阅读说明：本技术 使用分布匹配器的集合的通信系统及方法 (Communication system and method using a set of distributed matchers ) 是由 D·米勒 T·费恩贝格尔 秋浓俊昭 小岛启介 K·帕森斯 于 2018-07-04 设计创作，主要内容包括：一种通信系统包括：数据源,其接收比特块；存储器,其存储分布匹配器的集合。每个分布匹配器与概率质量函数(PMF)相关联,以将相等可能性的输入比特与具有根据分布匹配器的PMF而分布的值的固定数量的输出比特匹配。每个分布匹配器与选择概率相关联,使得所有分布匹配器的联合概率之和等于目标PMF。分布匹配器的联合概率是该分布匹配器的PMF与该分布匹配器的选择概率的乘积。通信系统还包括：整形映射器,其利用选择概率从分布匹配器的集合中选择分布匹配器,并且使用所选择的分布匹配器将比特块映射到具有非均匀分布的整形比特块；以及发送器前端,其在通信信道上发送整形比特块,使得整形比特块的序列中的比特根据目标PMF来分布。(A communication system comprising: a data source that receives a block of bits; a memory storing a set of distribution matchers. Each distribution matcher is associated with a probability quality function (PMF) to match input bits of equal likelihood with a fixed number of output bits having values distributed according to the PMF of the distribution matcher. Each distribution matcher is associated with a selection probability such that the sum of the joint probabilities of all distribution matchers equals the target PMF. The joint probability of the distribution matcher is the product of the PMF of the distribution matcher and the selection probability of the distribution matcher. The communication system further comprises: a shaping mapper selecting a distribution matcher from the set of distribution matchers using the selection probability and mapping the bit block to a shaped bit block having a non-uniform distribution using the selected distribution matcher; and a transmitter front end that transmits the block of shaped bits over the communication channel such that bits in the sequence of the block of shaped bits are distributed according to the target PMF.)

1. A communication system, the communication system comprising:

a data source that receives a block of bits;

a memory storing a set of distribution matchers, each distribution matcher associated with a probability quality function PMF to match input bits of equal likelihood with a fixed number of output bits having values distributed according to the PMF of the distribution matcher, wherein each distribution matcher is associated with a selection probability such that a sum of joint probabilities of all distribution matchers equals a target PMF, wherein a joint probability of a distribution matcher is a product of the PMF of that distribution matcher and the selection probability of that distribution matcher;

a shaping mapper selecting the distribution matcher from the set of distribution matchers using the selection probability and mapping the bit block to a shaped bit block having a non-uniform distribution using the selected distribution matcher; and

a transmitter front end that transmits the shaped block of bits over a communication channel such that bits in the sequence of the shaped block of bits are distributed according to the target PMF.

2. The communication system of claim 1, wherein the target PMF is a maxwell-boltzmann distribution.

3. The communication system of claim 1, wherein the shaping mapper selects the distribution matcher according to values of at least some bits in the block of bits, wherein a probability of occurrence of the values in the block of bits is equal to the selection probability of the distribution matcher.

4. The communication system of claim 1, wherein the memory stores a first distribution matcher associated with a first PMF and a first selection probability and a second distribution matcher associated with a second PMF and a second selection probability, wherein the first PMF is different from the second PMF, wherein the first selection probability is equal to the second selection probability, and wherein a sum of the joint probabilities of the first and second distribution matchers is equal to the target PMF.

5. The communication system of claim 1, wherein the memory stores a first distribution matcher associated with a first PMF and a first selection probability, a second distribution coordinator associated with a second PMF and a second selection probability, and a third distribution coordinator associated with a third PMF and a third selection probability, wherein the first PMF is different from the second PMF, wherein the third PMF is equal to the target PMF, and wherein the first selection probability is equal to the second selection probability, and a sum of the joint probabilities of the first, second, and third distribution coordinators is equal to the target PMF.

6. The communication system of claim 1, further comprising:

an FEC encoder that generates uniformly distributed parity bits from a block of shaped bits having non-uniformly distributed bits and combines the parity bits with the bits of the block of shaped bits.

7. The communication system of claim 6, wherein at least some of the parity bits are sign bits.

8. The communication system of claim 6, further comprising:

a modulator that modulates the sequence of the shaped block of bits over amplitude bits of QAM symbols, at least some of the symbol bits being determined by the uniformly distributed parity bits; and

a digital signal processor for processing the modulated sequence of shaped bit blocks for analog transmission over the communication channel.

9. The communication system of claim 1, wherein the symbols of the shaped bit block generated by the distribution matcher are selected from a finite set of symbols, and wherein the frequency of occurrence of different symbols in the shaped bit block is defined by the PMF of the distribution matcher.

10. The communication system of claim 9, wherein the selected distributed matcher arranges a sequence of symbols occurring in the sequence by a frequency of the PMF defining the distributed matcher for different values of the bits in the block of bits.

11. The communication system of claim 9, further comprising:

a processor, the processor:

generating a multiplicity of sets of symbols having a frequency of occurrence defined by the target PMF and a total number of symbols equal to a multiple of a number of symbols in the shaped bit block;

partitioning the multiple set of symbols to generate a plurality of subsets of symbols, wherein a total number of symbols in each subset is equal to a number of symbols in the block of shaped bits, wherein a number of subsets generated by the partitioning is equal to the multiple of a number of symbols for the multiple set of symbols;

selecting, for each generated subset, a maximum number of symbol permutations determined by a highest pair of 2 that is less than or equal to a polynomial coefficient determined by a number of occurrences of each symbol in the subset; and

the size of the bit block is determined as the maximum power of 2 in the subset with the least number of permutations.

12. The communication system of claim 9, further comprising:

a processor, the processor:

generating a multiplicity of sets of symbols having a frequency of occurrence defined by the target PMF and a total number of symbols equal to a multiple of a number of symbols in the shaped bit block;

performing a plurality of partitions of the multiple set of symbols to generate a plurality of subsets of symbols for each partition, wherein a total number of symbols in each subset is equal to a number of symbols in the block of shaping bits, wherein a number of subsets generated by the partitions is equal to the multiple of the number of symbols for the multiple set of symbols;

for each partition, selecting for each generated subset a maximum number of symbol permutations determined by the highest pair of 2 that is less than or equal to a polynomial coefficient determined by the number of occurrences of each symbol in the subset;

for each partition, determining the maximum power of 2 in the subset having the least number of permutations;

summing the maximum powers of 2 over all subsets of all partitions; and

determining the size of the bit block as the maximum power of 2 according to the sum of the maximum powers; and

selecting a subset from a list formed by ordering the partitions according to their maximum power of 2 until the total number of sequences over all selected subsets equals the required total number of sequences.

13. The communication system of claim 1, further comprising:

a processor, the processor:

selecting a binary tree from the memory having leaves defining the distribution matcher; and

selecting the distribution matcher from the binary tree using prefix bits of the bit block equal to a path length of the leaf through the binary tree to the distribution matcher.

14. The communication system of claim 1, further comprising:

a receiver front end that receives the shaped block of bits transmitted via a communication channel;

a receiver memory storing a set of distributed demanders, each distributed demander being associated with the distributed matcher;

a shaping demapper that selects the distributed demapper based on an occurrence frequency of a symbol in the transmitted shaped bit block and maps the transmitted shaped bit block to the bit block.

15. A method for communicating symbols of bits, wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor, perform at least some steps of the method, the method comprising the steps of:

receiving a block of bits;

selecting distribution matchers from a memory storing a set of distribution matchers, wherein each distribution matcher is associated with a probability quality function, PMF, to match input bits of equal likelihood with a fixed number of output bits having values distributed according to the PMF of the distribution matcher, wherein each distribution matcher is associated with a selection probability such that the sum of the joint probabilities of all distribution matchers equals a target PMF, wherein the joint probability of a distribution matcher is the product of the PMF of that distribution matcher and the selection probability of that distribution matcher;

mapping the bit blocks to shaped bit blocks having a non-uniform distribution using the selected distribution matcher; and

transmitting the shaped block of bits over a communication channel such that bits in the sequence of the shaped block of bits are distributed according to the target PMF.

Technical Field

The present invention relates generally to digital communication systems, and more particularly to encoding and decoding data transmitted over noisy channels.

Background

Since the advent of digital communications, it has been known that the optimal signal distribution of an additive white gaussian noise channel is not uniform. There are two main methods of generating a non-uniform distribution of a digital communication system: geometric shaping, such that equi-probability constellation points are arranged in a non-uniform manner to maximize performance; and probability shaping to optimize the probability of constellation points to maximize performance. Although for equal cardinality it is generally accepted that the performance of probability shaping is better than that of geometry shaping, the method of mapping evenly distributed bit sequences of information (such as the sequences we want to send) to non-equal probability symbol sequences has proven to be extremely challenging. The most common method is the Constant Composition Distribution Matching (CCDM) method, which maps equi-probability bits onto sequences that are permutations of a "canonical sequence" with the desired symbol Probability Mass Function (PMF). While this approach can achieve good performance (any low rate loss for an asymptotically long symbol sequence), it has two key drawbacks: the ability to achieve low rate loss requires very long sequences, which results in high complexity and latency; and the only known efficient mapping and demapping algorithms are in symbol order (that is, each symbol needs to be decoded in turn in the symbol sequence), which also results in high complexity and delay.

Disclosure of Invention

It is an object of some embodiments to convert a symbol input sequence of bit values having an equal probability (i.e. uniform) distribution into a symbol output sequence of bit values having a desired non-uniform distribution. Some embodiments are based on the following recognition: the set of symbols may be partitioned into a plurality of unique subsets, each unique subset having a plurality of possible unique permutations. According to this implementation, the desired overall distribution of the symbol sets may be achieved by using a plurality of smaller sets that individually have no desired distribution but rather have an average distribution equal to the desired distribution. In some embodiments, the distribution is defined by a Probability Mass Function (PMF) that reflects the discrete nature of digital signal processing. For this reason, the desired distribution is referred to herein as the target PMF.

In particular, some embodiments are based on the following recognition: the input sequence of symbols may be transformed on a block-by-block basis. For example, some embodiments transform a block of bits having uniformly distributed bit values into a shaped block of bits having non-uniformly distributed bit values. However, some embodiments are based on the following recognition: the non-uniformly distributed PMFs of the shaped bit blocks may be different from the target PMF as long as the different shaped bit blocks with different PMFs form a bit sequence with the target PMF. Such recognition allows reducing the length of the bit block to be transformed relative to the length of the bit block transformed only according to the target PMF. This results in a reduced rate loss, which corresponds to an increase in the maximum rate at which data can be transmitted over the channel.

Some embodiments are based on the following recognition: of the target PMF of the transmitted bit sequenceThe PMFs are formed depending on each individual shaping bit block and on the frequency of occurrence of shaping bit blocks having different PMFs in the transmitted bit sequence. For example, if the target PMF is equal to 0.6PMF₁+0.3PMF₂+0.1PMF₃The transmitted bit sequence should have an and-transform to have a bit sequence according to PMF₂Has twice as many transforms as there are according to the PMF₁Should have a bit-shaped block of bits distributed and should have an and-transform according to the PMF₃Three times as many transforms as there are reshaped bit blocks of the bit distribution according to the PMF₂A block of shaped bits of the bit distribution. This implementation allows different implementations to combine distribution matching with different PMFs with selection probabilities of different distribution matching to achieve design flexibility for transmission with a target PMF.

Some embodiments are based on the following recognition: for transmission of binary symbols, the symbols are typically selected from a finite alphabet. Some embodiments are based on the following recognition: the PMF of the shaped bit block may be defined by the frequency of occurrence of each symbol in the shaped bit block. However, the order of the symbols in the shaping bit block is independent of the PMF, and thus the arrangement of the shaping bit block with a particular PMF may encode different input bit blocks with the same particular PMF. Such an understanding simplifies the mapping of bit blocks to shaped bit blocks with a particular PMF.

Some embodiments are based on the following recognition: when transmitting binary information, the total number of desired shaping bit blocks should be a power of 2, and selecting a particular subset and arrangement thereof to achieve a total sequence of numbers of powers of 2 may be advantageous in constructing mapping and demapping algorithms.

Some embodiments are based on the following recognition: the total number of permutations in each set of subsets may be rounded down to the nearest power of 2 achievable for all subsets in the partition, allowing an integer number of bits to be assigned to each subset. This structure allows for a fixed word length including variable length headers (used to assign subsets with PMFs used in the distributed matcher), and a variable number of bits that determine the desired permutation assigned by the distributed matcher.

Some embodiments are based on the following further recognition: by partitioning the desired multi-set into subsets each having a certain number of permutations, the mapping and demapping algorithm can be described as: (i) determining the number of each possible symbol in the symbol sequence according to the prefix bit; (ii) the arrangement of the symbol sequence is determined from the remaining bits in the input bit block.

Accordingly, one embodiment discloses a communication system comprising: a data source that receives a block of bits; a memory storing a set of distribution matchers, each distribution matcher associated with a probability quality function (PMF) to match input bits of equal likelihood with a fixed number of output bits having values distributed according to the PMF of the distribution matcher, wherein each distribution matcher is associated with a selection probability such that a sum of joint probabilities of all the distribution matchers is equal to a target PMF, wherein the joint probability of a distribution matcher is a product of the PMF of that distribution matcher and the selection probability of that distribution matcher; a shaping mapper selecting a distribution matcher from the set of distribution matchers using the selection probability and mapping the bit block to a shaped bit block having a non-uniform distribution using the selected distribution matcher; and a transmitter front end that transmits the shaped bit block over the communication channel such that bits in the sequence of shaped bit blocks are distributed according to the target PMF.

Another embodiment discloses a method for communicating symbols of bits, wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor, perform at least some steps of the method, the method comprising: receiving a block of bits; selecting distribution matchers from a memory storing a set of distribution matchers, wherein each distribution matcher is associated with a probability quality function (PMF) to match input bits of equal likelihood with a fixed number of output bits having values distributed according to the PMF of the distribution matcher, wherein each distribution matcher is associated with a selection probability such that the sum of the joint probabilities of all the distribution matchers is equal to a target PMF, wherein the joint probability of a distribution matcher is the product of the PMF of that distribution matcher and the selection probability of that distribution matcher; mapping the bit blocks to shaped bit blocks having a non-uniform distribution using the selected distribution matcher; and transmitting the block of shaped bits over the communication channel such that bits in the sequence of the block of shaped bits are distributed according to the target PMF.

Drawings

[ FIG. 1A ]

Fig. 1A is a block diagram of a digital communication system employing probabilistic amplitude shaping according to some embodiments of the present invention.

[ FIG. 1B ]

Fig. 1B is a probability shaping mapper according to some embodiments of the invention.

[ FIG. 1C ]

Fig. 1C is an encoder and symbol modulator according to some embodiments of the present invention.

[ FIG. 2A ]

FIG. 2A is an exemplary structure of a signal histogram including a comparison of a constant composition distribution matcher and a partition-based distribution matcher according to some embodiments of the present invention.

[ FIG. 2B ]

FIG. 2B is a schematic diagram illustrating binary partitioning of a target distributed multi-set according to some embodiments of the invention.

[ FIG. 2C ]

Fig. 2C is a collection of exemplary symbol sequences with different PMFs and permutations.

[ FIG. 3]

Figure 3 is a set of schematic diagrams illustrating a rounding process for binary subsets to ensure that an integer number of bits per subset is used, according to some embodiments of the invention.

[ FIG. 4A ]

Fig. 4A is a block diagram of a tree-based subset bit marking process that enables variable length headers, according to one embodiment of the invention.

[ FIG. 4B ]

Fig. 4B is a block diagram of a process for determining PMFs for subsets for use in a distributed matcher, according to some embodiments of the present invention.

[ FIG. 5]

Fig. 5 is a block diagram of a distributed matching, coding and modulation process at a transmitter according to some embodiments of the present invention.

[ FIG. 6]

Fig. 6 is a block diagram of demodulation, decoding, and dematching processes at a receiver according to some embodiments of the invention.

[ FIG. 7]

Fig. 7 is a block diagram of a shaping mapper and distribution matcher in accordance with some embodiments of the present invention.

Detailed Description

Fig. 1A illustrates a block diagram of a probability-shaped digital communication system, according to some embodiments. Data from a source (001) is sent to a transmitter (Tx) (010). For example, the data is first sent to a probability shaping mapper (011) and then to a Forward Error Correction (FEC) encoder block (012) to generate a set of bits some of which are shaped and others (in particular, parity bits from the FEC encoder) are evenly distributed. After encoding, the bits are mapped to Quadrature Amplitude Modulation (QAM) symbols (013) before the signal is subjected to Digital Signal Processing (DSP) (014). In some embodiments, the DSP also performs other functions such as mapping, filtering, and pre-equalization. The signal is then sent to a transmitter front end (015) where analog operations such as amplification, filtering, modulation, and frequency up-conversion take place, and then the signal is sent to a receiver (Rx) (030) via a channel (020).

At the receiver, the signal first passes through a receiver front end (031) to perform analog operations such as down-conversion, amplification, filtering, and quantization on the received signal to generate a digital signal. The digital signal is processed by a digital processor (032) to perform functions such as front end correction, dispersion compensation, equalization and carrier phase estimation. The noisy QAM symbols are then demapped (033) into, for example, bit log-likelihood ratios (LLRs). The FEC code is then decoded (034) before the decoded bits are sent to a probability shaping demapper (035). The demapped and evenly distributed bits are then sent to their destination, e.g., a data sink (040).

Fig. 1B illustrates a block diagram of a communication system, according to some embodiments. A data source (110) receives a block of bits, at least some of which are sent to a distributed matcher selector (120). A memory (130) stores a set of distribution matchers, each distribution matcher associated with a probability quality function (PMF) to match input bits of equal likelihood with a fixed number of output bits having values distributed according to the PMFs of the distribution matchers. A shaping mapper (125) is configured to select a distribution matcher (140) from a set of distribution matchers using a selection probability, and to map the block of bits to a shaped block of bits having a non-uniform distribution using the selected distribution matcher. The transmitter front end (150) is then used to transmit the shaped block of bits over the communication channel such that bits in the sequence of the shaped block of bits are distributed according to the target PMF.

In this manner, some embodiments convert a symbol input sequence of bit values having an equal probability (i.e., uniform) distribution to a symbol output sequence of bit values having a desired non-uniform distribution. Some embodiments partition the set of symbols into a plurality of unique subsets, each unique subset having a plurality of possible unique permutations. In this way, the desired overall distribution of the symbol sets is achieved by using a plurality of smaller sets, where the smaller sets alone do not have the desired distribution, but rather have an average distribution equal to the desired distribution. In some embodiments, the distribution is defined by a Probability Mass Function (PMF) that reflects the discrete nature of digital signal processing. For this reason, the desired distribution is referred to herein as the target PMF. According to some embodiments, the target PMF is a Maxwell-Boltzmann (Maxwell-Boltzmann) distribution.

In particular, some embodiments are based on the following recognition: the input sequence of symbols may be transformed on a block-by-block basis. For example, some embodiments transform a block of bits having uniformly distributed bit values into a shaped block of bits having non-uniformly distributed bit values. However, some embodiments are based on the following recognition: the non-uniformly distributed PMFs of the shaped bit blocks may be different from the target PMF as long as the different shaped bit blocks with different PMFs form a bit sequence with the target PMF. Such recognition allows reducing the length of the bit block to be transformed relative to the length of the bit block transformed only according to the target PMF. Since the entire sequence with the target PMF is contained within this scheme, it can be observed that since additional sequences can be introduced, a partition-based design will be able to represent multiple sequences equal to or greater than the constant constituent system, and thus with equal or lower rate loss, which can correspond to a higher achievable data rate to be transmitted over the channel.

Some embodiments are based on the following recognition: the formation of the target PMF of the transmitted bit sequence depends on the PMF of each individual distribution matcher and on the frequency with which the bit block is transformed using the distribution matcher. For example, if the target PMF is equal to 0.6PMF₁+0.3PMF₂+0.1PMF₃The transmitted bit sequence should have an and transform to have a PMF-based₂Has twice as many transforms as there are according to the PMF₁Should have a bit-shaped block of bits distributed and should have an and-transform according to the PMF₃Three times as many transforms as there are reshaped bit blocks of the bit distribution according to the PMF₂A block of shaped bits of the bit distribution. For this reason, the same shall be used for PMF₂Is twice as many as the distribution matcher for PMF and₃six times as same as the distribution matcher used for PMF₁The distribution matcher. This implementation allows different implementations to combine distribution matching with different PMFs with selection probabilities of different distribution matching to achieve design flexibility for transmission with a target PMF.

To this end, in some embodiments, each distribution matcher 140 is associated with a selection probability such that the sum of the joint probabilities of all the distribution matchers is equal to the target PMF. In various embodiments, the joint probability of the distribution matcher is the product of the PMF of the distribution matcher and the selection probability of the distribution matcher. For example, in the above example, the joint probability of the first distribution orchestrator is 0.6PMF₁The joint probability of the second distributor is 0.3PMF₂And a third distribution of the joint probability of the dispensersIs 0.1PMF₃。

According to one embodiment, the shaping mapper (125) selects the distribution matcher (140) based on values of at least some of the bits in the block of bits. In this embodiment, the probability of occurrence of a value in a bit block is equal to the selection probability of the distribution matcher. This embodiment is based on the following recognition: different lengths of evenly distributed input bits may be used to achieve the desired selection probability.

For example, a selection probability of 50% can be achieved by analyzing the value of a single bit. For example, when the value of the input bit is "0", a distribution matcher having a selection probability of 50% may be selected. On the other hand, a selection probability of 25% can be achieved by analyzing the values of 2 bits. For example, when the value of the input bit is "10", a distribution matcher having a selection probability of 25% may be selected. By analyzing different sequences of input bits of different lengths, different distribution matchers can be selected.

In various embodiments, the memory 130 may store distribution matchers having the same and/or different PMFs and having the same and/or different selection probabilities. For example, in one embodiment, the memory (130) stores a first distributor associated with a first PMF and a first selection probability, and a second distributor associated with a second PMF different from the first PMF and a second selection probability, wherein the first selection probability is equal to the second selection probability, and a sum of joint probabilities of the first distributor and the second distributor is equal to the target PMF. In another embodiment, the memory (130) stores a first distribution matcher associated with the first PMF and the first selection probability, a second distribution matcher associated with a second PMF different from the first PMF and the second selection probability, and a third distribution matcher associated with a third PMF different from the second PMF and the third selection probability, wherein the third PMF is equal to the target PMF, and wherein the first selection probability is equal to the second selection probability, and a sum of joint probabilities of the first, second, and third distributors is equal to the target PMF.

Fig. 1C illustrates a block diagram of an encoder and a modulator according to some embodiments. The FEC encoder (162) is arranged to generate uniformly distributed parity bits (165) from a block of shaped bits (160) having a non-uniform distribution and to combine the parity bits in the modulator (190) with the bits of the block of shaped bits (160). According to some embodiments, at least some of the parity bits (165) are symbol bits (190). Some of the symbol bits (180) may optionally be composed of evenly distributed information bits (170).

For example, according to some embodiments, the modulator (190) modulates the sequence of shaped bit blocks (160) onto amplitude bits (168) of the QAM symbol using at least some of the symbol bits determined by the uniformly distributed parity bits (165). The sequence of modulated shaped bit blocks is then processed using a Digital Signal Processor (DSP) (195) for analog transmission over a communication channel.

Fig. 2A shows a schematic diagram illustrating the concept of a non-constant composition distribution used by some embodiments. In a Constant Composition Distribution Matcher (CCDM), each of the possible symbols having the same number of occurrences is prepared for each of the shaping bit blocks prepared for transmission. In contrast, in the non-constant composition distribution used in some embodiments, different shaping bit blocks have different distributions of symbol occurrences.

For example, in the exemplary diagram of FIG. 2A, the symbols are selected from a finite alphabet comprising four symbols { S1, S2, S3, S4 }. Each block of shaped bits comprises ten symbols, but the distribution of symbols in different blocks varies. For example, in distribution 201, the distribution of occurrences of the four possible symbols S1, S2, S3, S4 is {4,3,2,1 }. The total number of different sequences with this composition is therefore made up of the polynomial coefficient 10! And/4 | 3 | 2 | 1 |) 12600. This determines the entropy of the distribution matcher, given by log2(12600)/10 ═ 1.36 bits/symbol. The entropy of PMF X is given by sum (-X log2(X)), which in this example is 1.85 bits/symbol. Thus, in this example, the rate loss is 1.85-1.36-0.49 bits.

Some embodiments of the invention are based on the recognition that: the non-constant composition distribution matcher may be described as a summation of several distributions that average out to a desired distribution. For example, the four possible symbols { S1, S2, S3, S4} of distributions (202) and (203) occur by {4, 2, 3, 1} and {4, 4, 1, 1} respectively. Some embodiments are based on the following recognition: by combining one occurrence of the distribution described in (202) with one occurrence of the distribution described in (203), the average behavior is described in (201).

Furthermore, the number of different sequences with the distribution shown in (202) is defined by the polynomial coefficient 10! Whereas (4! 2! 3! 1!) ═ 12600, and the complementary distribution (203) is given by the polynomial coefficient 10! This is given by 6300/(| 4 | 1 |) 1 |. For each composition described by the distributions of (202) and (203), respectively, while maintaining the overall distribution described in (201), the pair-wise partition (pair-wise partition) based distribution matcher is only 6300 sequences. By considering the distributions in (201), (202), and (203), some embodiments use 12600 sequences from (201); 6300 sequences from (202); and 6300 sequences from (203), for a total of 25200 sequences. This increases the entropy of the distribution matcher by 0.1 bits/symbol and reduces the rate loss from 0.49 bits to 0.39 bits.

Fig. 2B shows a schematic diagram of a method of partitioning (212) a large multiset (211) into two smaller subsets (213) and (214) each with an equal number of elements. Although pairwise partitioning is shown here for simplicity, the larger multiset may be arbitrarily partitioned into many smaller subsets, which are not necessarily unique. It is noted that the possible number of different sequences of the smaller subsets (213) and (214) is typically not equal. Thus, some embodiments select a plurality of sequences drawn from each subset that allows the overall composition of the distribution matcher to be the overall composition of the desired distribution.

Fig. 2C shows a schematic of sequences having different compositions and arrangements according to some embodiments. Some embodiments are based on the following recognition: for transmission of binary symbols, the symbols are typically selected from a finite alphabet. Some embodiments are based on the following recognition: the PMF of the shaped bit block may be defined by the frequency of occurrence of each symbol in the shaped bit block. However, the order of the symbols in the shaping bit block is independent of the PMF, and thus the arrangement of the shaping bit block with a particular PMF may encode different input bit blocks with the same particular PMF. Such an understanding simplifies the mapping of bit blocks to shaped bit blocks with a particular PMF.

For example, a set of symbols (221) is shown in order (222), with the composition described in the histogram of (201). We see the difference (228) of the same symbol set (227) also drawn from the subset with the composition given by (201). Notably, the sequence order (222) and (228) are different and unique. The second set of symbols (223) is also given an ordering (224) having a composition described by the histogram in (202). A third set of symbols (225) is also given an ordering (226) having a composition described by the histogram in (203). Notably, the sequences (224) and (226) have an average composition given by the histogram (201).

FIG. 3 shows a schematic diagram of a method used by some embodiments to generate fixed-length blocks for a distribution matcher. The multiple set (305) includes symbols having a frequency of occurrence defined by the target PMF and a total number of symbols equal to a multiple of the number of symbols in the shaped bit block. For example, if the multiple is 2, the multiple set (305) may include twice the symbols shown in the histogram 201.

The multiple set (305) is then partitioned to generate a number of subsets of symbols (310), the total number of symbols in each subset being equal to the number of symbols in the block of shaping bits, wherein the number of subsets generated by partitioning is equal to a multiple of the number of symbols of the multiple set of symbols (305). For example, when the multiple is 2, twice the symbols shown in the histogram 201 may be partitioned into multiple sets 202 and 203. When the multiple is 3, three times the symbols shown in the histogram 201 may be partitioned into three multiplets, and so on.

The number of permutations per subset is then calculated (320), ending the maximum number of symbol permutations per generated subset calculated in (320) as determined by the highest pair of 2 (330) that is less than or equal to the polynomial coefficient determined by the number of occurrences of each symbol in the subset. The size of the bit block is taken as the maximum power of 2 in the subset with the least number of permutations (330).

According to some other embodiments, a multiple set of symbols is generated (305) having a frequency of occurrence defined by the target PMF and a total number of symbols equal to a multiple of a number of symbols in the shaped bit block. Performing a plurality of partitions of the multiple set of symbols to generate a plurality of subsets of symbols for each partition (310), wherein a total number of symbols in each subset is equal to a number of symbols in the block of shaping bits, wherein a number of subsets generated by the partitions is equal to a multiple of the number of symbols for the multiple set of symbols. For each partition, the maximum number of symbol permutations for each generated subset (330) is determined by the highest pair that is less than or equal to 2 of the polynomial coefficients determined by the number of occurrences of each symbol in the subset (320). For each partition, a maximum power of 2 is generated (330) in the subset with the least number of permutations before forming a sum of the maximum powers of 2 over all subsets of all partitions (350) and determining the size of the bit block as the maximum power of 2 from the sum of the maximum powers (360). A subset is then selected from the list formed by sorting the partitions according to their maximum power of 2 (370) until the total number of sequences over all selected subsets equals the required total number of sequences (360).

Some of these embodiments are based on the following recognition: by rounding the constituent partitions to a sequence of numbers of powers of 2, the full number of bits can be represented by each partition. This enables the use of a pre-existing constant composition distribution matching algorithm to determine which sequence to use within a partition. Some embodiments of the invention are based on the further recognition that: by rounding the total number of sequences to a power of 2, an integer number of bits can be represented by the total distribution distributor, thus enabling a fixed block length with a variable length header to determine which partition is used.

Fig. 4A illustrates a method for generating a variable length header of a tree structure to provide bit labels for different partitions, according to some embodiments. The different partitions are sorted according to the number of times they are used in the matcher (410), and then pairs of Pk and Pk' are labeled 1 and 0 to form the outermost branches in the tree (420). The two sets of least used total partitions are then merged to form a branch (430), with one element labeled 1 and the other element labeled 0 (450). If more than one branch remains, the merge and mark process is repeated (450). When only a single branch remains, the prefix tree is completed (460).

Fig. 4B illustrates a tree structure for selecting a distribution matcher according to variable length prefixes according to an embodiment of the present invention. A binary tree is selected from memory having leaves (472), (482), (484) defining a distribution matcher. The distribution matcher is selected from the binary tree using prefix bits (470) of a block of bits equal to the path length through the binary tree to the leaves of the distribution matcher. The path is determined by a binary decision at nodes (471), (480), (481), (483) according to the value of prefix bit (470).

Some of these embodiments are based on the following recognition: for variable length prefixes, the best label for the prefix may be determined using standard source coding techniques such as those described herein.

Fig. 5 depicts a system for encoding a fixed length bit sequence onto a fixed length symbol sequence including forward error correction and probabilistic amplitude shaping according to some embodiments of the present invention. A fixed length bit sequence (510) is used at least in part as an input to a variable length prefix lookup table (520) to determine the composition of the sequence to be encoded. The composition of the sequence and at least some of the remaining bits are then sent to a constant composition distribution matcher (530) that outputs a shaped bit sequence. These bits are then used as input to a forward error correction encoder (540). The output of the FEC encoder (540) is then sent to a symbol modulator (550), where the shaped information bits are used to determine the amplitude size of the QAM symbol, while the uniformly distributed parity bits, and optionally some of the uniformly distributed information bits (510), are used to determine the symbol bits of the QAM symbol. The symbol sequence is then sent on (560) for further processing before transmission over the channel.

Fig. 6 illustrates a system for decoding and demodulating a fixed length sequence of symbols with probabilistic amplitude shaping and forward error correction onto a fixed length bit sequence according to some embodiments of the present invention.

A sequence of symbols is transmitted (610) from a receiver front end to receive a block of shaped bits transmitted over a communication channel. The receiver memory (642) stores a set of distributed demanders, each distributed demander (650) being associated with a distributed matcher. A shaping demapper (645) is used to select a distributed demapper (650) based on symbol occurrence frequencies (640) in the transmitted shaped bit blocks and to map the transmitted shaped bit blocks to bit blocks. The distribution dematching (650) then generates a fixed-length block of bits (660).

Fig. 7 illustrates a shaping mapper and distribution matcher according to some embodiments of the present invention. The symbols of the shaped bit block (750) generated by the distribution matcher (740) are selected from a finite set of symbols, and wherein the frequency of occurrence of the different symbols in the shaped bit block is defined by the PMF of the distribution matcher (730).

According to another embodiment, the selected distribution matcher arranges the sequence of symbols occurring in the sequence in terms of frequencies of the PMFs defining the distribution matcher (730) for different values (715) of the bits in the block of bits (710).

The above-described embodiments of the present disclosure may be implemented in any of a variety of ways. For example, embodiments may be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether located in a single computer or distributed among multiple computers. Such a processor may be implemented as an integrated circuit having one or more processors in an integrated circuit component. However, a processor may be implemented using circuitry in any suitable format.

Additionally, embodiments of the invention may be embodied as a method, examples of which have been provided. The actions performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts concurrently, even though shown as sequential acts in exemplary embodiments.

Use of ordinal terms such as "first," "second," and the like in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.