence as an input to the single systematic error correction encoder Further comprising a bitwise interleaving element configured as such, The optical transmitter according to Supplementary Note 8. (Supplementary Note 11) A method for error correction in an optical network by probabilistic shaping and symbol rate optimization, comprising: Receiving binary data to be transmitted as an optical signal, Assigning respective probabilities to symbols of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the received binary data supplied to each of one or more matcher elements, according to the target probability distribution of the symbols, Outputting respective shaped bit sequences corresponding to the portions of the received binary data supplied to each of the one or more matcher elements by each of the one or more matcher elements, Collectively adding parity bits to each of the respective shaped bit sequences across the respective shaped bit sequences to generate a first complex-shaped bit sequence including data representing the respective shaped bit sequences and the collectively added parity bits, Supplying each portion of the first complex-shaped bit sequence to each of a plurality of mapping elements, each mapping element generating a respective codeword for each symbol represented in the respective portion of the first complex-shaped bit sequence supplied to the mapping element, Combining, by subcarrier multiplexing, binary data representing each of the codewords generated by the plurality of mapping elements for transmission on an optical transmission line A method having. (Appendix 12) The number of mapping elements is equal to the number of subcarrier channels selected for symbol rate optimization and depends on the characteristics of the transmission medium for the optical transmission line and the target reach of the transmission The method according to Appendix 11. (Appendix 13) The one or more matcher elements have two or more matcher elements The method further includes combining each of the shaped bit sequences output by the two or more matcher elements to generate binary data representing a second composite shaped bit sequence Adding parity bits collectively to each of the shaped bit sequences across each of the shaped bit sequences includes adding the parity bits to the second composite shaped bit sequence The method according to Appendix 11. (Appendix 14) Receiving, via the optical transmission line, binary data representing the first composite shaped bit sequence Extracting the collectively added parity bits from the binary data representing the first composite shaped bit sequence Outputting a third composite shaped bit sequence from which the collectively added parity bits have been extracted Supplying each part of the third composite shaped bit sequence to each of two or more dematcher elements Recovering, by each of the two or more dematcher elements, binary data representing the information received via the optical transmission line from each part of the third composite shaped bit sequence The method according to Appendix 13, further having. (Appendix 15) The method is To each of the two or more matcher elements, in a parallel binary data stream, supply each part of the serial binary data received for transmission; Tap one or more bits from each of the parallel binary data streams; further comprising; Collectively adding a parity bit to each of the shaped bit sequences over each of the shaped bit sequences, for the second composite shaped bit sequence, further comprises adding the one or more tapped bits received from each of the plurality of tap elements as additional parity bits; The method according to appendix 13. (Appendix 16) The method is; To each of the two or more matcher elements, in a parallel binary data stream, supply each part of the serial binary data received for transmission; Before converting the serial binary data into the parallel binary data stream, tap one or more bits from the received serial binary data; further comprising; Collectively adding a parity bit to each of the shaped bit sequences over each of the shaped bit sequences, for the second composite shaped bit sequence, further comprises adding the one or more tapped bits from the received serial binary data as additional parity bits; The method according to appendix 13. (Appendix 17) The one or more matcher elements have a single matcher element; The method according to appendix 11. (Appendix 18) Receiving binary data representing the first composite shaped bit sequence via the optical transmission path; Extracting the collectively added parity bit from the binary data representing the first composite shaped bit sequence; outputting a second complex-shaped bit sequence from which the collectively added parity bits have been extracted; supplying the second complex-shaped bit sequence to a single dematcher element; recovering, by the single dematcher element, binary data representing information received via the optical transmission path from the second complex-shaped bit sequence; The method according to appendix 17, further comprising: (Appendix 19) Supplying each part of the first complex-shaped bit sequence to each of a plurality of mapping elements includes applying symbol-wise interleaving to the first complex-shaped bit sequence. The method according to appendix 17. (Appendix 20) The method comprises: receiving the first complex-shaped bit sequence from the single matcher element; applying bit-wise interleaving to the first complex-shaped bit sequence to generate binary data representing a second complex-shaped bit sequence; further comprising: Collectively adding parity bits to each of the shaped bit sequences includes adding parity bits to the second complex-shaped bit sequence. The method according to appendix 17.

Explanation of Signs

[0175] 101 Optical transmission network 102 Optical transmitter 106 Optical fiber 112 Optical receiver 300 Network management system 400 Optical transmission system 402, 602, 902, 1002, 1102, 1202, 1302, 1402 Binary data 404,604,904,1004,1104,1204,1304,1404 Distribution matcher 406,606,906,1006,1106,1106,1306,1406 FEC coder 418,626,926,1026,1126,1326,1426 FEC decoder 420,624,924,1024,1124,1324,1424 Distribution dematcher 600,900,1000,1100,1200,1300,1400 Transmitter section 603,903,912,932,1003,1012,1032,1034,1103,1112,1132,1212,1312,1412 Serial / parallel converter 605,905,1005,1105,1205 Sub-carrier multiplexer 607,907,1007,1107,1207 Symbol mapper 608,908,1008,1108,1208 Nyquist filtering element 609,909,1009,1109,1209 Frequency offset element 620,920,1020,1120,1320,1420 Receiver section 627,927,1027,1127,1327,1427 Symbol demapper 629,929,1029,1129,1329,1429 Sub-carrier demultiplexer 623,910,923,930,1010,1023,1030,1110,1123,1130,1330,1430 Parallel / serial converter 622,922,1022,1122,1322,1422 Recovered data 1414 Bit-wise interleaver 1434 Inverse bit-wise interleaver

Claims

1. An optical transmitter for probabilistic shaping and symbol rate optimization, One or more matcher elements, each of which Assigns each probability to a symbol of the M-QAM constellation of a given M-QAM modulation format in the complex plane represented in the binary data received by the matcher element, according to the target probability distribution of the symbol, Outputs each shaped bit sequence corresponding to the binary data received by the matcher element Is configured to A single systematic error correction coder configured to add parity bits to each of the shaped bit sequences over each of the shaped bit sequences and output a first composite shaped bit sequence including data representing each of the shaped bit sequences and the added parity bits; At least one tap element that taps one or more bits from the binary data before being received by the one or more matcher elements, wherein the parity bits are based on the one or more tapped bits, the at least one tap element; A plurality of mapping elements each configured to generate a respective codeword for each symbol represented in the received portion of the first composite shaped bit sequence; A first serial / parallel converter configured to supply each portion of the first composite shaped bit sequence to each of the plurality of mapping elements; A multiplexer configured to combine the binary data representing each of the codewords generated by the plurality of mapping elements for transmission on an optical transmission line by subcarrier multiplexing And has The one or more matcher elements have two or more matcher elements, The optical transmitter, Further includes a first parallel / serial converter configured to combine the shaped bit sequences output by the two or more matcher elements to generate binary data representing a second composite shaped bit sequence and supply the binary data representing the second composite shaped bit sequence as an input to the single systematic error correction coder, Optical transmitter.

2. The number of mapping elements is equal to the number of sub - carrier channels selected for symbol rate optimization and depends on the characteristics of the transmission medium for the optical transmission path and the target reach of the transmission. The optical transmitter according to claim 1.

3. Further comprising a second serial - to - parallel converter configured to supply each part of the binary data received by the optical transmitter to each of the two or more matcher elements in a parallel binary data stream. The at least one tap element includes a plurality of tap elements each configured to tap one or more bits from each of the parallel binary data streams and supply the one or more tapped bits to the first parallel - to - serial converter. The first parallel - to - serial converter is further configured to supply the one or more tapped bits received from each of the plurality of tap elements to the single systematic error correction encoder as parity bits to be added across each of the shaped bit sequences output by the two or more matcher elements. The optical transmitter according to claim 1.

4. The optical transmitter further comprises a combining element. Each of the plurality of tap elements is further configured to supply the one or more tapped bits to the combining element. The combining element is configured to integrate the tapped bits supplied by the plurality of tap elements into the first composite shaped bit sequence before supplying the first composite shaped bit sequence as an input to the first serial - to - parallel converter. The optical transmitter according to claim 3.

5. Further comprising a second serial - to - parallel converter configured to supply each part of the serial binary data received by the optical transmitter to each of the two or more matcher elements in a parallel binary data stream. The at least one tap element is configured to tap one or more bits from the serial binary data received by the optical transmitter before converting the serial binary data into the parallel binary data stream, and supply the one or more tapped bits to the single systematic error correction encoder as parity bits to be added across each of the shaped bit sequences output by the two or more matcher elements. The optical transmitter according to claim 1.

6. The optical transmitter further comprises a combining element. The tap element is further configured to supply the one or more tapped bits to the combining element. The combining element is configured to integrate the tapped bits supplied by the tap element into the first composite shaped bit sequence before supplying the first composite shaped bit sequence as an input to the first serial / parallel converter. The optical transmitter according to claim 5.

7. An optical transmitter for probabilistic shaping and symbol rate optimization, comprising: One or more matcher elements, each of which assigns respective probabilities to symbols of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in the binary data received by the matcher element, according to the target probability distribution of the symbols; outputs each shaped bit sequence corresponding to the binary data received by the matcher element; is configured as follows, a single systematic error correction encoder configured to add parity bits across each of the shaped bit sequences and output a first composite shaped bit sequence including data representing each of the shaped bit sequences and the added parity bits; at least one tap element configured to tap one or more bits from the binary data before being received by the one or more matcher elements, wherein the parity bits are based on the one or more tapped bits, the at least one tap element; a plurality of mapping elements each configured to generate respective codewords for each symbol represented in the received portion of the first composite shaped bit sequence. A first serial / parallel converter configured to supply each part of the first composite shaping bit sequence to each of the plurality of mapping elements; A multiplexer configured to combine, by subcarrier multiplexing, binary data representing each of the codewords generated by the plurality of mapping elements for transmission on an optical transmission line; having The one or more matcher elements have a single matcher element, receiving a shaped bit sequence corresponding to the binary data from the single matcher element, performing bit swapping for each pair of two symbols in the shaped bit sequence to generate an intermediate shaped bit sequence, supplying the intermediate shaped bit sequence as an input to the single systematic error correction encoder; further having a bitwise interleaving element configured as such; an optical transmitter. **Claim 8** A method for error correction in an optical network by probabilistic shaping and symbol rate optimization, comprising: receiving binary data to be transmitted as an optical signal; assigning, by each of the one or more matcher elements, to a symbol of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the received binary data supplied to the matcher element, each probability according to the target probability distribution of the symbol; outputting, by each of the one or more matcher elements, each shaped bit sequence corresponding to the portion of the received binary data supplied to the matcher element; adding parity bits to each of the shaped bit sequences across each of the shaped bit sequences to generate a first composite shaping bit sequence including data representing each of the shaped bit sequences and the added parity bits; tapping one or more bits from the binary data before being received by the one or more matcher elements, the parity bits being based on the tapped one or more bits; Supply each part of the first composite shaping bit sequence to each of a plurality of mapping elements, and each mapping element generates respective codewords for each symbol represented in each part of the first composite shaping bit sequence supplied to the mapping element; Combine binary data representing the respective codewords generated by the plurality of mapping elements by subcarrier multiplexing for transmission on an optical transmission line; having; The one or more matcher elements have two or more matcher elements; further comprising combining the respective shaped bit sequences output by the two or more matcher elements to generate binary data representing a second composite shaped bit sequence; Adding a parity bit to each of the shaped bit sequences includes adding the parity bit to the second composite shaped bit sequence; method. **Claim 9** The number of mapping elements is equal to the number of subcarrier channels selected for symbol rate optimization and depends on the characteristics of the transmission medium for the optical transmission line and the target reach of the transmission; The method according to claim 8. **Claim 10** Receiving binary data representing the first composite shaping bit sequence via the optical transmission line; Extracting the added parity bit from the binary data representing the first composite shaping bit sequence; Outputting a third composite shaping bit sequence from which the added parity bit has been extracted; Supplying each part of the third composite shaping bit sequence to each of two or more dematcher elements; Recovering binary data representing information received via the optical transmission line from each part of the third composite shaping bit sequence by each of the two or more dematcher elements; The method according to claim 8, further comprising. **Claim 11** The method further comprises: Supplying each part of the serial binary data received for transmission to each of the two or more matcher elements in a parallel binary data stream; Tapping one or more bits from the binary data before being received by the one or more matcher elements includes tapping one or more bits from each of the parallel binary data streams. Adding a parity bit to each of the shaped bit sequences across each of the shaped bit sequences further includes adding the one or more tapped bits as additional parity bits to the second composite shaped bit sequence. The method according to claim 8.

12. The method is further comprising supplying each portion of the serial binary data received for transmission in a parallel binary data stream to each of the two or more matcher elements. Tapping one or more bits from the binary data before being received by the one or more matcher elements includes tapping one or more bits from the received serial binary data before converting the serial binary data into the parallel binary data stream. Adding a parity bit to each of the shaped bit sequences across each of the shaped bit sequences further includes adding the one or more tapped bits from the received serial binary data as additional parity bits to the second composite shaped bit sequence. The method according to claim 8.

13. A method for error correction in an optical network by probabilistic shaping and symbol rate optimization, comprising receiving binary data to be transmitted as an optical signal; assigning each probability to a symbol of an M-QAM constellation of a given M-QAM modulation format in the complex plane represented in a portion of the received binary data supplied to each of the one or more matcher elements according to the target probability distribution of the symbol; outputting, by each of the one or more matcher elements, each shaped bit sequence corresponding to the portion of the received binary data supplied to the matcher element. Adding a parity bit to each of the shaped bit sequences to generate a first composite shaped bit sequence including data representing each of the shaped bit sequences and the added parity bit; Tapping one or more bits from the binary data before being received by the one or more matcher elements, the parity bit being based on the one or more tapped bits; Supplying each portion of the first composite shaped bit sequence to each of a plurality of mapping elements, each mapping element generating a respective codeword for each symbol represented in each portion of the first composite shaped bit sequence supplied to the mapping element; Combining the binary data representing the respective codewords generated by the plurality of mapping elements for transmission on an optical transmission line by subcarrier multiplexing; comprising; the one or more matcher elements having a single matcher element; receiving a shaped bit sequence corresponding to the binary data from the single matcher element; performing bit swapping for each pair of two symbols in the shaped bit sequence to generate an intermediate shaped bit sequence; further comprising; adding a parity bit to each of the shaped bit sequences includes adding a parity bit to the intermediate shaped bit sequence; method.

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