WO2021083488A1

WO2021083488A1 - A distribution matcher and distribution matching method

Info

Publication number: WO2021083488A1
Application number: PCT/EP2019/079426
Authority: WO
Inventors: Ronald BOEHNKE; Onurcan ISCAN; Wen Xu
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2019-10-28
Filing date: 2019-10-28
Publication date: 2021-05-06
Also published as: CN114616773A

Abstract

The present invention provides a distribution matcher. The distribution matcher is configured to map an input sequence onto an output sequence based on a plurality of target probability distributions, wherein each element of the output sequence has a corresponding target probability distribution, and wherein at least two elements of the output sequence have different target probability distributions. The present invention also provides a device comprising a distribution matcher. The device may, for example, map a plurality of input sequences onto a plurality of output sequences, wherein at least one input sequence is mapped using the distribution matcher, and wherein the control sequence depends on at least one output sequence.

Description

A DISTRIBUTION MATCHER AND DISTRIBUTION MATCHING METHOD

TECHNICAL FIELD

The present disclosure relates generally to the field of distribution matching. In particular, the invention relates to a distribution matcher and to a distribution matching method that maps an input sequence onto an output sequence, for example, based on one or more target probability distributions. The disclosure relates also to a device including the distribution matcher, and to a method for mapping an input sequence onto an output sequence, for example, by using one or more of the distribution matchers.

BACKGROUND

A conventional distribution matcher maps a sequence of uniformly distributed input symbols b onto a sequence of output symbols x with a given target probability distribution P(x), which can be used to emulate a Discrete Memoryless Source (DMS).

An application is reliable data transmission over a noisy channel. In order to achieve the channel capacity, the channel input symbols in general need to have a non-uniform distribution. For instance, for an Additive White Gaussian Noise (AWGN) channel with an average power constraint, the optimal input distribution is Gaussian, which can be well approximated, in practice, by a discrete Maxwell-Boltzmann distribution. Using a uniform symbol distribution instead, as it is done in many practical communication systems, results in a shaping loss of up to 1.53 dB.

Conventional distribution matching is also known as signal shaping. There exist many different approaches, e.g. shell mapping, trellis shaping, Constant Composition Distribution Matching (CCDM), Multi-Composition Distribution Matching (MCDM), and Bit-level or Product Distribution Matching.

The conventional devices and methods have the following disadvantages:

Optimal distribution matchers like shell mapping have high complexity for large symbol alphabets, and are only feasible for short block lengths. • Restricting the output sequences x to a certain subset, in order to reduce the complexity as in CCDM, leads to poor performance for short block lengths.

• The complexity can be reduced for large symbol alphabets by bit-level shaping using binary distribution matchers, but the existing schemes can only approximate the target distribution P(x) by a product distribution.

SUMMARY

In view of the above-mentioned problems and disadvantages, embodiments of the invention aims to improve the conventional distribution matchers, devices and methods. An objective is to provide a distribution matcher and a corresponding method, which use a novel distribution matching scheme that can generate arbitrary symbol distributions with low complexity, and which performs close to optimal for any sequence length. In particular, the complexity should grow (only) logarithmically with the size of the output alphabet A.

The objective of the present invention is achieved by the solution provided in the enclosed independent claims. Advantageous implementations of the present invention are further defined in the dependent claims.

A first aspect of the invention provides a distribution matcher configured to map an input sequence onto an output sequence based on a plurality of target probability distributions, wherein each element of the output sequence has a corresponding target probability distribution, and wherein at least two elements of the output sequence have different target probability distributions.

The distribution matcher may be, or may be incorporated in, an electronic device (for example, a transmitter of a communication system). For example, the distribution matcher may obtain an input sequence b. The input sequence b may have k symbols. The distribution matcher may map the input sequence b with k symbols onto an output sequence x with n symbols having a target distribution P(x).

The distribution matcher may comprise a circuitry. The circuitry may comprise hardware and software. The hardware may comprise analog or digital circuitry, or both analog and digital circuitry. In some embodiments, the circuitry comprises one or more processors and a non- volatile memory connected to the one or more processors. The non-volatile memory may carry executable program code which, when executed by the one or more processors, causes the distribution matcher to perform the operations or methods described herein.

The distribution matcher of the first aspect employs a distribution matching scheme that can generate arbitrary symbol distributions with low complexity, and that performs close to optimal for any sequence length. In particular, the complexity grows only logarithmically with the size of the output alphabet A. Thus, an improved distribution matcher is provided.

In an implementation form of the first aspect, at least one target probability distribution is configurable based on a control sequence.

A control sequence is an external signal that defines the operations of the distribution matcher.

In particular, the control sequence may be, for example, a codeword selected by the distribution matcher (e.g., the codeword may be generated previously by the distribution matcher, it may be received from another distribution matcher, etc.).

Another example for a control sequence is a sequence containing channel state information for parallel channels, which require different target probability distributions.

A control sequence may also correspond to a feedback signal from an intended receiver in a communication system.

For example, target symbol distribution P(x ) may be represented by, e.g., a set of (in) conditional distributions P(c_i \c₁ ... c_{i -1} ) . Moreover, the distribution matcher may select the codeword c_i according to the target distribution P(c_i \c₁ ... c_{i -1} ) depending on the previously selected codewords c_i ... c_i -1 .

In a further implementation form of the first aspect, the distribution matcher comprises a channel decoder, in particular a polar decoder, a Low-Density Parity-Check (LDPC) decoder or a convolutional decoder.

In particular, the distribution matcher may map the input sequence onto the output sequence by using a channel decoder or using a device that includes a channel decoder. The channel decoder allows efficiently implementing the distribution matching scheme using a low complexity device.

In a further implementation form of the first aspect, the channel decoder is configured to receive a channel decoder input sequence, wherein the channel decoder input sequence is a function of the target probability distributions.

In a further implementation form of the first aspect, the channel decoder is a polar decoder, wherein at least one frozen symbol is defined by the input sequence.

The polar decoded provides a particularly efficient implementation of the distribution matching scheme.

In a further implementation form of the first aspect, the distribution matcher comprises a Constant Composition Distribution Matching (CCDM), a Multi-Composition Distribution Matching (MCDM), or a shell mapper.

Thus, the distribution matcher of the first aspect is compatible with various conventional techniques.

A second aspect of the invention provides a device for mapping a plurality of input sequences onto a plurality of output sequences, comprising a distribution matcher according to any of the implementation forms of the first aspect, wherein at least one input sequence is mapped using the distribution matcher, and wherein the control sequence depends on at least one output sequence.

By employing the distribution matcher of the first aspect, all the above described advantages and effects are achieved. The device may be an electronic device comprising a distribution matcher (for example, the device may be a transmitter device of a communication system).

The device may map (for example, it may comprise a distribution matcher such as multi-level distribution matcher) an input sequence b with k symbols onto an output sequence x with n symbols having a target distribution P(x) by performing the following operations: • Representing the target symbol distribution P(x) by m conditional distributions P(c_i \c₁

... Ci- 1).

• Splitting the input sequence b into m sub-sequences b₁ ... b_m.

• Applying to each subsequence bi a distribution matcher that selects the codeword c_i according to the target distribution P(c_i \c₁ ... c_{i -1} ) depending on the previously selected codewords c_i ... c_i -1 .

• Mapping the resulting codewords c₁ ... c_m onto the output symbol sequence x.

In some embodiments, the elements of the symbol alphabet A may be associated with different labels.

In some embodiments, the number of symbols in the sub-sequences b₁ ... b_m may be optimized based on different criteria.

In some embodiments, different distribution matching algorithms may be used to generate the codewords c₁ ... c_m.

In some embodiments, instead of a single codeword c_i, each level may provide a set of parameters that are used by the subsequent distribution matchers (e.g., a list of candidates forc_i associated with a parameter that indicates the likelihood of each candidate).

In some embodiments, the device may use different channel decoding algorithms in different bit-levels. For example, SC decoders may be used in some bit-levels, and SCL decoders with different list sizes in others. The decoders may also make use of different approximations (e.g., min-sum, clipping or quantization of LLRs, etc.).

In some embodiments, other distribution matching algorithms (e.g., shell mapping, enumerative sphere shaping, CCDM, or MCDM) may be used in at least one bit-level. For example, shell mapping may be used to shape either one bit-level or multiple bit-levels jointly. It is also possible to split the input sequences bi further and apply a different distribution matcher to each of the resulting subsequences, e.g. in order to reduce the complexity or increase the throughput. The device may comprise a circuitry. The circuitry may comprise hardware and software. The hardware may comprise analog or digital circuitry, or both analog and digital circuitry. In some embodiments, the circuitry comprises one or more processors and a non-volatile memory connected to the one or more processors. The non-volatile memory may carry executable program code which, when executed by the one or more processors, causes the device to perform the operations or methods described herein.

In an implementation form of the second aspect, the device is further configured to successively map the input sequences onto the output sequences such that each control sequence depends on the previously generated output sequences.

In a further implementation form of the second aspect, the device is further configured to map the output sequences onto a symbol sequence.

In a further implementation form of the second aspect, each element in the symbol sequence is based on elements in predefined positions of the output sequences.

In a further implementation form of the second aspect, the input sequences correspond to sub- sequences of a first input sequence.

A third aspect of the invention provides a device for multi-level distribution matching of an input message into an output symbol sequence comprising information bits, the device configured to divide the input message into a plurality of sub-messages; apply, to a first sub- message, a first distribution matching for obtaining a first codeword; successively apply, to each subsequent sub-message, a respective subsequent distribution matching for obtaining a respective subsequent codeword, wherein each subsequent distribution matching is selected based on one or more codewords obtained from previously applied distribution matching; and map the codewords into corresponding symbols.

The device of the third aspect may be based on the device of the second aspect. For example, the device of the third aspect may be the device of the second aspect configured for multi-level distribution matching of the input message into the output symbol sequence. In an implementation form of the third aspect, the device is further configured to obtain a target distribution for the symbol sequence, wherein the target distribution is composed of a plurality of bit probabilities, and wherein each distribution matching applied to a respective sub-message obtains the respective codeword according to one of the bit probabilities.

In a further implementation form of the third aspect, the bit probability for each subsequent distribution matching depends on one or more codewords obtained from previously applied distribution matching.

In a further implementation form of the third aspect, the first distribution matching applied to the first sub-message is based on a uniform distribution, and wherein each subsequent distribution matching is based on a non-uniform distribution.

In a further implementation form of the third aspect, the target distribution is based on a Log- Likelihood Ratio (LLR) composed of a plurality of conditional LLRs, and wherein the bit probability of each respective subsequent distribution matching is based on one of the conditional LLRs.

In a further implementation form of the third aspect, each conditional LLR of a respective subsequent distribution matching depends on one or more codewords obtained from previously applied distribution matching.

In a further implementation form of the third aspect, at least one distribution matching is based on a channel decoder.

In a further implementation form of the third aspect, the channel decoder is based on a polar decoder, in particular a Successive Cancellation (SC) decoder, or a Successive Cancellation List (SCL) decoder.

In a further implementation form of the third aspect, the device is further configured to allocate, to each sub-message from the plurality of sub-messages, a sequence of shaping bits determined by the channel decoder, and wherein the obtained codewords depend on the type of channel decoder and the number of allocated shaping bits. In a further implementation form of the third aspect, at least one distribution matching is based on: shell mapping,

Enumerative Sphere Shaping,

- CCDM,

- MCDM.

In a further implementation form of the third aspect, the device is further configured to classify the plurality of sub-messages to a first group of sub-messages and a second group of sub- messages, and apply, to the first group of sub-messages, a first type of distribution matching, in particular a channel decoder, and apply, to the second group of sub-messages, a second type of distribution matching that is different from the first type of distribution matching.

In a further implementation form of the third aspect, the device is based on a transmitter device of a communication system.

A fourth aspect of the invention provides a method for a distribution matcher, the method comprises mapping an input sequence onto an output sequence based on a plurality of target probability distributions, wherein each element of the output sequence has a corresponding target probability distribution, and wherein at least two elements of the output sequence have different target probability distributions.

In an implementation form of the fourth aspect, at least one target probability distribution is configurable based on a control sequence.

In a further implementation form of the fourth aspect, the distribution matcher comprises a channel decoder, in particular a polar decoder, a Low-Density Parity-Check (LDPC) decoder or a convolutional decoder.

In a further implementation form of the fourth aspect, the method further comprises receiving a channel decoder input sequence, wherein the channel decoder input sequence is a function of the target probability distributions. In a further implementation form of the fourth aspect, the channel decoder is a polar decoder, wherein at least one frozen symbol is defined by the input sequence.

In a further implementation form of the fourth aspect, the distribution matcher comprises a Constant Composition Distribution Matching (CCDM), a Multi-Composition Distribution Matching (MCDM), or a shell mapper.

The method of the fourth aspect and its implementation forms are able to achieve the same advantages and effects as described above for the distribution matcher of the first aspect.

A fifth aspect of the invention provides a method for a device, the method comprises mapping a plurality of input sequences onto a plurality of output sequences, wherein at least one input sequence is mapped according to any one of the implementation form of the fourth aspect, and wherein the control sequence depends on at least one output sequence.

In an implementation form of the fifth aspect, the method further comprises successively mapping the input sequences onto the output sequences such that each control sequence depends on the previously generated output sequences.

In a further implementation form of the fifth aspect, the method further comprises mapping the output sequences onto a symbol sequence.

In a further implementation form of the fifth aspect, each element in the symbol sequence is based on elements in predefined positions of the output sequences.

In a further implementation form of the fifth aspect, the input sequences correspond to sub- sequences of a first input sequence.

The method of the fifth aspect and its implementation forms are able to achieve the same advantages and effects as described above for the device of the second aspect.

A sixth aspect of the invention provides a method for multi-level distribution matching of an input message into an output symbol sequence comprising information bits, the method comprises dividing the input message into a plurality of sub-messages; applying, to a first sub- message, a first distribution matching for obtaining a first codeword; successively applying, to each subsequent sub-message, a respective subsequent distribution matching for obtaining a respective subsequent codeword, wherein each subsequent distribution matching is selected based on one or more codewords obtained from previously applied distribution matching; and mapping the codewords into corresponding symbols.

In an implementation form of the sixth aspect, the method further comprises obtaining a target distribution for the symbol sequence, wherein the target distribution is composed of a plurality of bit probabilities, and wherein each distribution matching applied to a respective sub-message obtains the respective codeword according to one of the bit probabilities.

In a further implementation form of the sixth aspect, the bit probability for each subsequent distribution matching depends on one or more codewords obtained from previously applied distribution matching.

In a further implementation form of the sixth aspect, the first distribution matching applied to the first sub-message is based on a uniform distribution, and wherein each subsequent distribution matching is based on a non-uniform distribution.

In a further implementation form of the sixth aspect, the target distribution is based on a LLR composed of a plurality of conditional LLRs, and wherein the bit probability of each respective subsequent distribution matching is based on one of the conditional LLRs.

In a further implementation form of the sixth aspect, each conditional LLR of a respective subsequent distribution matching depends on one or more codewords obtained from previously applied distribution matching.

In a further implementation form of the sixth aspect, at least one distribution matching is based on a channel decoder.

In a further implementation form of the sixth aspect, the channel decoder is based on a polar decoder, in particular an SC decoder, or an SCL, decoder. In a further implementation form of the sixth aspect, the method further comprises allocating, to each sub-message from the plurality of sub-messages, a sequence of shaping bits determined by the channel decoder, and wherein the obtained codewords depend on the type of channel decoder and the number of allocated shaping bits.

In a further implementation form of the sixth aspect, at least one distribution matching is based on: shell mapping,

Enumerative Sphere Shaping,

- CCDM,

- MCDM.

In a further implementation form of the sixth aspect, the method further comprises classifying the plurality of sub-messages to a first group of sub-messages and a second group of sub- messages, and applying, to the first group of sub-messages, a first type of distribution matching, in particular a channel decoder, and applying, to the second group of sub-messages, a second type of distribution matching that is different from the first type of distribution matching.

In a further implementation form of the sixth aspect, the method is for a transmitter device of a communication system.

A seventh aspect of the invention provides a computer program which, when executed by a computer, causes the method of fourth aspect and/or fifth aspect and/or sixth aspect and/or one of their implementation forms to be performed.

In some embodiments, the computer program can be provided on a non-transitory computer- readable recording medium.

It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

BRIEF DESCRIPTION OF DRAWINGS

The above described aspects and implementation forms of the invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

FIG. 1 is a schematic view of a distribution matcher, according to an embodiment of the invention;

FIG. 2 is a schematic view of a device for mapping a plurality of input sequences onto a plurality of output sequences, according to an embodiment of the invention;

FIG. 3A-C shows exemplarily target probability distribution (FIG. 3A), exemplary conditional bit probabilities (FIG. 3B), and exemplary conditional FFRs (FIG. 3C);

FIG. 4 is a schematic view of a device for multi-level distribution matcher, according to an embodiment of the invention;

FIG. 5 is a schematic view of the distribution matcher comprising a polar decoder;

FIG. 6A-B shows distribution generated using 5G NR polar codes with n= 256 using [0, 21, 195] shaping bits per level;

FIG. 7A-B shows distribution generated using 5G NR polar codes with n= 256 using [7, 27, 145] shaping bits per level;

FIG. 8A-B shows distribution generated using 5G NR polar codes with n=256 using [0, 11, 165] shaping bits per level; FIG. 9 is a schematic view of a device comprising a CCDM and a channel decoder;

FIG. 10 is a flowchart of a method for a distribution matcher, according to an embodiment of the invention;

FIG. 11 is a flowchart of a method for a device, according to an embodiment of the invention;

FIG. 12 shows a schematic representation of a conventional Bit-level distribution matching; and

FIG. 13 shows a schematic representation of using a conventional channel decoder for distribution matching.

DETAILED DESCRIPTION OF EMBODIMENTS

Embodiments of the present invention may be implemented, for example, in distribution matching approaches that will be briefly described in the following. For ease of exposition, it is assumed that binary input sequences b comprising of k bits and output sequences x comprising of n symbols are drawn from an alphabet A with cardinality 2^m according to the target distribution P(x).

Shell Mapping or Enumerative Sphere Shaping: each element of the alphabet A is associated with a certain weight, and the 2^k possible input sequences b are then mapped onto the output sequences x with minimum sum weight. The classical weight function that minimizes the average transmit power is given by the symbol energy |x|², while divergence optimal distribution matchers can be obtained by using the self-information -log P(x) as weight function. Shell mapping and enumerative sphere shaping mainly differ in the way the sequences are indexed.

Storing all 2^k possible output sequences in a look-up-table quickly becomes infeasible. There are several implementations that offer different tradeoffs between storage and computational complexities. For an efficient approximate trellis-based algorithm, the required memory is quadratic in the sequence length n, and the number of bit operations per symbol is proportional to the alphabet size 2^m.

Trellis Shaping: this scheme is closely related to convolutional channel codes. Each sequence x is represented by a path in a trellis structure. The Viterbi algorithm can be used to find the sequence with minimum sum weight corresponding to the input bits b.

Constant Composition Distribution Matching (CCDM): here the target distribution P(x) is approximated by sequences with the same composition, where each symbol from the alphabet A appears exactly n_x ≈ n.P(x ) times in x. For binary symbol alphabets, this corresponds to an m-out-of-n code. CCDM can be efficiently implemented using arithmetic coding and approaches the target distribution for large block lengths n.

Multi-Composition Distribution Matching (MCDM): this is an extension of CCDM that can also be implemented using arithmetic coding. As the name suggests, it allows for sequences with different compositions to obtain a better approximation of the target distribution.

Bit-level or Product Distribution Matching: each element x from the alphabet A can be associated with a binary label c1...c_m. An example for in = 3 where the label c1...c_m corresponds to the binary representation of x is provided in Table 1.

Table 1: Natural labeling for m = 3

In order to reduce the complexity of distribution matching for non-binary symbol alphabets, the m bit-levels are shaped independently using binary distribution matchers and subsequently mapped onto the output sequence x as shown in diagram 1200 of FIG. 12. The diagram 1200 of FIG. 12 shows a schematic representation of a conventional Bit-level distribution matching in which the input sequences b 1210 are then mapped onto the output sequences x 1220. Moreover, since the bits-levels are independently distributed, this means that the target distribution P(x) is approximated by the product of the bit-level distributions P(c_i) for i = 1...m. Binary Distribution Matching Based on Channel Decoding: similar to a channel encoder, a distribution matcher adds redundancy to the uniformly distributed input sequence b, but the mapping between b and the output c is in general not linear. However, a channel decoder can be used for this task as illustrated in diagram 1300 of FIG. 13. The diagram 1300 shows a schematic representation of using a conventional channel decoder for distribution matching. The target distribution is represented by a sequence of log-likelihood ratios (FFRs) L(c) = [L(c₁) ... L(c_n )] 1330, which can be determined according to Eq. (1):

Eq. (1)

The codeword c 1320 depends on the input b 1310 and additional shaping bits s 1340. For a linear code with a generator matrix G, this can be expressed as c = [b s] · G. For a given input sequence b 1310, the channel decoder tries to choose the shaping bits s 1340 such that the resulting codeword c 1320 is most likely for the LLRs L(c) 1330 representing the target distribution.

FIG. 1 is a schematic view of a distribution matcher 100, according to an embodiment of the invention.

The distribution matcher 100 configured to map an input sequence 110 onto an output sequence 120 based on a plurality of target probability distributions P(121), P(122), and P(123), wherein each element 121, 122, 123 of the output sequence 120 has a corresponding target probability distribution P(121), P(122), P(123), and wherein at least two elements 121, 122, 123 of the output sequence 120 have different target probability distributions P(121), P(122), P(123).

For example, the distribution matcher 100, may be, or may be incorporated in, a transmitter device of a communication system. Moreover, the element 121 of the output sequence 120 has a corresponding target probability distribution P(121), the element 122 of the output sequence 120 has a corresponding target probability distribution P(122), and the element 123 of the output sequence 120 has a corresponding target probability distribution P(123).

Similar to the bit-level distribution matching, the distribution matcher 100 may split up the input sequence b 110 into m subsequences b₁ ... b_m (e.g., indicated with reference number 121, 122, 123, etc.). Moreover, the bit-levels may not be shaped independently, but successively depending on the output of the distribution matcher in the previous bit-levels.

The distribution matcher 100 may comprise a circuitry (not shown in FIG. 1). The circuitry may comprise hardware and software. The hardware may comprise analog or digital circuitry, or both analog and digital circuitry. In some embodiments, the circuitry comprises one or more processors and a non-volatile memory connected to the one or more processors. The non- volatile memory may carry executable program code which, when executed by the one or more processors, causes the distribution matcher 100 to perform the operations or methods described herein.

FIG. 2 is a schematic view of a device 200 for mapping a plurality of input sequences 110, 210 onto a plurality of output sequences 120, 220, according to an embodiment of the invention.

The device 200 comprises a distribution matcher 100. The device 200 may map the plurality of input sequences 110, 210 onto the plurality of output sequences 120, 220, wherein at least one input sequence 110 is mapped using the distribution matcher 100, and wherein the control sequence 201 depends on at least one output sequence 220.

For instance, the device 200 may (initially) create the output sequence 220 by the distribution matcher 230. The distribution matcher 230 may be some kind of mapper (the distribution matcher 230 may be, for example, identical or similar to the distribution matcher 100, it may be another type of distribution matcher, etc.). Afterwards, the output sequence 220 may be used as the control sequence 201 for the distribution matcher 100. In other words, the control sequence 201 is an input of the distribution matcher 100 and depends on the output sequence 220.

For example, the device 200 may comprise the distribution matcher 100. Moreover, similar to the bit-level distribution matching, the input sequence b 110 is split up into m subsequences b₁ ... b_m (may be indicated with reference number 121, 122, 123, etc.). The bit-levels may not be shaped independently, but successively depending on the output of the distribution matcher in the previous bit- levels. Without loss of generality, it may be assumed that the sequences d are generated in the order i = 1, 2,..., m.

For any binary labelling associated with the elements x of the alphabet A, the target symbol distribution may be factorized into conditional bit probabilities according to Eq. (2):

The conditional bit probabilities are given by:

and the joint probabilities may be calculated through marginalization of the target distribution according to Eq. (4)

P

(C1 . Ci) x:c₁...c_i P(x), where the sum goes over all symbols x in A with fixed binary labels c₁...c_i. The device 200 may comprise a circuitry (not shown in FIG. 2). The circuitry may comprise hardware and software. The hardware may comprise analog or digital circuitry, or both analog and digital circuitry. In some embodiments, the circuitry comprises one or more processors and a non-volatile memory connected to the one or more processors. The non-volatile memory may carry executable program code which, when executed by the one or more processors, causes the device to perform the operations or methods described herein.

An example for the natural labeling from Table 1 is given in FIG. 3A-C.

Reference is now made to FIG. 3 A, FIG. 3B and FIG. 3C, in which FIG. 3A shows the target symbol distribution (i.e., exemplary target probability distribution), FIG. 3B shows exemplary conditional bit probabilities, and FIG. 3C shows exemplary conditional LLRs. Note that in this example, the bits c₁ in the first bit-level are uniformly distributed with P(c₁ =0) = P(c₁ =1) = 0.5, so there may be no need for a distribution matcher for these bits and can simply set c₁ = b₁. In contrast to this, the conditional distribution of c₂ depends on c₁ and the conditional distribution of C₃ depends on both c₁ and C₂.

The sequences c_i are now generated in the order i = 1, 2,..., m using binary distribution matchers. For example, for the distribution matcher 100 based on a channel decoder (for example, a channel decoder such the one shown in diagram 1300 of FIG. 13), it may be needed to (simply) replace the input LLRs L(c_i) and representing the target distribution by the conditional LLRs according to Eq. (5):

which are shown in FIG. 3C for the target symbol distribution in FIG. 3A. Note that the bits in the codeword c_i do in general have different distributions depending on the corresponding bits in the codewords c₁ ... C_i-1.

For example, the target probability distribution and/or the conditional bit probabilities and/or the exemplary conditional LLRs may be used, e.g., by the distribution matcher 100 and/or the device 200 for mapping the input sequence 110 onto the output sequence 120.

Reference is now made to FIG. 4, which is a schematic view of a device 200 for multi-level distribution matcher, according to an embodiment of the invention.

The device 200 of FIG. 4 is for multi-level distribution matcher. The device 200 comprises a distribution matcher 1 (for example, it is based on distribution matcher 100), a distribution matcher 2 indicated with reference 410 and a distribution matcher m indicated with reference 420.

Moreover, the control sequence 201 depends on the output sequence 120 of the distribution matcher 100. The device 200 (e.g., the proposed multi-level distribution matcher illustrated FIG. 4, and/or the distribution matcher 100), may offer the following advantages:

• It can generate arbitrary symbol distributions P(x) using simple binary distribution matchers.

• In particular, distribution matchers can be based on standard channel codes employed in current or future communication standards.

• In contrast to existing bit-level distribution matchers, the binary labelling of symbols can be arbitrary and the target distribution P(x) is not approximated by a product of independent bit-level distributions P(c_i).

• The complexity grows linearly with the number of shaped bit-levels and thus at most logarithmically with the size of the symbol alphabet A.

In addition, the following conditions may be satisfied (e.g., by the distribution matcher 100 and/or the device 200):

• As noted for the above example (in FIG.3A-C), some bit-levels may not need to be shaped if the target conditional bit probabilities correspond (at least approximately) to a uniform distribution, which further reduces the complexity.

• If bit-levels are (approximately) independently distributed, the corresponding codewords C_i can be generated in parallel by independent distribution matchers, or jointly by a single distribution matcher that allows for output symbols having different distributions.

• Different distribution matching algorithms can be combined to generate the output sequences c_i ... c_m. For example, we may use shell mapping or CCDM in some bit- levels, and distribution matchers based on channel decoding in others.

• The performance can be improved, e.g., by passing a list of candidates to the subsequent bit-levels and choosing the output sequences c_i ... c_m jointly from these lists.

• If the symbol alphabet A is smaller than 2^m, we can introduce some additional dummy symbols with target probability zero that will never be selected by the distribution matcher. • Although it is focused in the description on binary distribution matchers and symbo 1 alphabets of size 2^m for simplicity, the idea can be naturally extended to the more general case where at least one of the sequences d is taken from a non-binary alphabet.

• The symbols x may represent elements of an arbitrary set A. For example, they can be chosen from the real or complex numbers, or they may represent sequences of symbols or different functions (e.g. time-continuous transmit signals in a communication system).

• Additional operations (e.g., interleaving, scrambling, puncturing) may be applied to at least one of the input or output sequences.

• The input sequence b may contain some redundancy (e.g., in order to protect a corresponding message against transmission errors on a noisy channel).

Reference is now made to FIG. 5, which is a schematic view of the distribution matcher 100 comprising a polar decoder 510.

In the embodiment of FIG. 5, the distribution matcher 100 (e.g., the distribution matcher 100 of FIG. 4) is implemented using a polar decoder.

Polar codes are constructed by mapping an input sequence u of length n onto a codeword c of length n using a polar transform matrix G according to c = u G. The matrix G may be constructed, e.g., based on a recursive application of a Kronecker product to the kernel .

If the elements of u are successively decoded based on a noisy observation of the codeword c represented by the LLRs L(c ) assuming correct decisions in previous steps, a polarization effect can be observed: The resulting sub-channels tend to have either very high or very low reliabilities for large n. The order of the reliabilities can be determined numerically for a given transmission channel and stored in a sequence Q. Alternatively, a universal sequence Q may be defined that approximates the optimal order for a set of transmission channels, as in the 5G New Radio (NR) specification. For data transmission, the elements of u corresponding to the k most reliable sub-channels are typically used to represent a message to be transmitted, and the remaining n-k sub-channels are frozen to fixed values known to the decoder (e.g., zero). Note that the performance can be improved by replacing the simple successive cancellation decoder by better polar decoders, e.g., a successive cancellation list decoder. For the distribution matcher 100 of FIG. 5, it may also be possible to use any standard polar decoder. For instance, the most reliable sub-channels may be reserved for shaping bits S_i, which is determined by the decoder, and the remaining (frozen) sub-channels may be determined by the input sequence bi. Then, by interpreting the conditional LLRs L(c_i \c₁ ... c_{i -1} ) representing the target distribution as noisy observations of a received codeword. The resulting distribution of the output sequence c_i depends on the decoder type (e.g., SC or SCL with a certain list size) and the number of shaping bits, which may be optimized in order to obtain the best approximation of the target distribution (e.g., based on the Kullback-Leibler divergence).

In order to demonstrate the feasibility of this approach, and without limiting the present disclosure, in the following, some exemplary distributions are presented (e.g., in FIG. 6A, FIG. 6B, FIG. 7A, FIG. 7B, FIG. 8A, and FIG. 8B) based on 5G NR polar codes of length n = 256 using SCL decoding with list size 8 in each level. The distribution matcher 100 and/or the device 200 may generate the distributions, for example, the distribution matcher 100 and/or the device 200 may map the input sequences onto the output sequences based on the distributions.

Reference is now made to FIG. 6A-B, which shows distribution generated using 5G NR polar codes with n=256 using [0, 21, 195] shaping bits per level. FIG. 6A shows the generated symbol distribution for the target distribution from FIG. 3A, and FIG. 6B shows the generated distribution for three bit levels.

The generated symbol distribution for the target distribution from FIG. 3A with natural labelling of the symbols, where 0, 21, and 195 are used as shaping bits in the bit-levels 1, 2, and 3, respectively. As mentioned before, no shaping is required in the first bit-level, so it is possible to directly set c₁ = b₁. The generated symbol distribution is almost equal to the target distribution. The rate of the distribution matcher (i.e., the number of input bits per output symbol) is 2.16 bit/symbol, which is very close to the entropy of the target distribution 2.21 bit/symbol. The example shows that the proposed multi-level distribution matcher can generate symbol distributions that cannot be represented by a product distribution of independent bits.

Reference is now made to FIG. 7A-B, which shows distribution generated using 5G NR polar codes with n= 256 using [7, 27, 145] shaping bits per level. FIG. 7A shows the target and generated symbol distribution and FIG. 7B shows the generated distribution for three bit levels. This example presents another target distribution that does not have any symmetries. Note that in this case, all three bit-levels need to be shaped. The generated symbol distribution is again almost equal to the target distribution. The rate of the distribution matcher is 2.30 bit/symbol, which is very close to the entropy of the target distribution 2.36 bit/symbol.

Reference is now made to FIG. 8A-B, which shows distribution generated using 5G NR polar codes with n=256 using [0, 11, 165] shaping bits per level. FIG. 8A shows the target and generated symbol distribution and FIG. 8B shows the generated distribution for three bit levels.

In FIG. 8A-B, the same target distribution as in FIG. 7A-B is considered, but now with Gray labelling of the symbols. The generated symbol distribution still matches the target distribution almost perfectly, and the rate of the distribution matcher is slightly increased to 2.31 bit/symbol.

In one version of the preferred embodiment, the list of candidates for the codeword c_i generated by the SCL decoder in the i^th bit-level may be passed together with the corresponding path metrics to subsequent bit-levels. The lists of candidates received from previous bit-levels may be used to generate the input of the SCL decoder, e.g., a list of conditional LLR sequences L(c\_i c₁ ... c_i-1) representing the target distribution depending on the codewords in the previous bit- levels.

Reference is now made to FIG. 9, which is a schematic view of a device 200 comprising a CCDM 910 in the first bit-level and a channel decoder 100.

The device 200 may use different channel decoding algorithms in different bit-levels. For example, the device 200 may use CCDM 910 in at least one bit-level. Since the number of ones and zeros in c_i is fixed to n₁ = m and n₀ = n-m, respectively, the second distribution matcher 100 may generate an output sequence c₂ assuming an arbitrary sequence

having this property for the first bit-level. The output sequence c₂ is then interleaved according to the actual positions of ones and zeros in c₁. Note that this allows both distribution matchers to operate in parallel. FIG. 10 shows a method 1000 according to an embodiment of the invention for a distribution matcher 100. The method 1000 may be carried out by the distribution matcher 100, as it is described above. The method 1000 comprises a step 1001 of mapping an input sequence 110 onto an output sequence 120 based on a plurality of target probability distributions P(121), P(122), P(123), wherein each element 121, 122, 123 of the output sequence 120 has a corresponding target probability distribution P(121), P(122), P(123), and wherein at least two elements 121, 122, 123 of the output sequence 120 have different target probability distributions P(121), P(122), P(123).

FIG. 11 shows a method 1100 for a device 200, according to an embodiment of the invention. The method 1100 may be carried out by the device 200, as it is described above. The method 1100 comprises a step 1101 of mapping a plurality of input sequences 110, 210 onto a plurality of output sequences 120, 220, wherein at least one input sequence 110 is mapped using the method 1000 for the distribution matcher 100, and wherein the control sequence 201 depends on at least one output sequence 220. The present invention has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the 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 fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

1. A distribution matcher (100) configured to : map an input sequence (110) onto an output sequence ( 120) based on a plurality o f target probability distributions (P(121), P(122), P(123)), wherein each element (121, 122, 123) of the output sequence (120) has a corresponding target probability distribution (P(121), P(122), P(123)), and wherein at least two elements (121, 122, 123) of the output sequence (120) have different target probability distributions (P(121), P(122), P(123)).

2. The distribution matcher (100) according to claim 1, wherein: at least one target probability distribution (P(121), P(122), P(123)) is configurable based on a control sequence (201).

3. The distribution matcher (100) according to claim 1 or 2, wherein: the distribution matcher (100) comprises a channel decoder, in particular a polar decoder (510), a Low-Density Parity-Check, LDPC, decoder or a convolutional decoder.

4. The distribution matcher (100) according to claim 3, wherein: the channel decoder is configured to receive a channel decoder input sequence, wherein the channel decoder input sequence is a function of the target probability distributions (P(121), P(122), P(123)).

5. The distribution matcher (100) according to claim 3 or 4, wherein: the channel decoder is a polar decoder (510), wherein at least one frozen symbol is defined by the input sequence.

6. The distribution matcher (100) according to claim 1 or 2, wherein: the distribution matcher (100) comprises a Constant Composition Distribution Matching, CCDM, a Multi-Composition Distribution Matching, MCDM, or a shell mapper.

7. A device (200) for mapping a plurality of input sequences (110, 210) onto a plurality of output sequences (120, 220), comprising a distribution matcher (100) according to any of the claims 2 to 6: wherein at least one input sequence (110) is mapped using the distribution matcher (100), and wherein the control sequence (201) depends on at least one output sequence (220).

8. The device according to claim 7, further configured to: successively map the input sequences (110, 210) onto the output sequences (120, 220) such that each control sequence (201) depends on the previously generated output sequences (120).

9. The device according to claim 7 or 8, further configured to: map the output sequences (120, 220) onto a symbol sequence.

10. The device according to claim 9, wherein: each element in the symbol sequence is based on elements in predefined positions of the output sequences.

11. The device according to claim 7 or 8, wherein: the input sequences (110, 210) correspond to sub-sequences of a first input sequence.

12. A method (1000) for a distribution matcher (100), the method (1000) comprises: mapping (1001) an input sequence (110) onto an output sequence (120) based on a plurality of target probability distributions (P(121), P(122), P(123)), wherein each element (121, 122, 123) of the output sequence (120) has a corresponding target probability distribution (P(121), P(122), P(123)), and wherein at least two elements (121, 122, 123) of the output sequence (120) have different target probability distributions (P(121), P(122), P(123)).

13. A method (1100) for a device (200), the method (1100) comprises: mapping (1101) a plurality of input sequences (110, 210) onto a plurality of output sequences (120, 220): wherein at least one input sequence (110) is mapped using the method (1000) of claim 12, and wherein the control sequence (201) depends on at least one output sequence (220).

14. A computer program which, when executed by a computer, causes the method (1000) of claim 12 and/or the method (1100) of claim 13 to be performed.