Device for multi-level encoding

Abstract

The present application relates to an apparatus and method for multi-stage encoding of an input message sequence into a symbol sequence, for example, based on polar coding. The input message includes information bits. The apparatus is configured to divide the input message into multiple sub-messages, encode each sub-message into a codeword, wherein a set of sub-messages is encoded based on a codeword obtained by encoding a sub-message not in the set and a predefined function of the symbol sequence, and map the encoded sub-messages into corresponding symbols.

Description

Technical Field

[0001] The present disclosure generally relates to the field of message encoding. In particular, the present disclosure relates to an apparatus and method for multi-stage encoding of an input message into a symbol sequence, such as encoding based on polar coding. The present disclosure also relates to an apparatus and method for multi-stage decoding of an input symbol sequence. The present disclosure also relates to providing a symbol sequence having predefined characteristics. Background Art

[0002] To achieve the maximum capacity of a transmission channel, the channel input symbols must have a certain probability distribution. For example, a Gaussian distribution is required to achieve the capacity of an additive white Gaussian noise (AWGN) channel with a constrained average transmit power. However, in many practical systems, a uniform distribution of channel input symbols is used, resulting in a capacity gap. This loss, known as shaping loss, can reach 1.53 dB on an AWGN channel if a uniform distribution of channel input symbols is used.

[0003] Especially for higher-order modulations, the shaping loss becomes very large. In many systems, binary coded modulation is used, where the input message is first mapped into binary codewords (using a channel encoder), and then the codewords are further mapped into channel input symbols (such as Amplitude Shift Keying (ASK) or Quadrature Amplitude Modulation (QAM) symbols) by a symbol mapper. The symbol mapper typically takes m bits as input and converts them into channel input symbols.

[0004] Typically, binary codewords have a uniform bit distribution, meaning the number of 1s and 0s within a codeword is roughly the same on average. This results in a uniform distribution of channel input symbols, which is the cause of shaping losses because a uniform distribution of channel input symbols is not optimal for many channels.

[0005] Different methods are known to reduce the shaping loss (ie, shaping methods), such as Probabilistically Shaped Coded Modulation (PSCM), which can be implemented on the basis of Bit-Interleaved Coded Modulation (BICM) or Multi-Level Coding (MLC).

[0006] In BICM, the message d is first encoded into a codeword c by the channel encoder, which is interleaved and then mapped into the channel input symbol x by the symbol mapper. At the receiver, a single-stage demapping and decoding can be performed (seeFigure 1 ).

[0007] In MLC, a message d is first divided into m parts (d1,…,d m ), and then each part is encoded with a different channel encoder to produce codewords of the same length (c1,…,c m The symbol mapper maps each bit from the m codewords to a different bit level of a modulation symbol. At the receiver, the information obtained from decoding the previous bit level (see Figure 2 and Figure 3 , MLC transmitter and receiver, respectively), and successively demapping and decoding each bit level (i.e., multi-level demapping).

[0008] In the work results published by Iscan et al. at the 2018 IEEE Global Communications Symposium (GC Wkshps), "Multi-level Coding with Polar Coded Probabilistic Shaping for Fading Channels", pages 1-5, a polar coding PSCM scheme based on MLC was proposed. Figure 4 A block diagram of the scheme is shown in .

[0009] Figure 5 An example of the resulting probability distribution is shown. It can be seen that symbols close to the origin (with low energy) have a higher probability than symbols far from the origin (with high energy). This approach is known as "single-bit shaping." It can be further observed that the resulting probability distribution is only a rough approximation to the (optimal) Gaussian distribution. Therefore, this approach allows only limited shaping gains.

[0010] The following facts can be summarized about this traditional approach:

[0011] The scheme in the work of Iscan et al. encodes each bit level independently and only shapes the single bit level.

[0012] The resulting distribution is only a crude approximation of the optimal distribution, so only limited shaping gain can be achieved.

[0013] The encoder at the m-th bit level is more complex than the traditional encoder.

[0014] In summary, there is a need for an improved apparatus and method for encoding an input message into symbols. Summary of the Invention

[0015] In light of the challenges and shortcomings described above, embodiments of the present application are intended to improve upon conventional methods for encoding an input message into a symbol sequence. Therefore, an apparatus and method for multi-stage encoding is provided that can reduce shaping losses. Specifically, it should be able to provide a symbol sequence with desired characteristics, for example, a predefined probability distribution of symbols, such as a Gaussian probability distribution.

[0016] The objects of the present application are achieved by the solutions provided in the attached independent claims. Advantageous embodiments of the present application are further defined in the dependent claims.

[0017] According to a first aspect, a device for multi-stage encoding an input message into a symbol sequence including information bits is provided. The device is configured to divide the input message into a plurality of sub-messages; encode each sub-message into a codeword, wherein a set of sub-messages is encoded based on a codeword obtained by encoding a sub-message not in the set and a predefined function of the symbol sequence; and map the codeword into a corresponding symbol.

[0018] The sub-message set includes one or more sub-messages. This provides the advantage that the symbol sequence output by the apparatus can have predefined characteristics, such as a predefined probability distribution, such as a probability distribution that approximates a Gaussian distribution. Therefore, a large shaping gain can be obtained. Consequently, when the symbol sequence is transmitted over a channel (e.g., AWGN), shaping loss can be reduced.

[0019] In an implementation form of the apparatus of the first aspect, the function is at least one of the following: a probability distribution function of the symbol; or a norm associated with the symbol sequence.

[0020] In an implementation form of the apparatus of the first aspect, the apparatus is configured to encode the set of sub-messages so as to obtain a predefined probability distribution of the symbols after symbol mapping of the plurality of codewords to a plurality of symbols.

[0021] This may provide the advantage that the symbols have a probability distribution that is approximately Gaussian, and thus a larger shaping gain may be obtained.

[0022] In a further implementation form of the apparatus of the first aspect, the apparatus is configured to encode each sub-message in the set of sub-messages by using a channel decoder.

[0023] Specifically, the apparatus can encode each sub-message using a device that includes or is implemented by a channel decoder. That is, the channel decoder can be included in the device. Using the channel decoder to encode the sub-messages can encode them based on codewords obtained by encoding the sub-messages not in the set. Therefore, the encoding of the sub-messages in the set can be influenced based on a predefined function of the symbol sequence. This has the advantage of reducing shaping losses.

[0024] In a further implementation form of the apparatus of the first aspect, the apparatus is further configured to assign a sequence of shaping bits to each sub-message in the set of sub-messages, wherein each sequence of shaping bits is selected based on the sub-message to which the sequence of shaping bits is assigned and a codeword obtained by encoding a sub-message not in the set.

[0025] In implementations using polar codes, the sequence of shaped bits can be transmitted on polar subchannels, particularly reliable polar subchannels. This can influence how the codeword is generated. Using some reliable subchannels to transmit the sequence of shaped bits may reduce the transmission rate, but if chosen appropriately, they can positively impact the generated symbols (e.g., increase the signal-to-noise ratio), such that the gain from this positive impact outweighs the loss in transmission rate.

[0026] The sequence of each shaping bit can be further selected based on a predefined function of the symbol sequence. This shaping bit has the advantage of obtaining a symbol sequence with desired characteristics, such as a predefined probability distribution. For example, a good approximation of a non-uniform probability distribution, such as a Gaussian probability distribution, can be achieved.

[0027] In a further implementation form of the apparatus of the first aspect, the apparatus is configured to map the codeword into symbols having a plurality of bit levels.

[0028] In a further implementation form of the apparatus of the first aspect, the apparatus is configured to map the codewords in such a way that at least one bit level contains bits only from a specific codeword.

[0029] In another implementation form of the apparatus of the first aspect, the at least one bit level corresponds to a flag bit level.

[0030] The flag bit level is a bit level that defines the sign of the result symbol. If the result symbol is a complex number, there are two bit levels that define the signs of the real part and the imaginary part of the complex number.

[0031] In a further implementation form of the apparatus of the first aspect, the apparatus is configured to map the encoded sub-messages based on natural binary labeling, Gray labeling or set partitioning labeling.

[0032] In another implementation form of the apparatus of the first aspect, the probability distribution of the symbols is non-uniform.

[0033] The non-uniform distribution may be a Gaussian distribution. The advantage of the non-uniform probability distribution is that it can reduce shaping loss.

[0034] In another implementation form of the apparatus of the first aspect, the apparatus is configured to encode each sub-message in the sub-message set based on polar coding.

[0035] This offers the advantage that the polarization effects of polar coding can be used in the encoding process.

[0036] In a further implementation form of the apparatus of the first aspect, the channel decoder is a polar decoder, such as a successive cancellation decoder, a list decoder, a belief propagation decoder or a flip decoder.

[0037] The channel decoder is in particular the one mentioned above. This offers the advantage that different decoders with low complexity can be used.

[0038] In another implementation form of the apparatus of the first aspect, the multiple symbols are amplitude shift keying symbols or quadrature amplitude modulation symbols.

[0039] This offers the advantage that well-known symbols can be used.

[0040] In a further implementation form of the apparatus of the first aspect, the apparatus is configured to provide the symbol to a receiver, and further provide at least one of the following parameters to the receiver using a channel different from the channel providing the symbol: the size of the sequence of shaping bits contained in the symbol; the predefined function of the symbol sequence; and a rule for allocating the shaping bits.

[0041] According to a second aspect, the present application relates to a method for multi-stage encoding of an input message into a symbol sequence including information bits, the method comprising the following steps: dividing the input message into multiple sub-messages; encoding each sub-message into a codeword, wherein a set of sub-messages is encoded based on the codeword obtained by encoding a sub-message not in the set and a predefined function of the symbol sequence; and mapping the encoded sub-messages into corresponding symbols.

[0042] The implementation form of the method of the second aspect can be formulated according to the implementation form of the device of the first aspect. The method of the second aspect and its implementation form respectively provide the same advantages as the device of the first aspect and its implementation form.

[0043] According to a third aspect, the present application relates to a computer program comprising program code for performing the method of the second aspect when executed on a computer.

[0044] According to a fourth aspect, the present application relates to a device for multi-stage decoding, which is used to demap a sequence of input symbols based on a predefined function of the symbol sequence to obtain a demapped sequence, wherein the input symbols include encoded shaped bits; decode the demapped sequence; and discard the decoded shaped bits.

[0045] The apparatus of the fourth aspect supports decoding according to the coding scheme provided by the apparatus of the first aspect. Therefore, the apparatus of the fourth aspect supports all of the aforementioned advantages. The apparatus of the first aspect may be a transmitter, and the apparatus of the fourth aspect may be a receiver. The apparatus of the first aspect and the apparatus of the fourth aspect may together constitute a transmission system.

[0046] It must be noted that all devices, elements, units and methods described in this application for an apparatus for multi-stage encoding can be implemented in software or hardware elements or any combination thereof. All steps performed by the various entities described in this application and the functions to be performed by the various entities described refer to the respective entities being suitable or configured to perform the respective steps and functions. Even if in the description of the following specific embodiments, the specific functions or steps to be performed by an external entity are not reflected in the description of the specific details of the entity performing the specific steps or functions, it should be clear to the technician that these methods and functions can be implemented in the respective software or hardware elements, or any combination thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The above aspects and implementation forms of the present application will be described in the following description of specific embodiments in conjunction with the accompanying drawings, in which:

[0048] Figure 1 A schematic diagram of a conventional encoder and decoder is shown;

[0049] Figure 2 shows a schematic diagram of a conventional encoder;

[0050] Figure 3 shows a schematic diagram of a conventional decoder;

[0051] Figure 4 shows a schematic diagram of a conventional encoder;

[0052] Figure 5 The probability distribution of ASK symbols is shown;

[0053] Figure 6 A system consisting of an encoder and a decoder communicating through a communication channel according to an embodiment of the present application is shown;

[0054] Figure 7 The present invention shows an apparatus for encoding an input message according to an embodiment of the present application;

[0055] Figure 8 The probability distribution of ASK symbols obtained by the apparatus according to the embodiment of the present application is shown;

[0056] Figure 9 The present invention shows an apparatus for encoding an input message according to an embodiment of the present application;

[0057] Figure 10 A table containing information of bit mapping performed by an apparatus according to an embodiment of the present application is shown;

[0058] Figure 11 The present invention shows an apparatus for encoding an input message according to an embodiment of the present application;

[0059] Figure 12 A method for encoding an input message according to an embodiment of the present application is shown. DETAILED DESCRIPTION

[0060] By analyzing existing solutions, it can be concluded that MLC performs better than BICM in the asymptotic case (with infinite codewords). The reason is that the single-stage demapping used by BICM does not take into account the dependencies between bit levels, while the multi-stage demapping of MLC allows full utilization of the dependencies between bit levels.

[0061] On the other hand, MLC can exhibit performance degradation in the non-asymptotic regime of finite codeword length. This is due to the finite-length effect of the channel coding scheme: the performance of the channel coding degrades as the codeword length decreases. MLC requires multiple shorter codewords (compared to the single long codeword in BICM), so the finite-length penalty is greater. Consequently, BICM is preferred in many communication systems.

[0062] In general, any binary channel code (e.g., turbo codes, LDPC codes, convolutional codes, polar codes) can be used with BICM and MLC. Polar codes are recently developed forward error correction schemes (i.e., channel coding schemes) that can achieve the capacity of binary input memoryless channels. However, their performance in BICM is often poor compared to other modern coding schemes. On the other hand, polar codes are known to work well with MLC.

[0063] Polar coding relies on the phenomenon of channel polarization, where the physical channel is converted into polarization sub-channels that asymptotically tend to have very high or very low reliability. The polar encoder assigns message bits to reliable channels and (known) frozen bits to unreliable channels. A polar decoder (such as a successive cancellation (SC) or SC list (SCL) decoder) processes noisy observations of the polar codeword along with the frozen bits to estimate the message bits.

[0064] Let G denote the polarization transformation matrix of size n×n, defined as the log2nth Kronecker power of a 2×2 kernel:

[0065]

[0066] The polar codeword c is obtained from the input sequence u by c = uG. Here, u contains k message bits d, indexed by I, and n k frozen bits, indexed by F, where I and F represent the sets containing the indices of polarization subchannels with high and low reliability, respectively. The performance of the polar code depends on the choice of sets I and F.

[0067] Typically, the reliability of the polarization subchannels can be calculated (for a given physical channel) and the most reliable subchannels assigned to the message bits and the rest assigned to the frozen bits. A simpler approach is to use a polarization sequence Q, similar to the polarization sequence specified in the 5G new wireless specification. This polarization sequence defines the reliability order of the polarization subchannels. For example, Q can include subchannel indices sorted in ascending order of reliability. Therefore, I and F can be easily calculated by taking the last k and first nk indices in Q, respectively.

[0068] The symbol mapper used in BICM or MLC schemes takes as input a sequence of m bits and maps them to channel input symbols based on a bit labeling scheme. For example, the 8-ASK mapper maps 3 bits to an ASK symbol, which can take on 8 possible values ​​depending on the input bits. Generally, Gray labeling is preferred for BICM, while Natural Binary Labeling or Set Partitioning Labeling is preferred for MLC.

[0069] Figure 6 A system 600 is shown comprising an apparatus (or encoder) 601 according to an embodiment and an apparatus 603 (or decoder) according to an embodiment for communicating via a communication channel 602, eg via AWGN.

[0070] The apparatus 601 is configured to multi-stage encode an input message into a symbol sequence, wherein the input message and the symbol sequence include information bits. The apparatus 601 is specifically configured to perform the following steps:

[0071] Divide the input message into multiple sub-messages. Each of the multiple sub-messages can have a different length.

[0072] Encode each submessage into a codeword. Thus, the set of submessages is encoded based on the codewords obtained by encoding the submessages not in the set and based on a predefined function of the symbols (i.e., the symbol sequence). That is, the submessages not in the set are encoded, and the resulting codewords are used as input to encode the submessages in the set. Another input to the encoding is a predefined function of the symbol sequence, which can be a norm associated with the symbol sequence or a probability distribution function (or probability mass function) of the symbols.

[0073] Mapping the encoded sub-messages into corresponding symbols. For example, the apparatus 601 may use a symbol mapper to perform the mapping.

[0074] Therefore, the symbol sequence can have predefined characteristics, for example, after symbol mapping, the symbols can have a predefined probability distribution (or target probability distribution). The symbol sequence can also satisfy a predefined norm (for example, the Euclidean norm, the p-norm, or the distance between the symbol sequence and the predefined sequence).

[0075] After the device 601 encodes the input message and outputs symbols, the symbol sequence can be sent to the device 603, which is used to perform multi-stage decoding on the input symbol sequence. The device 603 will be described in more detail below.

[0076] Figure 7 The device 601 according to an embodiment of the present application is shown. Figure 6 In particular, Figure 7 The apparatus 601 is shown with further optional features. Figure 7 The device 601 is used to encode an input message d into a symbol sequence of ASK symbols.

[0077] In this embodiment, the device 601 is also used to encode the m-th bit level (defining the sub-message set; associated with encoder m) in dependence on the previous bit level (the sub-message not in the sub-message set; associated with encoders 1, 2). In addition, the encoding in this embodiment can rely on a predefined function, for example, a predefined probability distribution, which can be obtained from the codeword of the previous bit level or from an external input. Thus, for example, a predefined probability distribution of ASK symbols can be obtained, in particular a probability distribution that very accurately approximates a Gaussian distribution (see Figure 8 ).

[0078] The decoder can act as an encoder to encode each sub-message in the set of sub-messages, wherein the decoder is configured to search for a codeword representing the sub-message while having certain properties, such as a probability distribution (or conditional probability distribution) of the bits in the codeword. For example, this can be implemented according to the description of polar codes in the work "Multi-level Coding with Polar Coded Probabilistic Shaping for Fading Channels" by Iscan et al., presented at the 2018 IEEE Global Communications Symposium (GC Wkshps), pages 1-5.

[0079] Furthermore, a simple successive cancellation (SC) decoder can be used as the encoder to encode each sub-message in the set of sub-messages, i.e., here as an m-th bit-level encoder. This has a much lower computational complexity than, for example, a list decoder. In fact, the SC decoder has a complexity of the same order of magnitude as a traditional polar encoder. Therefore, the proposed scheme is advantageously no more complex than a traditional MLC scheme based on polar codes.

[0080] The following can be given by Figure 7 A summary of the steps performed by the device 601 is shown:

[0081] Device 601 is configured to use an MLC scheme in which only a single bit level can be (probabilistically) shaped. However, the bit level is encoded based on previously encoded bit levels. Thus, for example, the probability distribution of the resulting ASK symbols can be determined, e.g., a Gaussian distribution can be very accurately approximated. Consequently, shaping losses in channel 602 (particularly AWGN) can be significantly reduced.

[0082] • The apparatus 601 may be configured to encode the m-th bit level using an SC decoder. This provides the advantage that the apparatus 601 is also advantageous from a complexity perspective.

[0083] The apparatus 601 facilitates reliable data transmission, is based on multi-level coding (MLC), and can be further configured to:

[0084] Transmitting a polar codeword in each bit level (or in at least one bit level, in particular, at least in the mth bit level). That is, the apparatus 601 may be configured to encode each sub-message in the sub-message set based on polar coding.

[0085] At (at least) one bit level (denoted as the shaping bit level), generate codewords that depend on codewords at other bit levels, such that after symbol mapping, a predefined probability distribution or a target probability distribution is obtained. That is, the apparatus 601 may be further configured to assign a sequence of shaping bits to each sub-message in the set of sub-messages.

[0086] • Encoding is performed at the bit level using a polar decoder.

[0087] • Set the shaping bit level to the flag bit level, ie the bit level that defines the flag of the result sign.

[0088] In the following, the steps that can be performed by the apparatus 601 on the transmitter side will be described in further detail.

[0089] Can be used Figure 7 The transmission scheme given in

[15] can also be used with symbol mappers with, for example, natural (binary) labels. In one embodiment, for natural labels with m bit levels, the mapper output can take the values ​​{±1, ±3, ±5, ..., ±(2 m -1)}. The mapper output can be scaled by a predefined constant, for example, to meet power requirements.

[0090] For example, for 8-ASK (m=3), the output symbols {-7, -5, ..., 5, 7} are possible. The mapping of each bit sequence of m bits to ASK symbols can be done in the order of 0 to (2 m -1) in ascending or descending order. Figure 10 The table in gives an example where m=3, where three bits b1b2b3 are mapped to the 8-ASK symbol x. Note that the last bit level (b3) contains the flag bit, i.e., the generated ASK symbol x has a negative or positive sign depending on whether b3 is 1 or 0.

[0091] This scheme can be easily extended to symbols with complex numbers. In this case, there will be two flag bit levels in total (one for each complex dimension).

[0092] In one embodiment, such a symbol mapper may be configured as Figure 11 Here, the codeword bits ci (0 and 1) are first mapped to a sequence b containing ±1. i , then press a i =2 (i-1) Scaling. The sequence x containing the ASK symbols is obtained by summing these scaled sequences. The cumulative sum of the scaled sequences of bit levels 1 to i can be recorded as x i .

[0093] As mentioned above, the encoder at the mth bit level (i.e., the flag bit level) is a modified encoder. This encoder is denoted as ε s In one embodiment, a polar decoder is used as an encoder, for example, a successive cancellation (SC) decoder, a successive cancellation list (SCL) decoder, a belief propagation (BP) decoder or a flip decoder can be used. In addition, the encoder ε s According to x m-1 Generate its output. Note that xm-1 is constructed based on the codewords in bit levels 1 to m-1. Therefore, ε s The output of depends on the codewords in all previous bit levels.

[0094] More specifically, the encoder ε s Find the part d representing the mth message m The code word c m (i.e. ε s Right m Encoding), while making the ASK symbols in x according to the target probability distribution P X To this end, some reliable polarization subchannels can be allocated in the m-th bit level for shaping bits. These bits do not carry any information, but make x according to the target probability distribution P X To distribute.

[0095] The number of shaping bits (s) defines how many resources (in this case, polarimetric subchannels) are allocated for signal shaping. In traditional schemes without shaping, no resources are allocated for shaping, i.e., s = 0. The number of shaping bits can be selected to best approximate the target distribution. On the other hand, each shaping bit uses additional resources. Therefore, an excessive number of shaping bits should not be used. The optimal number of shaping bits is the minimum number that provides the maximum gain.

[0096] If you want to use the mth bit level (ie d m The length is k m )Transmission k m message bits, and s shaping bits are used. Assuming that the polarization sequence is fixed, the most reliable s polarization sub-channels (represented by the set S) are assigned to the shaping bits, followed by the most reliable k m Polarization sub-channels (denoted by set I) are allocated to message bits, and the rest (denoted by set F) are allocated to frozen bits.

[0097] Under these conditions, we can use ε s (The codeword length is n, the rate is (k m +s) / n) polar decoder, where the following parameters are used:

[0098] • A known bit (eg 0) can be used as a frozen bit of index F.

[0099] Message bit d m Can be used as additional frozen bits with index I.

[0100] • S can be used as an index to the unknown bits (recovered by the decoder).

[0101] Λ (defined below) can be used as decoder input (noisy channel observation) in the form of log-likelihood ratio (LLR).

[0102] In general, Λ can be defined as x m-1 Therefore, it is also a function of the codeword bits from the previous bit level. For the Maxwell-Boltzmann target distribution, Λ is related to -x m-1 The distribution minimizes the transmission power at a given rate. Therefore, we can use Λ = -x m-1 Furthermore, a simple successive cancellation (SC) decoder is sufficient to achieve good gain. A more complex SCL decoder will yield better performance, but at the expense of increased complexity.

[0103] Note that this polar decoding operation will search for the shaped bits (and the resulting codeword c m ), which will result in the codeword having m-1 is the expected probability distribution conditional on . Figure 8 The resulting distribution of ASK symbols is shown, where m=4 and approximately 1 / 3 of the polarization sub-channels in the m-th bit level are allocated to shaping bits.

[0104] From another perspective, this polar decoding operation can also be seen as a solution to the energy minimization problem, that is, the decoder searches for a codeword so that the resulting ASK symbol has the minimum average energy, that is, the minimum Euclidean norm.

[0105] In summary, the device 601 may have the following features:

[0106] • An MLC scheme can be used based on polar codes, where a polar codeword is used for each bit level.

[0107] Natural (binary) labels can be used.

[0108] Modified encoder ε s Available in the mth bit level (which corresponds to the flag bit level).

[0109] Codeword c m Can be determined by the encoder ε s According to the data from the previous bit level (c1 to c m-1 ) codeword to generate.

[0110] Encoder ε s This can be achieved by using a polar decoder, for example, a simple SC decoder or a more complex SCL decoder.

[0111] The m-th bit-level codeword may contain (in addition to the message and frozen bits) shaped bits that do not carry any additional information but result in a codeword with a probability distribution conditioned on the bits of the previously encoded codeword, further yielding the target or first probability distribution P of the ASK symbols after symbol mapping. X .

[0112] The number of shaping bits, s, is a parameter that can be chosen to optimize performance: if no shaping bits are used (s=0), no shaping gain is achieved. If too many shaping bits are used, this can lead to inefficient use of available resources. Our results suggest that using approximately one-third of the polarimetric subchannels at the flag bit level is a good choice.

[0113] Figure 9 The device 601 according to an embodiment of the present application is shown. Figure 7 In particular, Figure 9 The apparatus 601 is shown with further optional features. Figure 9 The device 601 is used to encode an input message into a symbol sequence, for example, ASK symbols.

[0114] In this embodiment, the means 601 is used to encode the m-th bit level (defining the sub-message set; associated with encoder m) according to the previous bit levels (sub-messages not in the sub-message set; associated with encoders 1, 2) and according to a predetermined function (external input), for example a predetermined probability distribution. Thus, for example, a predefined probability distribution of ASK symbols can be obtained, in particular a probability distribution that is very accurately close to a Gaussian distribution (see Figure 8 ). In particular, the m-th bit level can be encoded using a channel decoder.

[0115] Typically, an encoder maps a message sequence to a codeword sequence. This operation is one-to-one, meaning that for every message sequence, there is another codeword sequence. Typically, the codeword sequence is longer than the message sequence. For example, suppose the encoder maps a binary message sequence of k bits to a codeword sequence of n bits where n>k. In this case, any binary sequence of length k can be used as input to the encoder (a binary sequence of length k has 2 k possibilities), and there are 2 k possible codeword sequences of length n. Note that there are usually 2 n There are different binary sequences of length n, but not every sequence of length n is a codeword. The set of all possible codeword sequences is called a codebook.

[0116] In this context, a channel decoder is a device that takes an unconstrained sequence of length n as input and searches a codebook for a codeword sequence and its corresponding message sequence. Both the encoder and decoder define a mapping between sequences. Traditionally, the encoder generates codewords at the transmitter, while the decoder searches for the most likely codeword (and its corresponding message sequence) that causes the received noise signal at the receiver.

[0117] In the device 601 according to an embodiment of the present application, a (channel) decoder can be used so that the codeword found by the channel decoder has two properties: it represents the message and it has certain desired properties (i.e., the bits in the codeword are distributed according to the desired probability distribution or the desired conditional probability distribution). This can be achieved by introducing shaping bits as described above, which provides new degrees of freedom for mapping message sequences to codewords. The shaping bits can be regarded as additional bits (to be appended to the message bits) that do not carry any information but give the codeword bits the desired probability distribution. How to obtain the value of the shaping bits can be expressed as a channel decoding operation (as described in the work of Iscan et al.). Therefore, in the current problem, a channel decoder can be used in the device 601 instead of an encoder.

[0118] After device 601 (any of the above) encodes the input message and outputs a symbol sequence, it can send the symbol sequence to device 603 (see Figure 1 ), which is used to perform multi-stage decoding on the input symbol sequence. The device 603 can, for example, be used to:

[0119] • Performing demapping of the sequence of input symbols based on a predefined function of the symbol sequence (eg based on a predefined function of the apparatus 601 obtained from the apparatus 601 or from another entity) to obtain a demapped sequence, wherein the input symbols comprise the encoded shaped bits.

[0120] • Decode the demapped sequence.

[0121] Discard the decoded shaping bits.

[0122] In particular, the device 603 may be based on Figure 3 However, certain modifications may be made. In particular, compared to a conventional MLC receiver, the following parameters are preferably known in the device 603:

[0123] A predefined function of the symbol sequence, for example, the probability distribution function P of ASK symbols X .

[0124] The number of shaping bits s.

[0125] A set S indicating the index of the shaping bits.

[0126] Generally speaking, all of these parameters may be signaled (eg, using a control channel) to device 603 so that device 603 may use these parameters to resume operations performed at device 601. However, some simplifications may be made because all of these parameters are interrelated.

[0127] In the above embodiment, a fixed polarization sequence is assumed, and the most reliable s indices in this sequence are used to construct S. Therefore, in this case, if the number of shaping bits s is known, the device 603 can already obtain S. In addition, using about 1 / 3 of the polarization sub-channels as shaping bits is a good choice. Therefore, a fixed rule can be used to obtain the number of shaping bits. Finally, since s and P X is relevant, so the result P for each choice of s can be precomputed X and store it in a lookup table, thus avoiding additional control signaling.

[0128] The traditional MLC receiver assumes that the ASK symbols are uniformly distributed (P X In one embodiment, P X is non-uniform, so the demapper needs to be based on P X Generate its output. For some typical distributions (such as Gaussian or Maxwell-Boltzmann), this can be achieved by scaling the demapper input by a constant that depends on P X and channel noise variance.

[0129] Compared to traditional MLC receivers, additional shaping bits are allocated to some polarization subchannels at the flag bit level. The values ​​of the shaping bits are unknown to device 603. When decoding at this bit level, the decoder can treat the shaping bits as message bits, and the information bits are also unknown. At the end of the decoding process, device 603 can essentially discard the shaping bits, as they carry no additional information. Furthermore, if all message bits are recovered during the decoding process, the decoder can perform early termination without completing the entire decoding process (because the remaining unknown bits are only the shaping bits). Alternatively, device 603 can extract all shaping bits and message bits at the decoder output and calculate another copy of the shaping bits based on the message bits (as performed at the transmitter). Device 603 can then compare this copy of the shaping bits with the shaping bits at the decoder output. If they differ, device 603 can declare an error. This can be considered an additional error detection mechanism that can also be used to select the correct codeword from the output of a list decoder.

[0130] In summary, in the embodiment of the present application, the receiving-side device 603 can implement the following features:

[0131] Probability distribution P of ASK symbols X , the number of shaping bits s, and the set S are additional parameters used by device 603 to recover the transmitted information. Therefore, they can be transmitted to device 603 using signaling (e.g., using a control or communication channel other than channel 602). However, because they are related to each other, only a subset of these parameters can be signaled, thereby deriving the other parameters based on these parameters. Alternatively, these parameters can be derived using fixed rules, eliminating the need for additional signaling.

[0132] The demapper can use P in the demapping process X For some typical probability distributions, this can be achieved by using a function that depends on P X This is done by scaling the demapper input by a scalar factor of the channel noise variance.

[0133] The device 603 may treat the shaped bits as message bits. After decoding is complete, the device 603 may discard the shaped bits or use them as an error detection mechanism. Alternatively, if all message bits have been decoded, the decoder may perform early termination.

[0134] Figure 12 A method 1200 for encoding an input message into a symbol sequence according to an embodiment is shown. The method 1200 may be performed by the apparatus 601. The method 1200 for performing multi-stage encoding on an input message including information bits comprises the following steps:

[0135] • Divide 1201 the input message into multiple sub-messages.

[0136] • Encoding 1202 each sub-message into a codeword, wherein the set of sub-messages is encoded based on a predefined function of the codewords and symbol sequences obtained by encoding sub-messages not in the set.

[0137] • Mapping 1203 the encoded sub-messages into corresponding symbols.

[0138] The present application has been described with reference to various embodiments as examples and modes of implementation. However, other variations will be apparent to and will be realized by those skilled in the art and by those practicing the claimed application from a study of the drawings, the present disclosure, and the independent claims. In the claims and description, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may perform the functions of several entities or items mentioned in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Claims

1. A device (601) for multi-stage encoding an input message into a symbol sequence including information bits, the device being configured to: - dividing the input message into a plurality of sub-messages; - encoding each of said plurality of sub-messages into a codeword, wherein, - a first set of sub-messages among the plurality of sub-messages is encoded by a polarimetric decoder based on a predefined function of the codeword obtained by encoding a sub-message in a second set of sub-messages and the symbol sequence, wherein the predefined function is at least one of: a probability distribution function of symbols in the symbol sequence, and a norm associated with the symbol sequence, wherein the sub-messages in the second set of sub-messages are not included in the first set of sub-messages; and - each sub-message in the first set of sub-messages is assigned a sequence of shaping bits, wherein each sequence of shaping bits is selected based on the sub-message to which the sequence of shaping bits is assigned and the codeword obtained by encoding the sub-messages in the second set of sub-messages; and - mapping the codewords into symbols having a plurality of bit levels, wherein at least one bit level contains bits only from a specific codeword.

2. The device according to claim 1, wherein The at least one bit level corresponds to a flag bit level.

3. The device according to claim 1, wherein The apparatus is further configured to map the encoded sub-messages based on natural binary labels, Gray labels, or set partitioning labels.

4. The device according to claim 1, wherein The probability distribution of the symbols is non-uniform.

5. The device according to claim 1, wherein The polar decoder is a successive cancellation decoder, a list decoder, a belief propagation decoder or a flip decoder.

6. The device according to any one of claims 1 to 5, wherein: A plurality of the symbols are amplitude shift keying symbols or quadrature amplitude modulation symbols.

7. The apparatus according to any one of claims 1 to 5, further configured to provide the symbols to a receiver, and further provide at least one of the following parameters to the receiver using a channel different from the channel through which the symbols are provided: o the size of the sequence of shaping bits included in the symbol; o said predefined function of said sequence of symbols; o Indicators or rules for allocating the shaping bits.

8. A method for multi-stage encoding an input message into a symbol sequence comprising information bits, the method comprising the steps of: - dividing the input message into a plurality of sub-messages; - encoding each of said plurality of sub-messages into a codeword, wherein, - a first set of sub-messages among the plurality of sub-messages is encoded by a polarimetric decoder based on a predefined function of the codeword obtained by encoding a sub-message in a second set of sub-messages and the symbol sequence, wherein the predefined function is at least one of: a probability distribution function of symbols in the symbol sequence, and a norm associated with the symbol sequence, wherein the sub-messages in the second set of sub-messages are not included in the first set of sub-messages; and - each sub-message in the first set of sub-messages is assigned a sequence of shaping bits, wherein each sequence of shaping bits is selected based on the sub-message to which the sequence of shaping bits is assigned and the codeword obtained by encoding the sub-messages in the second set of sub-messages; and - mapping the codewords into symbols having a plurality of bit levels, wherein at least one bit level contains bits only from a specific codeword.

9. The method according to claim 8, wherein The at least one bit level corresponds to a flag bit level.

10. The method according to claim 8, wherein Mapping the codeword into symbols having a plurality of bit levels comprises: The codewords are mapped to corresponding symbols based on natural binary labels, Gray labels, or set partitioning labels.

11. The method according to claim 8, wherein The probability distribution of the symbols is non-uniform.

12. The method according to claim 8, wherein The polar decoder is a successive cancellation decoder, a list decoder, a belief propagation decoder or a flip decoder.

13. The method according to any one of claims 8 to 12, wherein: A plurality of the symbols are amplitude shift keying symbols or quadrature amplitude modulation symbols.

14. The method according to any one of claims 8 to 12, further comprising: providing the symbols to a receiver, and further providing at least one of the following parameters to the receiver using a channel different from the channel on which the symbols are provided: o the size of the sequence of shaping bits included in the symbol; o said predefined function of said sequence of symbols; o Indicators or rules for allocating the shaping bits.

15. A device for multi-stage decoding, the device being configured to: Demapping the sequence of input symbols based on a predefined function of the symbol sequence to obtain a demapping sequence, in, The input symbols are obtained based on a polar decoder, and the input symbols include encoded shaping bits. The polar decoder is configured to encode a first set of sub-messages in the input message based on a codeword obtained by encoding sub-messages in a second set of sub-messages in the input message divided into a plurality of sub-messages and the predefined function of the symbol sequence, wherein the sub-messages in the second set of sub-messages are not in the first set of sub-messages, and each sub-message in the first set of sub-messages is assigned a sequence of shaping bits, wherein each sequence of shaping bits is selected based on the sub-message to which the sequence of shaping bits is assigned and the codeword obtained by encoding the sub-messages in the second set of sub-messages. The predefined function is at least one of the following: a probability distribution function of symbols in the symbol sequence, a norm associated with the symbol sequence, and wherein the input symbol has a plurality of bit levels, and at least one bit level contains bits only from a particular codeword; Decoding the demapped sequence into a codeword; and Discard the decoded shaped bits.

16. A method for multi-stage decoding, the method comprising the steps of: Demapping the sequence of input symbols based on a predefined function of the symbol sequence to obtain a demapping sequence, The input symbols are obtained based on a polar decoder and include encoded shaping bits. The polar decoder is configured to encode a first set of submessages in the input message based on a codeword obtained by encoding submessages in a second set of submessages in the input message divided into multiple submessages and the predefined function of the symbol sequence, wherein the submessages in the second set of submessages are not in the first set of submessages, and each submessage in the first set of submessages is assigned a sequence of shaping bits, wherein each sequence of shaping bits is selected based on the submessage to which the sequence of shaping bits is assigned and the codeword obtained by encoding the submessages in the second set of submessages. The predefined function is at least one of the following: a probability distribution function of symbols in the symbol sequence, a norm associated with the symbol sequence, and wherein the input symbol has a plurality of bit levels, and at least one bit level contains bits only from a particular codeword; Decoding the demapped sequence into a codeword; and Discard the decoded shaped bits.

17. A computer program product comprising a program code for executing the method according to any one of claims 8 to 14, or a program code for executing the method according to claim 16, when executed on a computer.

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