Receiving device and method using uneven constellation

Abstract

Receiving device comprising: a receiver (41) for receiving one or more transmit streams sending a signal modulated with quadrature amplitude modulation (QAM) with a non-uniform constellation (NUC); a decoder (42) for decoding the received one or more received transmit streams into constellation values; a demodulator (44) for demodulating constellation values ​​of a non-uniform constellation into cell words; and a decoder (45) for decoding cell words into output data words, wherein the non-uniform constellation has 1024 constellation points, each constellation point having a common-phase component and a quadrature component, each of the common-phase component and quadrature component having a position of a one-dimensional non-uniform pulse amplitude modulation constellation with 32 positions (32-PAM).where the 32-PAM constellation has normalized constellation values ​​u'0-15 and -u'0-15, where u'0-15=(0.1275, 0.1276, 0.1294, 0.1295, 0.3424, 0.3431, 0.3675, 0.3666, 0.6097, 0.6072, 0.7113, 0.7196, 0.9418, 1.0048, 1.2286, 1.5031),(0.0773, 0.0773, 0.1614, 0.1614, 0.3086, 0.3085, 0.4159, 0.4163, 0.5810, 0.5872, 0.7213, 0.7604, 0.9212, 1.0349, 1.2281, 1.4800), or (0.0354, 0.0921, 0.1602, 0.2185, 0.2910, 0.3530, 0.4264, 0.4947, 0.5763, 0.6531, 0.7417, 0.8324, 0.9386, 1.0529, 1.1917, 1.3675).

Description

BACKGROUND Area of ​​Revelation

[0001] The present disclosure relates to an encoding and modulation device and an encoding and modulation method. Furthermore, the present disclosure relates to a transmitting device and a transmitting method. In addition, the present disclosure relates to a computer program and a non-perishable, computer-readable recording medium. Description of the state of the art

[0002] Modern communication systems typically utilize, among other elements, an encoding and modulation device (as part of a transmitter) and a decoding and demodulation device (as part of a receiver). The encoding and modulation device is often part of a so-called BICM (Bit Interleaved Coded Modulation) device, which generally (on the transmitter side) comprises a serial connection of an FEC (Forward Error Correction) encoder, a bit interleaver, and a modulator employing spectrally efficient modulation such as multi-stage PAM (Pulse Amplitude Modulation), PSK (Phase Shift Keying), or QAM (Quadrature Amplitude Modulation). It should be noted that the following use of this term is intended as a general term encompassing PAM, PSK, and QAM.

[0003] BICM enables good performance over both non-fading and fading channels due to the use of the interleaver and / or the FEC encoder. It exhibits a reasonable level of complexity compared to multi-level coding (MLC) models and is therefore frequently used in communication systems, such as all DVB systems and powerline communication (e.g., HomePlug AV, DAB, LTE, WiFi, etc.).

[0004] In principle, the coding and modulation capacity, such as the BICM capacity in systems that use a BICM device, is considered an objective function, and it is desirable to find optimal constellation points so that this capacity is maximized, whereby this is often subject to power normalization, that is, that the average power of the constellation points should be normalized to 1, for example.

[0005] The "background" description provided here is intended to present the general context of the disclosure. The work of the inventors currently named, to the extent described in this background section, as well as aspects of the description that do not otherwise qualify as prior art at the filing date, are neither expressly nor implicitly acknowledged as prior art against the present disclosure. SUMMARY

[0006] One task is to provide an encoding and modulation device and an encoding and modulation method that provide increased or even maximized encoding and modulation capacity. Another task is to provide a demodulation and decoding device and a demodulation and decoding method, as well as a corresponding computer program for implementing the methods and a non-perishable, computer-readable recording medium for implementing the methods.

[0007] According to one aspect, a comprehensive coding and modulation device is provided. – an encoder that encodes input data into cell words, and – a modulator that modulates the cell words into constellation values ​​of a non-uniform constellation, wherein the modulator is designed, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, to select a non-uniform constellation from a group of constellations that has one or more of the constellations defined by the constellation position vector u 1...v are defined, where v = sqrt(M) / 2 – 1, as detailed in claim 1.

[0008] According to another aspect, a comprehensive transmitting device is provided. – a coding and modulation device as proposed herein, which encodes and modulates input data into constellation values, – a converter that converts the constellation values ​​into one or more transmit streams, and – a transmitter that sends one or more transmission streams.

[0009] According to further aspects, corresponding methods, a computer program with programming means for causing a computer to execute the steps of the coding and modulation method as disclosed herein when the computer program is executed on a computer, and a non-perishable, computer-readable recording medium on which a computer program product is stored which, when executed by a processor, causes the coding and modulation method disclosed herein to be executed, are provided.

[0010] Preferred embodiments are defined in the dependent claims. It should be understood that the claimed methods, the claimed computer program, and the claimed computer-readable recording medium have similar and / or identical preferred embodiments to the claimed device and as defined in the dependent claims.

[0011] One aspect of the revelation is that the constellation points of the constellations used are not placed on a regular grid with equidistant symbols, but rather at optimized locations depending on the channel characteristics, e.g., channel transition probabilities due to AWGN (Additive White Gaussian Noise), fading, etc. Furthermore, the constellation used is selected based on the SNR (Signal-to-Noise Ratio) and the desired total number of constellation points for that constellation. A method for finding and optimizing these non-uniform constellations (hereinafter referred to as NUCs) is explained below.

[0012] It should be noted that for every M-QAM, the underlying sqrt(M)-PAM can also be considered. Furthermore, it should be noted that in other aspects, the group of constellations defined in the claims contains fewer constellations, e.g., only constellations for non-fading channels, only constellations for fading channels, only constellations for selected values ​​of M, only constellations for M-QAM or sqrt(M)-PAM, and / or constellations for fewer SNR values. In other words, fewer constellations may be included in the group of constellations available for use by the modulator; that is, the group of constellations available for use by the modulator may contain one or more of the constellations defined in the claims.Accordingly, the present disclosure is also directed to a coding and modulation device and a coding and modulation method which have a smaller group of constellations available for use (as explained above) and / or wherein fewer constellations are available for a given value of M.

[0013] It should also be noted that for some values ​​of M, there are two constellation options for fading channels and two constellation options for non-fading channels, provided for the same selection parameters (e.g., the same SMR value) from which the modulation can choose. These two options (designated as Option 1 and Option 2) are the result of separate optimizations of the encoding and modulation capacities. Therefore, the modulator can, for example, select a constellation from Option 1 or Option 2 based on the desired capacity, with the constellations according to Option 2 generally providing a slightly higher capacity.

[0014] However, the constellation points of the QAM constellations considered in this revelation are not placed on a regular grid with equidistant symbols, but rather at optimized positions depending on the channel characteristics, e.g., channel transition probabilities due to AWGN, fading, etc.

[0015] It should be understood that the above general description of the revelation and the following detailed description are exemplary, but not limiting, to the revelation. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] A more complete understanding of the revelation and many of its associated benefits will readily be obtained when it is better understood by referring to the following detailed description when considered in conjunction with the accompanying drawings, wherein:

[0017] Fig.1 shows an embodiment of a coding and modulation device according to the present disclosure,

[0018] Fig. 2 shows an embodiment of a transmitting device according to the present disclosure,

[0019] Fig. 3 shows a configuration of a communication system according to the present disclosure,

[0020] Fig. 4 shows a regular 4-QAM constellation as a simple example of a constellation,

[0021] Fig. 5 diagrams showing the integrand of the 1-dimensional BICM capacitance function at 10 dB and at 30 dB SNR,

[0022] Fig. 6. An 8-PAM uneven constellation and a 64-QAM uneven constellation are shown.

[0023] Fig. Figure 7 shows a constellation for a 64-QAM non-uniform constellation, which generally defines the constellation points, and

[0024] Fig.8 a diagram shows the performance of uneven N 2 -QAM constellations. DESCRIPTION OF THE DESIGNS

[0025] Referring to the drawings, in which the same reference numerals denote identical or corresponding parts in the different views, shows Fig. 1 an embodiment of a coding and modulation device 10 according to the present revelation. It includes an encoder. 11 , which encodes input data into cell words and a modulator 12 , which modulates the cell words into constellation values ​​of a non-uniform constellation. The modulator 12is designed, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, to utilize (and preferably preselect) a non-uniform constellation from a group of constellations, which includes predetermined constellations defined by the constellation position vector u 1...v are defined where v = sqrt(M) / 2 – 1. These predetermined constellations are derived and shown below.

[0026] In other embodiments of the coding and modulation device 10 Additional elements may be provided, such as a BCH encoder, an LDPC encoder, a bit interleaver, and / or a demultiplexer (for demultiplexing bits of encoded data into cell words). Some or all of these elements may be separate components or may be part of the encoder. 11It could be, for example, a BICM device, such as is commonly used in the transmitter of a DVB system, as an encoding and modulation device. 10 can be used.

[0027] Fig. Figure 2 shows an embodiment of a transmitting device 20 as disclosed herein, comprising a coding and modulation device 21 (referenced by 10 in Fig. 1) as proposed herein, the input data is encoded and modulated into constellation values, a converter 22 , which converts the constellation values ​​into one or more transmit streams, and a transmitter that sends the one or more transmit streams. In an exemplary embodiment, the converter can 22They contain one or more elements such as a time, cell, and / or frequency interleaver, a frame generator, an OFDM modulator, etc., as described, for example, in the various standards relating to DVB. The constellations and constellation values ​​are fundamentally predefined and stored, for example, in the constellation memory. 24 stored or obtained from an external source.

[0028] In other embodiments of the transmitting device 20 Additional elements may be provided, such as an input processing unit, a frame creation unit and / or an OFDM generation unit, as is commonly used in DVB system transmitters.

[0029] Fig. Figure 3 shows an embodiment of a communication system 30 according to the present disclosure, comprising one (or more) transmitting device 20 (Tx) as in Fig.2 shown and one or more receiving devices 40 , 40' (Rx).

[0030] A receiving device 40 generally includes a recipient 41 , which receives one or more transmitted streams, a decoder 42 , which decodes the received one or more transmitted streams into constellation values, and a demodulation and decoding device 43 , which demodulates and decodes the constellation values ​​in the output data. The demodulation and decoding device 43 It generally has a demodulator. 44 for demodulating constellation values ​​of a non-uniform constellation into cell words and a decoder 45for decoding cell words into output data words, wherein, based on the total number M of constellation points of the constellation, the signal-to-noise ratio in dB and the channel characteristics, a non-uniform constellation is used from the group of constellations that have the same predetermined constellations as those in the coding and modulation device. 10 can be used.

[0031] Predetermined demodulation and decoding takes soft values ​​into account, as opposed to hard-determined values ​​(0 and 1). Soft values ​​represent the continuously distributed received values ​​(possibly after A / D conversion including quantization) through more than two states (as in the case of a binary (hard) decision). The reason for this is that NUCs are fundamentally not optimal for hard-determination. Nowadays, BICM receivers are typically soft-determining anyway.

[0032] Basically, data (e.g., communication data, broadcast data, etc.) is transmitted by a sending device. 20 to one or more of the receiving devices 40 via a transmission channel 50 , 50' sent. The transmission channel 50 , 50' It can be a unicast channel, a multicast channel, a broadcast channel, and can be designed as a one-way or bi-directional channel (i.e., with a return channel from the receiving device to the transmitting device).

[0033] In one embodiment, the modulator 12The system is designed to select and utilize a non-uniform constellation based on the total number M of constellation points, the required signal-to-noise ratio (SNR) for error-free decoding in dB, and the channel characteristics. In broadcast applications, the constellation is generally not selected based on the SNR at the receiver, but rather based on the SNR required for error-free decoding with a channel code in use (if a code is used, for example, LDPC codes in the case of second-generation DVB broadcast systems) for an expected channel characteristic, such as static reception or multi-path fading.

[0034] The total number M of constellation points is generally selected according to the desired load throughput along with the code rate of the FEC encoder. The SNR for error-free decoding for a typical channel characteristic is generally known, for example, through simulation. In broadcasting, the channel characteristics of the receivers are unknown, meaning a compromise is chosen. For example, in broadcasting, a non-uniform constellation is selected for each code rate of the FEC encoder, optimized for an SNR that is a compromise for all channel characteristics.

[0035] The transmitter is fundamentally targeting a specific scenario. For example, a broadcast transmission via cable or satellite takes into account that the channel is a non-fading AWGN (suitable channel model), while a terrestrial broadcaster typically takes into account that the channel is a fading channel, for example with a Rayleigh distribution, since multiple echoes are usually received.

[0036] In another configuration, the modulator 12 designed to adaptively select and utilize a non-uniform constellation based on the total number M of constellation points, the signal-to-noise ratio (SNR) in dB, and the channel characteristics, wherein the signal-to-noise ratio (SNR) in dB and channel characteristics are determined by a receiving device 40The data to be sent can be received. Such adaptive selection of the constellation is only possible with a return channel in unicast environments. A non-uniform constellation can be adjusted, for example in the time and / or frequency domain, such as for different OFDM subcarriers.

[0037] Depending on the SNR, the optimal value for M and the code rate of the FEC encoder can be selected to achieve the highest throughput (equivalent to C). B ). In other words, a high value of M is selected for a large SNR, resulting in high data throughput (and vice versa).

[0038] Channel characteristics describe the statistical properties of the channel, such as the extent of multipath propagation between the transmitter and receiver. If the channel is characterized by no multipath propagation, as in an AWGN channel, the required SNR for error-free decoding is relatively low; therefore, the NUC must be selected accordingly for optimal performance. If the transmit channel is characterized by strong multipath propagation, the required SNR for error-free reception is higher compared to a channel without multipath propagation; therefore, a NUC optimized for higher SNR must be used. Furthermore, the NUCs should be optimized taking into account the fading characteristics, as will be discussed below.

[0039] As mentioned above, the number M of constellation points is selected according to the desired throughput. Larger values ​​of M allow for higher data throughput but require a higher SNR for error-free reception. This is further affected by the code rate of the FEC encoder, if any FEC encoder is used.

[0040] Another explanation (closely related to the optimization problem of the present disclosure) is that for each SNR, optimized constellations are proposed for different M values. The optimization goal is the BICM capacity. For an expected SNR, if, for example, 15 dB of SNR is to be guaranteed, M is selected for which the respective optimized NUC achieves the greatest BICM capacity. As a general rule, a small value of M should be chosen for low SNR and vice versa. However, from a theoretical point of view, it turns out that a high M is generally optimal; for example, the selection of M = 4096 or M = 1024 is preferred, since even for low SNR the optimized NUC will "(almost) look like" a constellation with an effectively smaller M, as several points will overlap. However, modulation and demodulation complexity increase with increasing M, so a trade-off must be considered.

[0041] As mentioned above, known communication systems often use, among other components, a so-called BICM device, which can also be used as an encoding and modulation device according to the present disclosure. The maximum possible capacity via a BICM device is given by the BICM capacity C. B described: where I denotes the i-th bit label of the constellation point and m is the total number of bits / QAM symbol points. Together, the QAM constellation comprises M = 2 m -constellation points, where each is assigned a specific bit label (00...00, 00...01, ..., 11...11). In (1) E[.] denotes an expectation operator, p(r k ) is the probability density function (pdf) of the received symbols, s kis the transmit symbol according to a specific bit label, k is the discrete time (or the subcarrier index in the case of OFDM modulation), x1 is a specific symbol from the set of all constellation symbols, where this set is represented by (= symbol alphabet, with cardinality M = 2 m ) is referred to.

[0042] P(r k |s k = x1) is the likelihood function (transition probability – defined by the channel characteristics) that r k is received in view of the fact that s k = x1 was sent. The subset x i b includes all symbols from x, where the i-th bit label is b (either b = 0 or b = 1).

[0043] As can be seen in (1), C B a 2-dimensional integral. If only constellations that can be divided into two 1-dimensional PAM constellations are considered, it can easily be seen that C B (2-dimensional) = 2 x C B(1-dim.) (2)

[0044] All channels examined here include AWGN (either alone or after the fading channel). This can be described by the signal-to-noise ratio (SNR), typically in dB: SNR = 10·log 10 (E s / σ 2 ) (3) where E s the average symbol power of the QAM constellation (typically normalized to 1) is and σ 2 the variance (= power) of the additive white Gaussian noise (which is assumed to be zero-mean).

[0045] In (2) the 1-dimensional approach is used for C B(1-dimensional) an N-PAM constellation exhibits only half the symbol power when only the projection onto the in-phase or quadrature phase is considered. However, when power normalization to 1 is again applied, the noise variance increases by a factor of 2. Therefore, to be more precise, the objective function for the optimization process considered according to the present disclosure is given by C B (2-dimensional SNR x) = 2 x C B (1-dim. at SNR x / 2), (4) where the 1-dimensional PAM has a normalized power of 1, i.e., exactly half the SNR (here in absolute values, i.e., not in dB) as explained above. The 1-dimensional BICM capacitance is also calculated according to (1), where the 2-dimensional integral is a 1-dimensional integral with The set of real numbers is...

[0046] This equation (4) is optimized, taking into account all degrees of freedom, namely the constellation points of the underlying 1-dimensional constellation that are subject to the power constraint, i.e.

[0047] For example, a regular 4-QAM consists of constellation points (e jπ / 4 , e j7π / 4 , e 3π / 4 e j5π / 4 ), as in Fig. 4 is recognizable. The average symbol power is 1 (all symbols are arranged on a unit circle here). The symbol vector above (e jπ / 4 , e j7π / 4 , e 3π / 4 e j5π / 4 ), must be understood to mean that the first entry (e jπ / 4 ) belongs to the bit vector 00, the second entry (ej 7π / 4) to 01 and so on, i.e., that the entries belong to bit vectors with increasing values, where the first bit position is the most significant bit (MSB) and the last bit position is the least significant bit (LSB). This 4-QAM is a specific case of an N 2 -QAM, with N = 2. It should be noted that this definition (that it is an N 2 QAM (which deals with) not only requires that N 2 a square number (N 2 = 2 2) is, but also that the constellation is symmetrical and can be described by two independent N-PAM constellations, here a 2-PAM: The in-phase component (real part of the complex symbols) is a 2-PAM with symbol vector (1 / sqrt(2), -1sqrt(2)) and describes the first bit of the 4-QAM, while the quadrature-phase component (imaginary part of the complex symbols) is the same 2-PAM, but this time describes the second bit of the 4-QAM. It should also be noted that the decomposition of the N 2 -QAM in two N-PAMs is only possible if the bit mapping is done according to the binary reflected gray mapping that is typically used (for example in DVB systems).

[0048] The above example can be applied to N 2Higher-order QAMs are extended with M > 2. Then the underlying N-PAM describes the 1st, 3rd, 5th, and so on bit label for one component, while it describes the 2nd, 4th, 6th, and so on label for the other component.

[0049] Constellation formation is generally known and has a long history. Only in recent years have constellations been investigated that affect the BICM capacity C. B maximize. In [6] the authors propose a heuristic approach to maximize C Bto maximize by forcing the underlying PAM to approximate a Gaussian-like shape (as is well known from Shannon's capacitance theorem, the optimal constellation over the AWGN channel is supposed to have a Gaussian distribution; it should be noted that this means there are an infinite number of continuously distributed input signals that have a Gaussian distribution, i.e., lower-power symbols are supposed to occur more frequently than higher-power symbols). There is no proof that this C B maximized, in fact, such NUCs designed according to this method maximize C B No. The resulting NUCs are generally not N 2NUCs, i.e., a 2-dimensional NUC was optimized, not the underlying PAM. However, in N. Muhammad, "Coding and modulation for spectral efficient transmission", Ph.D. Dissertation, University of Stuttgart, Institute for Telecommunications, Pfaffenwaldring 47, 70569 Stuttgart, Germany, June 2006, the first time constellations were directly optimized with respect to the objective function C. B This procedure differs from the current procedure in two ways: • M-NUCs were proposed for M = 8, 16 and 32. No higher-order NUCs were investigated because the optimization becomes very time-consuming and the optimization algorithms become numerically unstable. • The optimization algorithm was a handwritten gradient-search algorithm in which both the BICM capacity and its gradient consisted of improper integrals. No special care was taken regarding either the numerical solution of the improper integral or the problematic integrands. This consideration of these two problems is fundamental for obtaining results for higher-order constellations, such as 1k (i.e., 1024) NUC.

[0050] As described above, two problems arise when solving the optimization: a) Improper integral: selection of the integration limit; and b) Integrand.

[0051] With reference to problem a) (improper integral: selection of integration limits), as can be seen in equation (1), the BICM capacity entails an integral from -infinity to +infinity (= improper integral). Any numerical solution of this integral must consider finite integration limits, such as from -b to +b, with sufficiently large b. Matlab provides several functions for numerical integration, even for improper integrals, such as the function "quad", which internally optimizes the appropriate integration limits b. However, it has been observed that even these functions produce numerical instabilities and do not result in the correct integral.

[0052] It can be observed that the integrand in (1) approaches 0 when the variable r k sufficiently large (b → infinity). A naive approach would therefore be to gradually increase the variable r. kto increase until the integrand falls below a certain threshold (approximately 10 –300 or even if it becomes exactly 0), and to select this value for the integration limit b. However, it has been further observed that the integrand can take on very small values, even before it approaches 0, for large variables, as in the two in Fig. 5A and Fig. As can be seen in the examples shown in 5B: The Fig. The representation shown in 5B is the integrand of the 1-dimensional BICM capacitance function when a regular 32-PAM is used, at 10 dB SNR, while the one shown in Fig. 5A shows representation 30 dB taken into account.

[0053] It should be noted that for 30 dB, many very small integrand values ​​occur in the interval [-2,2], and any optimized integration limit in this interval would be misleading. Therefore, it is proposed to find the optimal (= numerically correct) integration limit b as follows: i) Start with a large positive value S, iteratively reduce the value by decrements D, calculate the integrand with this value as variable r. k , until the first non-zero value of the integrand is calculated. If no non-zero integrand can be found, before r k = 0, start again with a larger initial value S (about 10 times larger than before) and reduce D (by about a factor of 10) to have a larger search interval and finer granularity. ii) Since this search is time-consuming, it is proposed to adjust the initial value S and the decrement D according to the SNR. If σ 2 If the noise variance of the 1-dimensional mapping (see equation (3)) is, then S = 4000·σ was chosen as a good compromise. 2 and d = 50·σ 2 chosen.

[0054] Regarding problem b) (integrand), it has also been observed that the integrand of the BICM capacitance integral can cause numerical instabilities for large SNR values. As can be seen in equation (1), the integrand consists of sums containing terms such as x log(x), x log(1 / x), or x 1 / log(x).

[0055] The value of x is, for example, the transition probability p(r). k |s_k = x1), or a PDF, or parts thereof. The values ​​of x become increasingly small (even approaching 0) when the SNR is very large, since PDFs typically follow Gaussian distributions. Therefore, the following limits might occur: lim {x→0} x·log(x), lim {x→0} x·log(1 / x), or lim {x→0} x·1 / log(x).

[0056] It should be noted that theoretically every limit approaches 0 (see L'Hôpital's rule), but in a numerical calculation, values ​​such as + or -infinity or NaN ("not a number") will occur. Therefore, the following is proposed: During the calculation of each element (i.e., each summand in the integrand of (1)), the value must be checked to see if it is finite (otherwise infinity or NaN), and it is replaced by 0 if it is not finite. Only in this way can reliable integration results be obtained.

[0057] Based on the above considerations, N2-NUCs have been optimized as an embodiment with N 2 The values ​​are 16, 64, 256, 1024 (1k), 4k, 16k, 64k, 256k, and 1024k. This means that the objective function C B The underlying 1-dimensional PAM is used and the degrees of freedom (the real-valued constellation points of the PAM) are optimized. It should be noted that the PAM only N = sqrt(N2 ) degrees of freedom (i.e., a 64-NUC is based on an 8-PAM). Due to symmetry, the negative constellation values ​​are the same as their positive counterparts, so only N / 2 degrees of freedom remain. Finally, another degree of freedom is lost due to power normalization (5). The 54-NUC can therefore be optimized by considering only 3 degrees of freedom (“dof”, i.e., optimization variables).

[0058] The presented optimization is preferably based on Matlab's fmincon function for forced nonlinear optimization: The objective function is the BICM capacity, and the constraints are as follows: – all dof (degrees of freedom) > 0; – all DOF must meet the performance standardization if the N-PAM is created based on them; – the depth of field (dof) must appear in ascending order.

[0059] The function `fmincon` requires an initial set of `dof` values, taken from a regular (i.e., uniform) constellation, but subjected to a random mutation. It should be noted that the resulting values ​​should still be in ascending order; however, Gray bit labeling is no longer satisfied. The NUCs are described by their degrees of freedom; that is, a 64-NUC optimized for the AWGN channel at SNR = 11.5 dB achieves the following values ​​(optimized degrees of freedom): 2.2794 4.6229 7.5291.

[0060] This means that the positive constellation values ​​are 1 2.2794 4.6229 7.5291 (The 1 was redundant due to the performance normalization applied at the end.) The underlying 1-dimensional 8-PAM NUC is therefore described by the symbol vector. (1.6405 1.0073 0.2179 0.4967 –1.6405 –1.0073 –0.2179 –0.4967), where the values ​​are already normalized to average unit power.

[0061] As described above, the first entry (1.6405) corresponds to bit label 000, the next entry (1.0073) to bit label 001, and so on. The 2-dimensional 64-NUC is then obtained through symmetry, with both the in-phase and quadrature-phase components of the NUC based on the 8-PAM NUC.

[0062] Fig. 6 shows both 8-PAM NUC ( Fig. 6A) as well as 64-QAM NUC ( Fig. 6B). The bit labels are specified as integer numbers (000 → 0, 001 → 1, 010 → 2 and so on).

[0063] The generation of the 2-dimensional NUC based on the optimized degrees of freedom is described in detail below.

[0064] Since the performance of the NUCs depends on the SNR value for which they are optimized, careful selection based on the FEC code rate is preferably carried out to achieve optimal performance. If the channel characteristics are known, the required SNR value for FEC convergence can be determined by simulation. Then, the NUC optimized for this SNR value is selected for best performance. If the SNR at the receiver is lower than this SNR decoding threshold, the configuration is not optimal. However, this is not a disadvantage, as the BICM capacity is too low for successful decoding anyway. On the other hand, if the SNR at the receiver is clearly higher than the decoding threshold, a sufficient amount of BICM capacity is available for successful decoding, even if the NUC is suboptimal for this SNR range. Therefore, the NUC must be selected for the SNR value in the waterfall range (i.e.,The decoding threshold for (quasi-)error-free decoding of the FEC is optimized. Since the SNR value of the waterfall area depends on the code rate of the FEC, a different NUC is selected for each code rate.

[0065] The SNR value for (quasi-)error-free decoding also depends on the receiver's channel characteristics. For example, the required SNR for error-free decoding of the DVB-T2 LDPC code in the AWGN channel is 0.8 dB, while 2.5 dB is required in the Rayleigh P1 multipath channel. Therefore, the selected NUC for each code rate is not optimal in all channel environments, and a compromise is necessary in a broadcast environment that suits all (or most) users in the network. In a point-to-point network with a return channel, the optimal NUC can be selected based on the measured channel characteristics at the receiver.

[0066] Currently, there are no optimized constellations for fading channels. If the transmitter lacks channel state information (CSI) but the receiver has perfect CSI (due, for example, to pilot-based channel estimation), then the average BICM is the objective function that must be optimized for NUCs designed for fading channels. If the magnitude of the fading channel for a QAM symbol is denoted as h (for example, for a specific instant in time and / or a specific subcarrier in the case of OFDM), then the instantaneous BICM capacity C B (h) is called and is given according to equation (1). It should be noted that the pdfs and transition probabilities in (1) are now different from the pure AWGN channel. For example, in the AWGN case, the probability function p(r) k |s k = x1) by a Gaussian distribution with mean-free variance σ 2Given. Now, for fading with the value h, the distribution is still Gaussian with no mean, but with instantaneous variance σ. 2 / h 2 .

[0067] A good model for the fading statistics is given by a Rayleigh distribution of fading magnitude h. Therefore, the PDF of h is: p(h) = h / σ h 2 ·exp(–h 2 / (2·σ h 2 )), (6) where σ h 2 The variance of the Rayleigh distribution. For a passive channel, i.e., a channel that on average neither attenuates nor amplifies the signal, σ h 2 = ½. This means that the average SNR across a fading channel is the same as that of a non-fading channel.

[0068] The average BICM capacity across many channel implementations is now given by i.e., the instantaneous BICM capacity as a function of h must be multiplied by the pdf of h (see (6)) and integrated over all possible fading magnitudes (0 ... infinity).

[0069] Once again, an improper integral must be solved. This time, the integrand of (7) converges to 0 due to the pdf of h. It was found that a sufficiently large upper bound for the integral in (7) is given by 38, regardless of the instantaneous capacity C. B (h). This allows for a faster optimization of (7). Results are shown below for N 2 -NUCs, N 2 = 16, 64, 256, 1024 (1k), 4096 (4k) and 16384 (16k) are shown.

[0070] The same principle regarding NUC selection described for static channels also applies to receivers experiencing fading channels, such as portable or mobile receivers. However, because the SNR varies in the receiver due to the channel's fading effect, the NUC cannot always operate at its optimal SNR. Generally, NUCs optimized for fading channels perform better than those optimized for non-fading channels when used at SNR values ​​for which they were not initially optimized; that is, they perform better over wider SNR ranges. Furthermore, NUCs optimized for Rayleigh fading channels have been found to perform well for most fading channels, such as those with a Rice distribution, those with more than one echo component (e.g., TU6 channels), or those with time- and frequency-selective fading with correlation.This is because the optimization takes into account the average of multiple channel instances / implementations.

[0071] The following provides some further explanation regarding the uneven QAM constellations. Each input cell word (y 0,q... y m-1,q ) (i.e., provided to the modulator) is to be modulated using a non-uniform QAM constellation to obtain a constellation point z. q before normalization, where m corresponds to the number of bits per QAM symbol m = log2(M). It should be noted that the parameter q, used here for the discrete time or subcarrier index, corresponds to the parameter k as used above. The exact values ​​of the real and imaginary components Re(z) q ) and Im(z q ) for each combination of the relevant input bits y 0...m-1,qThe following tables provide the values ​​for the different constellation sizes, depending on the NUC position vector u. 1...v , which defines the constellation point position of the non-uniform constellation. The length of the MNUC position vector u is defined by

[0072] In one example, the corresponding constellation point is z. q for a 64-QAM NUC, defined by the NUC position vector (u 1...3 ) = (2, 5, 6) and the input cell word (y 0,q... y m-1,q ) = (100111) is defined, Re(z q ) = –u2 = –5 and Im (z q ) = u1 = 2. The complete constellation for this NUC position vector is in Fig. Figure 7 shows exemplary input cell words, which are marked at the corresponding constellation points.

[0073] The resulting constellation mapping (also called labeling) for the non-uniform constellations follows a binary reflected Gray mapping (labeling), meaning that neighboring constellation points differ by only one bit. The performance of the constellation points z q is normalized, so that the expected value of the normalized constellation point f q is equal to 1, i.e. E(|f q | 2 ) = 1. For example, the normalized constellation value f is obtained. q a uniform 16-QAM constellation through Fig. Figure 8 shows a diagram illustrating the performance of the uneven N 2 -QAM constellations illustrated.

[0074] The following tables define the constellation position vectors (before power normalization) as well as the bit labeling of the data cell words to the constellation points. Constellation mapping for the real part of 16-QAM y 0,q 1 1 0 0 y 2,q 0 1 1 0 Re(z q ) –3 –1 1 3 Evenly –u1 –1 1 u1 NUC Constellation mapping for the imaginary part of 16-QAM y 1,q 1 1 0 0 y 3,q 0 1 1 0 Im(z q ) –3 –1 1 3 Evenly –u1 –1 1 u1 NUC Constellation mapping for the real part of 64-QAM Constellation mapping for the imaginary part of 64-QAM Constellation mapping for the real part of 256-QAM Constellation mapping for the imaginary part of 256-QAM Constellation mapping for the real part of 1024-QAM Constellation mapping for the imaginary part of 1024-QAM Constellation mapping for the real part of 4096-QAM Constellation mapping for the imaginary part of 4096-QAM

[0075] The following section provides the definition of the NUC position vectors obtained using the procedure described above. The signal-to-noise ratio (SNR) is always given in dB and corresponds to the average SNR in the case of fading channels. a1) 16-QAM or 4-PAM for a non-fading channel (1st option) a2) 16-QAM or 4-PAM for a fading channel (1st option) a3) 16-QAM / 4-PAM for a non-fading channel (2nd option) a4) 16-QAM / 4-PAM for a fading channel (2nd option) b1) 64-QAM or 8-PAM for a non-fading channel (1st option) b2) 64-QAM or 8-PAM for a fading channel (1st option) b3) 64-QAM / 8-PAM for a non-fading channel (2nd option) b4) 64-QAM / 8-PAM for a fading channel (2nd option) c1) 256-QAM or 16-PAM for a non-fading channel (1st option) c2) 256-QAM or 16-PAM for a fading channel (1st option) c3) 256-QAM / 16-PAM for a non-fading channel (2nd option) c4) 256-QAM / 16-PAM for a fading channel (2nd option) d1) 1024-QAM or 32-PAM for a non-fading channel (1st option) d2) 1024-QAM or 32-PAM for a fading channel (1st option) d3) 1024-QAM / 32-PAM for a non-fading channel (2nd option) d4) 1024-QAM / 32-PAM for a fading channel (2nd option) e1) 4096-QAM or 64-PAM for a non-fading channel (1st option) e2) 4096-QAM or 64-PAM for a fading channel (1st option) e3) 4096-QAM / 64-PAM for a non-fading channel (2nd option) e4) 4096-QAM / 64-PAM for a fading channel (2nd option) f1) 16384-QAM / 128-PAM for a non-fading channel f2) 16384-QAM / 128-PAM for a fading channel g) 65536-QAM / 256-PAM for a non-fading channel h) 262144-QAM / 512-PAM for a non-fading channel i) 1048576-QAM / 1024-PAM for a non-fading channel

[0076] Obviously, numerous modifications and variations of the present disclosure are possible in light of the above teaching. It should therefore be understood that, within the scope of protection of the attached claims, the disclosure may be implemented in a manner other than specifically described herein (for example, if the NUC position vectors are rounded to a smaller number of digits).

[0077] In the claims, the word "comprising" or "comprising" does not exclude further elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit can perform the functions of several elements mentioned in the claims. The mere fact that certain measures are mentioned in separate dependent claims does not mean that a combination of these measures cannot also be advantageously used.

[0078] Insofar as embodiments of the disclosure have been described as implementations, at least partially, by a software-controlled data processing device, it should be noted that a non-perishable, machine-readable medium carrying such software, such as an optical disk, a magnetic disk, a semiconductor memory, or the like, is also considered to be an embodiment of the present disclosure. Furthermore, such software can also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0079] A circuit that can be used to implement one or more elements of the claimed device is a structural assembly of electronic components containing conventional circuit elements, integrated circuits with application-specific integrated circuits, standard integrated circuits, application-specific standard products, and field-programmable gate arrays. Furthermore, a circuit includes central processing units, graphics processing units, and microprocessors that are programmed or configured according to software code. A circuit does not contain pure software, although it includes the hardware described above for executing software.

[0080] Any reference numerals in the claims should not be interpreted as limiting protection.

Claims

[1] Coding and modulation device comprising – an encoder ( 11 ), which encodes the input data into cell words, and – a modulator ( 12 ), which modulates the cell words into constellation values ​​of a non-uniform constellation, where the modulator ( 12 ) is designed to select a non-uniform constellation from a group of constellations based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, which has one or more of the constellations defined by the constellation position vector u. 1...v are defined, where v = sqrt(M) / 2 – 1: a1) 16-QAM or 4-PAM for a non-fading channel (1st option) a2) 16-QAM or 4-PAM for a fading channel (1st option) a3) 16-QAM / 4-PAM for a non-fading channel (2nd option) a4) 16-QAM / 4-PAM for a fading channel (2nd option) b1) 64-QAM or 8-PAM for a non-fading channel (1st option) b2) 64-QAM or 8-PAM for a fading channel (1st option) b3) 64-QAM / 8-PAM for a non-fading channel (2nd option) b4) 64-QAM / 8-PAM for a fading channel (2nd option) c1) 256-QAM or 16-PAM for a non-fading channel (1st option) c2) 256-QAM or 16-PAM for a fading channel (1st option) c3) 256-QAM / 16-PAM for a non-fading channel (2nd option) c4) 256-QAM / 16-PAM for a fading channel (2nd option) d1) 1024-QAM or 32-PAM for a non-fading channel (1st option) d2) 1024-QAM or 32-PAM for a fading channel (1st option) d3) 1024-QAM / 32-PAM for a non-fading channel (2nd option) d4) 1024-QAM / 32-PAM for a fading channel (2nd option) e1) 4096-QAM or 64-PAM for a non-fading channel (1st option) e2) 4096-QAM or 64-PAM for a fading channel (1st option) e3) 4096-QAM / 64-PAM for a non-fading channel (2nd option) e4) 4096-QAM / 64-PAM for a fading channel (2nd option) f1) 16384-QAM / 128-PAM for a non-fading channel f2) 16384-QAM / 128-PAM for a fading channel g) 65536-QAM / 256-PAM for a non-fading channel h) 262144-QAM / 512-PAM for a non-fading channel i) 1048576-QAM / 1024-PAM for a non-fading channel [2] Coding and modulation device according to claim 1, wherein the non-fading channel is a channel with additive white Gaussian noise and the fading channel is a Rayleigh fading channel. [3] Coding and modulation device according to claim 1, wherein the encoder is a forward error correction encoder. [4] Coding and modulation device according to claim 1, wherein the modulator is configured to select a non-uniform constellation based on the total number M of constellation punctures of the constellation, the required signal-to-noise ratio SNR for error-free decoding in dB and the channel characteristics. [5] Coding and modulation device according to claim 1, wherein the modulator is configured to adaptively select a non-uniform constellation based on the total number M of constellation punctures, the required signal-to-noise ratio SNR in dB and the channel characteristics, wherein the receiver characteristics such as signal-to-noise ratio SNR in dB and the channel characteristics are received by a receiving device to which data are to be sent. [6] Coding and modulation techniques – Encoding input data into cell words, and – Modulating the cell words into constellation values ​​of a non-uniform constellation, where, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB, and the channel characteristics, a non-uniform constellation is selected from a group of constellations that exhibits one or more of the constellations defined by the constellation position vector u. 1...v are defined, where v = sqrt(M) / 2 – 1: a1) 16-QAM or 4-PAM for a non-fading channel (1st option) a2) 16-QAM or 4-PAM for a fading channel (1st option) a3) 16-QAM / 4-PAM for a non-fading channel (2nd option) a4) 16-QAM / 4-PAM for a fading channel (2nd option) b1) 64-QAM or 8-PAM for a non-fading channel (1st option) b2) 64-QAM or 8-PAM for a fading channel (1st option) b3) 64-QAM / 8-PAM for a non-fading channel (2nd option) b4) 64-QAM / 8-PAM for a fading channel (2nd option) c1) 256-QAM or 16-PAM for a non-fading channel (1st option) c2) 256-QAM or 16-PAM for a fading channel (1st option) c3) 256-QAM / 16-PAM for a non-fading channel (2nd option) c4) 256-QAM / 16-PAM for a fading channel (2nd option) d1) 1024-QAM or 32-PAM for a non-fading channel (1st option) d2) 1024-QAM or 32-PAM for a fading channel (1st option) d3) 1024-QAM / 32-PAM for a non-fading channel (2nd option) d4) 1024-QAM / 32-PAM for a fading channel (2nd option) e1) 4096-QAM or 64-PAM for a non-fading channel (1st option) e2) 4096-QAM or 64-PAM for a fading channel (1st option) e3) 4096-QAM / 64-PAM for a non-fading channel (2nd option) e4) 4096-QAM / 64-PAM for a fading channel (2nd option) f1) 16384-QAM / 128-PAM for a non-fading channel f2) 16384-QAM / 128-PAM for a fading channel g) 65536-QAM / 256-PAM for a non-fading channel h) 262144-QAM / 512-PAM for a non-fading channel i) 1048576-QAM / 1024-PAM for a non-fading channel [7] transmitting device comprising – a coding and modulation device according to claim 1, which encodes and modulates input data into constellation values, – a converter that converts the constellation values ​​into one or more transmit streams, and – a transmitter that sends one or more transmission streams. [8] Transmission procedures comprehensive – a coding and modulation method according to claim 6, which encodes and modulates input data into constellation values, – Converting the constellation values ​​into one or more transmit streams, and – Sends one or more transmission streams. [9] Computer program comprising programming means for causing a computer to perform the steps of the coding and modulation method according to claim 6 when the computer program is executed on a computer. [10] Non-perishable computer-readable recording medium on which a computer program product is stored which, when executed by a processor, causes the encoding and modulation method according to claim 6 to be executed. [11] Communication system comprising one or more transmitting devices according to claim 7 and one or more receiving devices.