A Low-Complexity Probabilistic Integer Shaping Encoding and Modulation Implementation Method

Abstract

This invention provides a low-complexity probabilistic shaping coding modulation implementation method, relating to the field of optical fiber communication systems. This method integrates probabilistic shaping into the modulation process, achieving the mapping from uniform bits to the desired symbol distribution through three steps: probability subset partitioning, subset weight calculation, and shaped frame construction. Simultaneously, it avoids the problems of low parallelism, severe error propagation, and poor compatibility with forward error correction codes in traditional shaping techniques.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical fiber communication, in particular to a high-order modulation optical fiber communication system with probability shaping. BACKGROUND

[0002] With the development of short video, Internet of Vehicles, Internet of Things, etc., the traffic in the communication network has increased explosively. In the face of the increasing bandwidth demand, the capacity expansion of the optical fiber communication system is imminent. Therefore, under the existing optical fiber facilities, how to achieve higher spectral efficiency or longer transmission distance is the key to system design. The standard modulation format can only provide discrete coarse granularity in spectral efficiency, and therefore cannot achieve transmission close to the channel capacity under different channel conditions.

[0003] In order to overcome this problem, probability shaping technology is applied to the optical fiber communication system. By changing the occurrence probability of different points in the constellation diagram, any fine rate or distance trade-off can be achieved, and shaping gain can be obtained. For the realization of probability shaping, the method of constant component distribution matching is generally used to convert a uniform source into an expected distribution. However, in practical applications, this method has the following defects: in principle, it relies on serial arithmetic coding, which is not conducive to parallel implementation in hardware; the input and output sequences are one-to-one mapped, and when there are a small number of errors in the received output sequence, the original input sequence cannot be recovered, causing large-scale decoding errors and error propagation; the combination with forward error correction codes relies on special architectures such as probability amplitude shaping, which limits the code rate and type of forward error correction codes.

[0004] The present application provides a low-complexity probability shaping encoding modulation implementation method, which combines the realization of probability shaping in the modulation process. Through three steps of probability subset division, subset weight calculation and shaping frame construction, the mapping of uniform bits to expected symbol distribution is realized, and the problems of low parallelization degree, serious error propagation and poor compatibility of forward error correction codes in traditional shaping technology are avoided. SUMMARY

[0005] The present application provides a low-complexity probability shaping encoding modulation implementation method, which realizes the expected probability shaping effect through three steps of probability subset division, subset proportion calculation and shaping frame construction. Compared with the traditional probability shaping implementation method, the implementation complexity is reduced, and the implementation architecture is more conducive to parallel implementation.

[0006] The low-complexity probability shaping coding modulation implementation method, in which the probability shaping implementation is not dependent on the generation of non-uniform distribution bits, but is realized by adjusting the bit-to-symbol modulation process. For any modulation format, first, the constellation diagram is divided into probability subsets to obtain several subsets, then the proportions of the subsets under the expected probability distribution are calculated, and finally, the input is divided according to the proportions and corresponding modulation is performed to realize the generation of the probability shaping signal.

[0007] The probability subset division divides and reconstructs the modulation constellation to form several subsets related to the probability distribution, and the distribution within the subset is uniform, and the steps are as follows:

[0008] Probability set division: the symbols with equal probability in the constellation diagram are divided into a set, and are arranged in descending order according to the probability value corresponding to the set, thereby obtaining a series of uniformly distributed sets χ1, χ2, …, χ p .

[0009] Subset division: in order to map the signals in the set with an integer number of bits, all the sets need to be reconstructed into new sets χ'1, χ'2, …, χ' q , so that the number of symbols in them satisfies the power of 2. Therefore, the probability set needs to be divided into several subsets satisfying the power of 2 first. Since the number of elements in the set χ1 with the maximum probability is the power of 2, and the number of elements in the remaining sets is an integer multiple of the number of elements in the set, all the sets χ1, χ2, …, χ p are split into subsets with the number of elements |χ1|. In the implementation, the subset division can follow the principle of maximizing the minimum Euclidean distance within the subset. In another implementation, the subset division can use any metric principle, such as the principle of maximizing the minimum Hamming distance within the subset.

[0010] Probability energy level setting: set p probability energy levels equal to the number of probability values and determine the subset range of each energy level, and each energy level has not less than 1 set composed of subsets. The sets in the energy level Pj only contribute to the first j probability values, i.e. the symbols of the set can only come from the subsets with index not greater than j. This setting principle guarantees the existence of solutions in the subset proportion calculation process.

[0011] Subset reconstruction: reconstruct the sets under each probability energy level from the subsets. For any energy level Pj, first determine whether the number of elements from to is the power of 2. If it is, then the energy level only needs a set containing all elements from to ; if not, only a certain number of elements can be selected from it. In the selection process, The smaller i is, the higher priority it is reserved, because we expect it to have a higher probability. In addition, At least one of i needs to be reserved because this energy level needs to contribute to χ j The probability of Pj. Meanwhile, we also need to make sure that the union of all sets of energy levels Pj contains all the probabilities of χ After the above operation on all energy levels, the final combined set χ'1, χ'2, …, χ'q is obtained. q .

[0012] After completing the subset division and reconstruction of the constellation, the next step is to calculate the subset ratio, which determines the ratio of each subset generated by the probability subset division in the probability shaping and modulation process, to achieve probability shaping.

[0013] The subset ratio calculation is as follows:

[0014] Consider that the constellation has p different probabilities under a certain distribution The p energy levels set finally divide q sets χ'1, χ'2, …, χ'q q , where the set χ'1, χ'2, …, χ'q j contains the probability value p i , and the proportion of χ'1, χ'2, …, χ'q j is called the contribution c i of p ij to the probability. If the set ratio is , the expected probability is achieved, and the relationship between them can be expressed as:

[0015]

[0016] Where C is a matrix composed of the contributions of each set to the probability:

[0017]

[0018] It can be proved that this equation has a solution, and the solution is:

[0019]

[0020] Where C T is the transpose of C.

[0021] After determining the set ratio, the number of sets is determined according to the length of the shaping frame, and then the input bits are processed in parallel and block, and the probability shaping signal is modulated to generate the shaping frame. This process is the shaping frame construction.

[0022] The shaping frame construction is as follows:

[0023] The number of subsets is calculated: for any given shaping output length n, i.e. n symbols are output, the number of subsets should be n i = nω i .

[0024] The number of subsets is quantized: since all n i should be non-negative integers and sum up to n, there can be multiple solutions for the quantization. In one implementation, a quantization technique that minimizes the cross-entropy with the expected distribution can be used to solve it, in another implementation, any quantization technique can be used, such as rounding to the nearest integer.

[0025] The input length is calculated: after the number of subsets n i ′ is determined, the input bit length of each shaping frame can be determined as:

[0026] The input bits are divided: in the process of generating the probability shaping signal, the serial input bits are converted into parallel bits with each m bits as a group, each group of bits is regarded as a shaping frame, in the frame, the data is divided into q blocks, the bits of different blocks are mapped to different sets in the modulation process, and finally n symbols are obtained. For the i-th block among them, the bit length is n' i log2|χ′ i |, in the modulation process, these bits are mapped to the symbols in χ′ i , and finally n i outputs are generated. The mapping process follows Gray mapping to reduce the bit error rate of the system.

[0027] At the receiving end, the system performs the corresponding inverse process to restore the symbols back to bits. Since the set corresponding to each symbol is known, in the demodulation process, only the metric value needs to be calculated in the signal within the set, which reduces the complexity and error probability. In addition, since the signals within the set are equally probable, it means that when soft decision is made, there is no need to modify the log-likelihood ratio calculation method as in other probability shaping schemes. BRIEF DESCRIPTION OF DRAWINGS

[0028] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:

[0029] In the drawings:

[0030] Figure 1 A 16QAM probability subset division schematic diagram provided for an embodiment of the application;

[0031] Figure 2A schematic diagram for generating a probability-shaped signal. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. These embodiments are only exemplary but not limiting of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort are within the scope of the present application. The specific embodiments of the present application will be described below with reference to the drawings.

[0033] Embodiment 1:

[0034] In a single-carrier 100G / 400G coherent optical communication system, 16QAM will be used as the main modulation format. With the increase of transmission distance and transmission power, the probability shaping technology is beneficial to reduce the nonlinear damage of the signal and is beneficial to improve the transmission distance. Therefore, it is of great significance to study the probability shaping implementation method for 16QAM.

[0035] In this embodiment, the probability subset division process in the low-complexity probability shaping encoding modulation implementation method will be described by taking 16QAM under MB distribution as an example.

[0036] Probability set division: 16QAM constellation under MB distribution contains three probability values, from high to low, respectively, the symbols with equal probability in the constellation are divided into a set, and are arranged in descending order according to the probability value corresponding to the set, thereby obtaining a series of uniformly distributed sets χ1, χ2, χ3, as shown in the accompanying Figure 1 The three sets are composed of points on three different rings of the 16QAM constellation.

[0037] Subset division: all sets χ1, χ2, χ3 are divided into subsets with |χ1| = 4 elements In this embodiment, the subset division follows the principle of maximizing the minimum Euclidean distance within the subset, and the accompanying Figure 1 χ2 is divided into and The process shown in the accompanying

[0038] Probability level setting: set 3 probability levels, each level has not less than 1 set composed of subsets. Among them, the sets in the level Pj only contribute to the jth probability value, that is, the symbols of the set can only come from the subsets with subscript not greater than j, as shown in the accompanying Figure 1 The subsets contained in P1 are only The subsets contained in P2 are and All subsets in P3.

[0039] subset reconstruction: reconstruct the set at each probability level by subset reconstruction. For any level Pj, first determine whether the number of elements from to is a power of 2. If yes, then the level only needs a set containing all elements from to ; if not, only a number of elements can be selected from it. In the selection process, , the smaller i is, the higher priority it has to be kept, because we expect it to have a higher probability. In addition, , at least one of them needs to be kept, because the level needs to contribute to the probability of χ j . At the same time, it is also necessary to ensure that in the union of all sets of level Pj, all χ For example, in the attached Figure 1 , the number of elements of all subsets in level P1 and P3 is 4 and 16 respectively, which is a power of 2, so these two levels only need a set containing all elements. In level P2, the sum of the number of elements of all subsets is 12, which is not a power of 2, and after preferentially keeping the elements of , only one of and can be selected with to form a set with 8 elements. When is selected, χ′2 is composed, but since does not appear in the union of all sets, another set χ′3 containing it is needed. Finally, the combined sets χ′1, χ′2, χ′3, χ′4 are obtained.

[0040] The subset division process is a one-time work related only to the modulation format. No matter how the distribution parameters and the output length of the shaping frame change, as long as the modulation format does not change, the result of the subset division is unchanged, so in actual implementation, this process does not need to be repeatedly executed. Only the division result needs to be stored as a codebook, and different sets are called in the modulation process. Therefore, the computational complexity of this process can be ignored in actual operation.

[0041] Embodiment 2:

[0042] This embodiment will take 16QAM under MB distribution as an example to explain the subset ratio calculation process in the low-complexity probability shaping encoding modulation implementation method.

[0043] All points in the 16QAM constellation have three probability values, and the subset division result produces four sets χ′1, χ′2, χ′3, χ′4. According to the attached Figure 1The composition of the middle set can be obtained from the matrix of the contribution of each set pair probability:

[0044]

[0045] When the expected MB distribution parameter v = 0.1373, the probability ratio of the three rings of 16QAM from inside to outside is:

[0046]

[0047] The subset ratio is:

[0048]

[0049] Next, the number of subsets in each shaping frame needs to be calculated according to the length of the shaping frame and the obtained subset ratio.

[0050] Embodiment 3:

[0051] This embodiment will take 16QAM under MB distribution as an example to explain the shaping frame construction step in the implementation method of the low-complexity probability shaping encoding modulation.

[0052] Subset number calculation: assuming that the shaping output length n = 20, the number of each subset should be:

[0053]

[0054] Subset number quantization: quantization is performed according to the principle of minimizing the cross entropy between the quantized and expected distribution, and the quantized number n' is obtained i = [5, 5, 5, 5] T .

[0055] Input length calculation: after the quantized number n' of each set is determined, i the input bit length of each shaping frame can be determined as: m = 5x2 + 5x3 + 5x3 + 5x4 = 60.

[0056] Input bit division: in the process of generating the probability shaping signal, every 60 bits are divided into a shaping frame, and in the frame, the data is divided into four blocks, and the bits of different blocks are mapped to different sets in the modulation process to finally obtain 20 symbols. For the first block among them, the bit length is 10, and in the modulation process, these bits are mapped to the symbols in χ'1, and finally 5 outputs are generated, and the other blocks are similarly processed, and finally 20 symbols are generated. The generation of the probability shaping signal after the construction of the shaping frame is shown in the accompanying Figure 2 .

Claims

1. A method for implementing low complexity probabilistic shaping coded modulation, characterized in that, The probability shaping is realized in the modulation stage, and is independent of the generation of non-uniform bits. The probability subset division divides and reconstructs the modulation constellation to form several subsets related to the probability distribution, and the distribution within the subset is uniform. The probability set division divides the symbols with equal probability in the constellation diagram into a set, and arranges the set in descending order according to the corresponding probability value. The probability subset division divides the probability set into several subsets with the number of elements satisfying the power of 2.

2. The subset proportion calculation of claim 1, wherein, The contribution matrix C of each energy level to the probability and the expected probability The proportion of each subset is obtained 3. The shaped frame construction of claim 1, wherein, The probability energy level setting sets the number of probability energy levels equal to the number of probability values and the subset range of each energy level. The subset reconstruction reconstructs the set under each probability energy level by the subset. The subset proportion calculation determines the proportion of each subset generated by the probability subset division in the shaping and coding modulation process according to the expected probability distribution, and realizes the probability shaping. The shaping frame construction determines the number of sets according to the length of the shaping frame, then parallelly and blockingly processes the input bits, and modulates to generate the probability shaping signal. It includes:

4. The probabilistic energy level setting of claim 1, wherein, The subset number calculation calculates the number of subsets for any set shaping output length; The subset number quantization quantizes the result of the subset number calculation to an integer, and the quantized result is unchanged; The input length calculation calculates the input bit length of each shaping frame according to the quantized result; The input bit division divides the serial input into shaping frames according to the input length, and the data in the frame is divided into different blocks, and different sets are selected for mapping in the modulation process. There are not less than 1 set composed of subsets in each energy level, wherein the set in the energy level Pj only contributes to the first j probability values, i.e. the symbols of the set can only come from the subsets with subscript not greater than j; the setting principle guarantees the existence of solution in the subset proportion calculation process.

5. The subset reconstruction of claim 1, wherein, For any energy level Pj, first determine whether the number of elements from to is a power of 2; if yes, then the energy level only needs a set containing all elements from to , if not, only a number of elements can be selected from it; in the selection process, , the smaller the i is, the higher the priority of being reserved is, in addition, , at least one of them needs to be reserved, at the same time, it also needs to ensure that in the union set of all sets of energy level Pj, all

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