WO2018133215A1

WO2018133215A1 - Lsc-crc decoding-based segmented polar code encoding and decoding method and system

Info

Publication number: WO2018133215A1
Application number: PCT/CN2017/079898
Authority: WO
Inventors: 何业军; 盖宝宏; 张威
Original assignee: 深圳大学
Priority date: 2017-01-22
Filing date: 2017-04-10
Publication date: 2018-07-26
Also published as: CN106888026B; CN106888026A

Abstract

Disclosed in the present invention are an LSC-CRC decoding-based segmented polar code encoding and decoding method and system. The method comprises: performing combining and splitting operations on multiple independent channels to obtain the same number of bit channels as the number of the independent channels, acquiring a capacity of each of the bit channels, and performing computation to acquire the number of fully polarized bit channels; dividing, according to the number of the fully polarized bit channels, a free information bit sequence to be transmitted into a corresponding number of sub-sequences, performing polar coding on each of the sub-sequences, and sending the encoded information in the corresponding bit channels; and receiving the encoded information at a receiving end, performing, according to an LSC-CRC decoding algorithm, decoding segment by segment, and joining decoded sub-sequences obtained from the decoding in a head-to-tail manner to obtain a decoded sequence. The channel encoding and decoding method of the present invention enables simple operation, lowers spatial complexity of encoding and decoding, and improves decoding accuracy.

Description

Segmented polarization code encoding and decoding method and system based on LSC-CRC decoding

Technical field

The present invention relates to the field of channel coding technologies, and in particular, to a segmentation polarization code coding method and system based on LSC-CRC decoding.

Background technique

Source coding is a symbol transformation performed to improve communication efficiency and reduce source redundancy. By seeking a method for the statistical characteristics of the output symbol sequence of the source, the source output symbol sequence is transformed into the shortest codeword sequence, so that the average information amount of each symbol of the latter is maximized, and at the same time, the object can be guaranteed. It is true to reply to the original symbol sequence. It is an important technical means in the field of digital communications.

Various communication systems, although their forms and uses are different, from the perspective of information transmission, storage and processing, there are essentially two communication systems for transceivers, see Figure 1. The source 10 is a source for generating a message, and the encoder 20 is a device for converting a message sent by a source into a signal suitable for channel transmission, and is generally divided into three parts, namely a source encoder, an error correction encoder and a modulator. The channel 30 is a medium or channel for transmitting signals from the originating end to the receiving end. It is a physical facility including the first transmitting device. The interference source 40 introduces various interferences in various parts of the entire communication system for analysis convenience. The statistical characteristics are important factors for dividing the channel, and are the determining factors determining the channel transmission capability. The decoder 50 is the inverse transform of the code, which extracts the maximum from the interfered signal. The source 10 outputs the message information, and the output of the source 10 should be restored as accurately as possible and passed to the sink 60, which is the recipient of the message and can make the person or object.

The channel coding before the polarization code mainly has a turbo code and an LDPC code. The Turbo code is formed by two or more simple component code encoders being cascaded in parallel by an interleaver. The information sequence is first sent to the first encoder, and then interleaved to the second encoder. The output codeword has three parts: the input information sequence, the check sequence generated by the first encoder, and the check sequence generated by the second encoder on the interleaved information sequence. The Turbo code is iteratively decoded. The iteration uses soft input and soft output. The Turbo code is currently the most efficient decoding method between the channel cutoff frequency and the channel capacity. The LDPC code is a special type of (n, k) linear block code, and most of the elements in the check matrix are 0, and only a small part is, that is, H is sparse. Sparseness reduces decoding complexity and makes implementation simpler.

Since the introduction of polarization codes by Arikan in 2009, research on polarization codes has become one of the research hotspots in the field of information theory and coding. The polarization code is a channel coding method that can gradually approach the Shannon limit, has low coding complexity, and can be widely used in various channels.

An important theoretical basis for polarization codes is the polarization characteristics of the channel. Use mapping: w:x→y to represent an abstract BDMC channel, the input of this channel is x={0,1}, the output symbol set is y,w(y|x),x∈x,y∈y: Transition probability of channel w, and definition

Bhattacharyya parameter (ie, Bahatacea parameter) for the discrete binary memoryless channel w

The channel capacity of the discrete binary memoryless channel w. The parameters z(w) and I(w) are a measure of the reliability of the channel w and the maximum transmission rate, respectively. A schematic diagram of a bit channel is given in Figure 2. Given a BDM channel w, the codeword will be encoded.

In this way, it is sent to the channel w and receives the vector.

For any given i, 1 ≤ i ≤ N, a formal channel can be defined

Its input is u _i ∈x and the output is

, the probability of transition is

For any BDM channel, N=2 ^m bit channels with the above transition probability

There is the following polarization phenomenon, for any δ∈(0,1), when N tends to infinity, it satisfies

The number of bit channels and the ratio of the total number of channels tends to I(w), but satisfies

The ratio of the number of bit channels to the total number of bit channels tends to be 1-I(w). It can be found from the above that when N tends to infinity, the symmetric channel capacity of the N bit channels either tends to 1 or tends to 0, which is the polarization phenomenon of the channel. Therefore, information bits can be transmitted with a channel having a channel capacity of 1 at the time of transmission, and fixed bits can be transmitted with a channel having a channel capacity of 0.

Therefore, a key technique for polarization code encoding is that the code construction, ie, the design algorithm, selects those channels that have been fully polarized to transmit information bits, and the remaining channels to transmit fixed bits. There are three algorithms for constructing commonly used codes, namely Monte Carlo method, density evolution method and Gaussian approximation method. All three methods are applicable to Gaussian channel, but Gaussian approximation. The polarization code construction method has better performance and lower complexity.

The most important idea of polarization code coding is to use polarization to construct an encoding system so that information bits can be transmitted through the combined and split channels, which have a capacity of one. The polarization code belongs to a linear block code. The construction of the generator matrix G _N is an important part of the coding process and the core content of the code. It is assumed that any n≥0 has N=2 ⁿ and the definition I _k is k-dimensional. The identity matrix, where k ≥ 1, gives the definition of G _{N for N} ≥ 2

Where G ₁ =I ₁ , matrix

Also due to

Available

Thereby getting

Where B _N is a bit flip matrix. Figure 3 shows a schematic diagram of a bit flip matrix with N = 4.

The polarization code belongs to a G _N coset code, so the coding method uses G _N as the generation matrix, but the method of selecting the information bits is different. The polarization code mainly depends on the channel polarization phenomenon, and the information bits The transmission is performed on a fully polarized channel. The coded block length of the polarization code encoding is strictly defined as a power of two. A vector consisting of K data and another NK fixed data vector for each frame of the coset code

Perform a binary multiplication operation with an N×N matrix G _N to generate a codeword of length N

which is

The classical method of polarization code decoding is to successively cancel the decoding algorithm (SC), which mainly utilizes the recursive property of the polarization code, but also causes delay in decoding due to the recursive property of the polarization code. Since the SC decoding algorithm only retains one decoding path, the front side The failure of the decoding of the bits will greatly increase the likelihood of subsequent decoding failures. The decoding delay direction is mainly implemented on the hardware architecture, and some algorithm implementations are as follows: MSC algorithm; in the direction of decoding accuracy, there is mainly a list cancellation decoding algorithm (LSC). The stack continues to decode the decoding algorithm such as the decoding algorithm (SSC).

As an evolution version of the SC decoding algorithm, the LSC decoding algorithm is not only a path stored every time, but each path is copied and stored in the list, if the path in the list When the number is less than the set value L, each existing path is copied in the next state. If the decoded path in the list is larger than the set value L, the maximum number of paths in the path guarantee list needs to be removed. L. The basis for deleting the path is to select the maximum posterior probability of L in the existing path. The SCL decoding algorithm saves L paths simultaneously in the list, and each path occupies O(N) space, so L paths occupy O(LN). Since the L paths are copied once during decoding, the space occupied by the L paths copied is also O(LN), and since there are N levels in the LSC decoding, the LSC will occupy O(LN ² ). The complexity of the space.

The SSC decoding algorithm can save a lot of unnecessary calculations compared to the LSC algorithm when the signal-to-noise ratio is large, but the stack used in the SSC algorithm is much larger than in the LSC. Generally, in order to reduce the reduction of the decoding effect, the capacity D of the stack should have a large LN, so that the spatial complexity of the decoding becomes O(LN ² ).

Therefore, the prior art has yet to be improved and developed.

Summary of the invention

In view of the above deficiencies of the prior art, it is an object of the present invention to provide an LSC-CRC based The decoded segmented polarization code encoding and decoding method and system aim to solve the problem that the decoding technique in the prior art has high spatial complexity and low decoding accuracy.

The technical solution of the present invention is as follows:

A segmentation polarization code encoding and decoding method based on LSC-CRC decoding, wherein the method comprises the following steps:

A. Combining and splitting multiple independent channels to obtain a bit channel having the same number of independent channels, obtaining the capacity of each bit channel, and counting the number of fully polarized bit channels; wherein, the bit channel The capacity is greater than the preset capacity threshold and is a fully polarized bit channel;

B. The free information bit sequence to be transmitted is divided into corresponding sub-sequences according to the number of fully-polarized bit channels, and each sub-sequence is subjected to polarization code encoding, and the encoded information is sent to corresponding bits. In the channel;

C. After receiving the information at the receiving end, the information is decoded according to the LSC-CRC decoding algorithm, and finally the decoded subsequence obtained after decoding is spliced together to obtain a decoding sequence.

The segmented polarization code encoding and decoding method based on LSC-CRC decoding, wherein the step A specifically includes:

A1. The n independent channels are recursively merged into a combined channel; where n is a positive integer;

A2. The combined channel is split according to the transition probability of the channel, and split into the same bit channel as the number of independent channels;

A3. Obtaining each bit channel according to Monte Carlo method, density evolution method or Gaussian approximation method Capacity

A4. Counting the number of fully polarized bit channels, and counting the number of fully polarized bit channels as m; wherein, if the capacity of the bit channel is greater than 0.9, it is a fully polarized bit channel, and m is a positive integer. And m ≤ n.

The segmentation polarization code encoding and decoding method based on LSC-CRC decoding, wherein the step B specifically includes:

B1, according to the information sequence (n, k) to be transmitted, obtain a free information bit sequence F=round(n×k) to be transmitted; where n is the code length and k is the code rate;

B2. The number of bit channels obtained and fully polarized is recorded as the power number M of the smallest difference of m, and it is determined whether F can be divisible by M;

B3, when F can be divisible by M, the free information bit sequence F to be transmitted is split into R sub-sequences; wherein R=F/M, and the length of each sub-sequence is M;

B4. When F cannot be divisible by M, the quotient of F divided by M is R, the remainder is denoted by Q, and the free information bit sequence F to be transmitted is split into R+1 subsequences; wherein R+1 The sub-sequences of the sub-sequences are filled with sub-sequences of F, and the first Q sub-sequences of the last sub-sequence of R+1 sub-sequences are filled with sub-sequences of F, and the last MQ bits are filled with 0;

B5. Perform polarization code encoding on each subsequence, and send the information after encoding to the corresponding bit channel.

The segmented polarization code encoding and decoding method based on the LSC-CRC decoding, wherein the step C specifically includes:

C1, receiving information after encoding at the receiving end, and according to the LSC-CRC decoding algorithm Segmentation is performed to obtain a decoding subsequence of the corresponding number of segments; wherein the corresponding formula of the LSC-CRC decoding algorithm is as follows:

among them,

Decoding a code likelihood ratio in which the code length is an N-bit sequence number of odd bits,

Indicates that the code length is N bits and the sequence number is even number is the decoding likelihood ratio.

Decoding a code likelihood ratio of a transmission channel by a code channel having a code length of N/2 and a bit channel being two bit channels, or combining channels,

The code length is N/2 and the bit channel is the decoding likelihood ratio of the channel corresponding to the pass bit after the XOR.

Representing a decoding likelihood ratio representing the i-th bit,

Decoding the decoded result of the ith bit;

C2: The decoding subsequences are spliced together to obtain a decoding sequence.

The segmented polarization code encoding and decoding method based on the LSC-CRC decoding, wherein the step C2 specifically includes:

C21, when the free information bit sequence F to be transmitted is split into R sub-sequences, the R decoding sub-sequences are spliced together to obtain a decoding sequence;

C22, when the free information bit sequence F to be transmitted is split into R+1 sub-sequences, Then, the first R decoding subsequences and the first M-Q bits of the last decoding subsequence are concatenated to obtain a decoding sequence.

A segmented polarization code encoding and decoding system based on LSC-CRC decoding, which comprises:

The channel processing and calculation statistics module is configured to combine and split a plurality of independent channels to obtain a bit channel having the same number of independent channels, obtain the capacity of each bit channel, and obtain a completely polarized bit channel by statistics. a number; wherein, the capacity of the bit channel is greater than a preset capacity threshold; then the fully polarized bit channel;

a dividing and encoding module, configured to divide the free information bit sequence to be transmitted into a sub-sequence of a corresponding number according to the number of fully-polarized bit channels, perform polarization code encoding on each sub-sequence, and encode the information after the information Sent to the corresponding bit channel;

The decoding splicing module is configured to receive the information after the encoding at the receiving end, perform segmentation according to the LSC-CRC decoding algorithm, and finally splicing the decoded subsequences obtained after decoding to obtain a decoding sequence.

The segmentation polarization code coding and decoding system based on LSC-CRC decoding, wherein the channel processing and calculation statistics module specifically includes:

a recursive merging unit for recombining n independent channels into a merged channel; wherein n is a positive integer;

a splitting unit, configured to split the merged channel according to a transition probability of the channel, and split the split channel into the same number of channels as the independent channel;

a capacity acquisition unit, configured to acquire a capacity of each bit channel according to a Monte Carlo method, a density evolution method, or a Gaussian approximation method;

Statistical unit for counting the number of fully polarized bit channels, which will be completely The number of bit channels is denoted by m; wherein, if the capacity of the bit channel is greater than 0.9, it is a fully polarized bit channel, m is a positive integer, and m ≤ n.

The segmentation and polarization coding and coding system based on LSC-CRC decoding, wherein the division and coding module specifically includes:

a free information bit sequence obtaining unit, configured to obtain a free information bit sequence F=round(n×k) to be transmitted according to the information sequence (n, k) to be transmitted; wherein n is a code length, and k is a code rate;

The divisibility determining unit is configured to obtain a power order M of 2, which is the smallest difference between the number of the fully polarized bit channels and m, and determine whether F can be divisible by M;

a first splitting unit, configured to split the free information bit sequence F to be transmitted into R subsequences when F can be divisible by M; wherein R=F/M, and each subsequence has a length of M;

a second splitting unit, when F cannot be divisible by M, then the quotient of F divided by M is R, the remainder is denoted by Q, and the free information bit sequence F to be transmitted is split into R+1 sub- a sequence; wherein the first R subsequences of the R+1 subsequences are filled with sub-sequences of F, and the first Q sub-sequences of the last sub-sequence of the R+1 sub-sequences are filled with sub-sequences of F, followed by MQ bits Filled with 0;

A polarization and transmitting unit is configured to perform polarization code encoding on each subsequence, and send the encoded information to a corresponding bit channel.

The segmented polarization code encoding and decoding system based on LSC-CRC decoding, wherein the decoding and splicing module specifically includes:

a decoding unit, configured to receive information after encoding at the receiving end, and according to LSC-CRC The decoding algorithm performs segmentation to obtain a decoding subsequence of the corresponding number of segments; wherein the corresponding formula of the LSC-CRC decoding algorithm is as follows:

among them,

It indicates that the code length is N/2 and the bit channel is the decoding likelihood ratio of the combined channel corresponding to the pass bit after no XOR.

Representing a decoding likelihood ratio representing the i-th bit,

Decoding the decoded result of the ith bit;

A splicing unit for splicing the decoding subsequences to obtain a decoding sequence.

The segmented polarization code encoding and decoding system based on LSC-CRC decoding, wherein the splicing unit specifically includes:

a first splicing sub-unit, configured to: when the free information bit sequence F to be transmitted is split into R sub-sequences, the R decoding sub-sequences are spliced together to obtain a decoding sequence;

a second splicing unit for splitting the free information bit sequence F to be transmitted In the case of R+1 subsequences, the first R decoding subsequences and the first M-Q bits of the last decoding subsequence are concatenated to obtain a decoding sequence.

The method and system for segmentation polarization code encoding and decoding based on LSC-CRC decoding provided by the present invention include: combining and splitting multiple independent channels to obtain a bit channel having the same number of independent channels. Obtaining the capacity of each bit channel, and counting the number of completely polarized bit channels; dividing the free information bit sequence to be transmitted into a corresponding number of sub-sequences according to the number of fully polarized bit channels, for each sub-sequence The sequence is subjected to polarization code encoding, and the information after encoding is sent to the corresponding bit channel; the information after encoding is received at the receiving end, segmented according to the LSC-CRC decoding algorithm, and finally decoded. The decoding subsequences are spliced together to obtain a decoding sequence. The source coding and decoding method in the present invention is simple in operation, the spatial complexity of the compiled code is reduced, and the decoding accuracy is improved.

DRAWINGS

Figure 1 is a schematic diagram of a communication system model.

2 is a schematic diagram of a bit channel.

Figure 3 is a schematic diagram of bit flipping when N = 4.

4 is a schematic diagram showing the relationship between capacity and channel number after channel polarization.

5 is a comparison diagram of bit error rates of the LSC-CRC decoding algorithm and the LPC-CRC decoding based segmentation polarization code encoding and decoding method according to the LSC-CRC decoding algorithm with a code rate of 0.5 code lengths of 0.5, 256, and 1024, respectively.

6 is a comparison of bit error rates between the LSC-CRC decoding algorithm and the LPC-CRC decoding based segmentation polarization code encoding and decoding method with a code rate of 0.5 code lengths of 128, 256, and 1024, respectively. Figure.

7 is a flow chart of a preferred embodiment of a segmentation polarization code encoding and decoding method based on LSC-CRC decoding according to the present invention.

FIG. 8 is a structural block diagram of a preferred embodiment of a segmented polarization code encoding and decoding system based on LSC-CRC decoding according to the present invention.

detailed description

The present invention provides a segmented polarization code encoding and decoding method and system based on LSC-CRC decoding. In order to make the objects, technical solutions and effects of the present invention more clear and clear, the present invention will be further described in detail below. It is understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

FIG. 7 is a flowchart of a preferred embodiment of a method for encoding and decoding a piecewise polarization code based on LSC-CRC decoding according to the present invention. The method includes the following steps:

Step S100: Combine and split a plurality of independent channels to obtain a bit channel having the same number of independent channels, obtain a capacity of each bit channel, and obtain a number of fully polarized bit channels according to statistics; wherein, the bit channel The capacity is greater than the preset capacity threshold and is a fully polarized bit channel;

Step S200: The free information bit sequence to be transmitted is divided into corresponding sub-sequences according to the number of fully-polarized bit channels, and each sub-sequence is subjected to polarization code encoding, and the encoded information is sent to the corresponding In the bit channel;

Step S300: After receiving the information after encoding, the information is decoded according to the LSC-CRC decoding algorithm, and finally the decoded subsequence obtained after decoding is stitched together. To the decoding sequence.

In the embodiment of the present invention, first, by using a method of constructing a polarization code, the capacity of a bit channel obtained after combining and splitting a plurality of independent channels is obtained, and then the capacity of the bit channel is calculated to be greater than a preset capacity. The number of channels of the threshold, and then split the sequence of free information bits to be transmitted into a plurality of sub-sequences, each of which has a length of M, and then encodes the polarization code of the sub-sequence after the split, and then encodes The information is transmitted to the corresponding bit channel, and after receiving the transmitted information, the receiving end performs segmentation decoding according to the LSC-CRC decoding algorithm, and then the first bit of each decoding subsequence is spliced to obtain a decoding sequence.

Specifically, the step S100 specifically includes:

Step S101: Combine n independent channels into a combined channel by recursion; wherein n is a positive integer.

The channel is merged by recursively combining n independent channels into one entire channel, which is recorded as a combined channel, and the sum of the capacity of the combined channel and the capacity of the N independent channels before the combining is the same. Where n can also represent the code length. When n=2, only the combination and splitting of the channel need to be performed once. When n is greater than 2, the splitting and combination of the log ₂ N channels are required, so the code length n is required. Must be a power of 2.

Step S102, splitting the combined channel according to the transition probability of the channel, and splitting into the same bit channel as the number of independent channels.

The splitting of the channel is to split the combined channel into n bit channels according to the transition probability of the channel. After the channel is merged and split, the bit channel has polarization characteristics, and a part of the channel tends to 1. It is used to transmit information bits. , another part of the channel tends to 0, its use To transmit fixed bits (usually 0).

Step S103: Obtain a capacity of each bit channel according to a Monte Carlo method, a density evolution method, or a Gaussian approximation method.

The method of constructing the polarization of each bit channel after channel splitting can be obtained by means of a polarization code. There are three specific methods for constructing a polarization code: Monte Carlo method, density evolution method and Gaussian approximation method. One of the methods can be selected to construct the bit channel capacity.

If the Monte Carlo method is used to obtain the capacity of the channel, the following steps are included:

(2A) The Gaussian channel transmits all 0 codewords, and is transmitted to the channel after BPSK modulation;

(2B) calculating an initial likelihood value on the channel based on the output of the channel, ie

(2C) calculation

among them

(2D) if

Then the estimate of the bit is 0, then the capacity of the ith channel is:

If

Then the channel estimate of the bit is 1, and the capacity of the ith channel is:

2E) The above process is repeated a plurality of times, for example, 1000 times, that is, 1000 codewords are transmitted, and 1000 Z values obtained on each subchannel are weighted and averaged to obtain an approximate Bhattacharyya value on the subchannel (ie, Bahatace Sub-values), then sort the values from small to arrival.

If the density evolution algorithm is used to obtain the channel capacity, the following steps are included:

(2a) is not general. All 0 codewords are still transmitted under Gaussian channel, and channel is transmitted after BPSK modulation.

(2b) Calculating the initial likelihood value on the channel based on the channel transmission

(2c) calculation

among them:

(2d) according to

Calculate the error probability function value of the subchannel:

(2e) Sorting the subchannel error probability to obtain the channel capacity.

If the Gaussian approximation method is used to obtain the channel capacity, the following steps are included:

(21) Calculate the initial likelihood value on the channel according to the output of the channel under the Gaussian channel

Here

(22) Calculated according to the following formula

If i is an odd number

If i is even, then

among them,

(23) Calculate the error probability of each channel

(24) The subchannel error probability is sorted to complete the construction of the code to obtain the capacity of the channel.

When the number m of fully polarized bit channels is acquired in step S103, the capacity of the bit channels after polarization is simultaneously arranged from large to small, and the sequence numbers of the corresponding bit channels are recorded to form a sequence of Inds.

Step S104: Statistics acquire the number of fully polarized bit channels, and fully polarize The number of bit channels is denoted by m; wherein, if the capacity of the bit channel is greater than 0.9, it is a fully polarized bit channel, m is a positive integer, and m ≤ n.

According to step S103, the capacity of each bit channel after splitting can be obtained. In the present invention, a bit channel whose channel capacity is greater than 0.9 can be regarded as a fully polarized bit channel, and the capacity of the bit channel obtained after statistically splitting the channel is greater than 0.9. The number of channels is the number of fully polarized bit channels. In the present invention, the number of fully polarized bit channels is denoted by m, m is a positive integer, and m ≤ n. The sequence of information after splitting is separately encoded

among them

The subscript is a portion of the free information bit sequence F to be transmitted that is split for the pre-M bits in the Inds sequence, with the remaining bits having a value of zero.

4 shows the relationship between the capacity after channel polarization and the channel number. The abscissa Bit Channel Index (i) of FIG. 4 indicates the channel number, and the ordinate Capacity of i th channel indicates the capacity of the ith channel.

When the code length is 64, 128, 256, 512, 1024 and the code rate is 0.5, 0.7, the number M of fully polarized channels is counted. Please refer to Table 1 below, and Figure 5 and Figure 6:

Table 1

In Figure 5 and Figure 6, the corresponding code rate is 0.5 (that is, rate = 0.5) when there are different error blocks. (ie EB, the abscissa of both Figures 5 and 6 are EB) corresponding bit error rate (ie BER, both BER of Figure 5 and Figure 6 are BER).

Preferably, the step S200 specifically includes:

Step S201: Obtain a free information bit sequence F=round(n×k) to be transmitted according to the information sequence (n, k) to be transmitted; where n is a code length and k is a code rate.

Describe the sequence of information to be transmitted as (n, k), then define the sequence of free information bits to be transmitted as F=round (n×k), and split the F according to the number of fully polarized bit channels. .

Step S202: Obtain a power number M of 2 which is the smallest difference between m and the fully polarized bit channel, and determine whether F can be divisible by M.

According to the number of fully polarized bit channels counted in step S104, the code length of the coded code must be a power of 2, and m may not be a power of 2, so m is required. Correction is made to specifically correct m to a power M of 2 closest to m.

Step S203, when F can be divisible by M, the free information bit sequence F to be transmitted is split into R sub-sequences; where R=F/M, and the length of each sub-sequence is M;

Step S204: When F cannot be divisible by M, then F is divided by M, the quotient is R, the remainder is recorded as Q, and the free information bit sequence F to be transmitted is split into R+1 subsequences; wherein R+ The first R subsequences of the one subsequence are filled with the subsequence of F, and the first Q subsequences of the last subsequence of the R+1 subsequences are filled with the subsequence of F, and the last MQ bits are filled with 0;

Step S205, performing polarization code encoding on each subsequence, and using the information after encoding Send to the corresponding bit channel.

The encoded information is sent to the bit channel for transmission. It is specified in the polarization code that the free bits are transmitted in the channel where the channel capacity tends to be perfect after polarization, and the fixed bits in the channel that becomes completely noisy after polarization are generally zero. For an information sequence with a code length of N and a code rate R, the number of bits of information bits to be transmitted is F. In the previous method, F bit channels are directly selected according to the channel capacity to transmit information bits. This will result in a bit channel whose channel capacity is not very large after some polarization is selected to transmit information bits, resulting in a greatly increased probability of decoding errors occurring at the receiving end decoding. Therefore, in the present invention, the information bit is transmitted by the channel having the capacity of the bit channel greater than 0.9 by the step S104 described above, so that the accuracy of decoding short decoding is greatly improved, which is also the channel transmission of the present invention. The characteristics are located.

Preferably, in the segmentation polarization code encoding and decoding method based on the LSC-CRC decoding, the step S300 specifically includes:

Step S301: Receive information after encoding at the receiving end, and perform segmentation according to the LSC-CRC decoding algorithm to obtain a decoding subsequence of the corresponding number of segments; wherein the corresponding formula of the LSC-CRC decoding algorithm is as follows:

among them,

Representing a decoding likelihood ratio representing the i-th bit,

Decoding the decoded result of the ith bit;

Step S302: splicing the decoding subsequences to obtain a decoding sequence.

The decoding algorithm employed in the present invention is an LSC-CRC decoding algorithm, and CRC is a loop check algorithm. The LSC-CRC decoding algorithm is an improvement proposed in the SC decoding algorithm. Only one path is reserved in the SC decoding algorithm, and the failure of the previous bit decoding may cause the subsequent bit decoding failure to be greatly increased. The LSC decoding algorithm can solve this problem by storing up to L paths for decoding, and then selecting the best decoding path among the L paths can greatly improve the decoding accuracy, since L paths are introduced. It is possible to make the loop check possible. The L paths after decoding are merged into the CRC checker for verification, and the path that can pass the CRC check is selected as the final decoding path. If all the paths cannot pass, The CRC check fails.

Preferably, in the segmentation polarization code encoding and decoding method based on the LSC-CRC decoding, the step S302 specifically includes:

Step S3021, when the free information bit sequence F to be transmitted is split into R subsequences When the R decoding subsequences are first and last spliced together to obtain a decoding sequence;

Step S3022: When the free information bit sequence F to be transmitted is split into R+1 sub-sequences, the first R decoding sub-sequences and the first MQ bits of the last decoding sub-sequence are spliced together to obtain a decoding sequence. .

It can be seen that the present invention greatly improves the accuracy of decoding the polarization code compared with the prior art. It can be seen from the simulation that when the code length is 1024 and the code rate is 0.5, the information sequence to be transmitted is split into two segments and then transmitted, and the bit error rate or the bit error rate can reach 0.

Based on the foregoing method embodiments, the present invention further provides a segmented polarization code encoding and decoding system based on LSC-CRC decoding. As shown in FIG. 8, the segmentation polarization code encoding and decoding system based on LSC-CRC decoding includes:

The channel processing and calculation statistics module 100 is configured to combine and split a plurality of independent channels to obtain a bit channel with the same number of independent channels, obtain the capacity of each bit channel, and obtain a fully polarized bit channel by statistics. a number; wherein, the capacity of the bit channel is greater than a preset capacity threshold; then the fully polarized bit channel;

The dividing and encoding module 200 is configured to divide the free information bit sequence to be transmitted into a corresponding number of sub-sequences according to the number of fully polarized bit channels, and perform polarization code encoding on each sub-sequence, after encoding Information is sent to the corresponding bit channel;

The decoding splicing module 300 is configured to receive the information after the encoding at the receiving end, perform segmentation according to the LSC-CRC decoding algorithm, and finally splicing the decoded subsequences obtained after decoding to obtain a decoding sequence.

Preferably, in the segmentation polarization code encoding and decoding system based on LSC-CRC decoding, The channel processing and calculation statistics module 100 specifically includes:

a statistical unit, configured to obtain the number of fully polarized bit channels, and record the number of fully polarized bit channels as m; wherein, if the capacity of the bit channel is greater than 0.9, it is a fully polarized bit channel, where m is A positive integer and m ≤ n.

Preferably, in the segmentation and polarization coding and coding system based on the LSC-CRC decoding, the division and coding module 200 specifically includes:

a second splitting unit, when F cannot be divisible by M, then the quotient of F divided by M is R, the remainder is denoted by Q, and the free information bit sequence F to be transmitted is split into R+1 a subsequence; wherein the first R subsequences of the R+1 subsequences are filled with sub-sequences of F, and the first Q sub-sequences of the last sub-sequence of the R+1 sub-sequences are filled with sub-sequences of F, followed by MQ bits Bits are filled with 0;

Preferably, in the segmentation polarization code coding and decoding system based on the LSC-CRC decoding, the decoding and splicing module 300 specifically includes:

The decoding unit is configured to receive the information after the encoding at the receiving end, and perform segmentation according to the LSC-CRC decoding algorithm to obtain a decoding subsequence of the corresponding number of segments; wherein the corresponding formula of the LSC-CRC decoding algorithm is as follows:

among them,

Decoding a code likelihood ratio of a transmission channel by a code length of N/2 and a bit channel of two exclusive ORs,

Representing a decoding likelihood ratio representing the i-th bit,

Decoding the decoded result of the ith bit;

Preferably, in the segmentation polarization code coding and decoding system based on the LSC-CRC decoding, the splicing unit specifically includes:

a second splicing sub-unit, configured to: when the free information bit sequence F to be transmitted is split into R+1 sub-sequences, the first R decoding sub-sequences and the first M-bits of the last decoding sub-sequence are spliced Get the decoding sequence

In summary, the method and system for segmentation polarization code encoding and decoding based on LSC-CRC decoding provided by the present invention include: combining and splitting multiple independent channels to obtain independent channel numbers. Obtaining the capacity of each bit channel by using the same bit channel, and counting the number of fully polarized bit channels; dividing the free information bit sequence to be transmitted into a corresponding number of subsequences according to the number of fully polarized bit channels Performing polarization code encoding on each subsequence, and transmitting the information after encoding to the corresponding bit channel; receiving the information after encoding at the receiving end, decoding according to the LSC-CRC decoding algorithm, and finally decoding The decoded subsequences obtained after decoding are spliced together to obtain a decoding sequence. The source coding and decoding method in the present invention is simple in operation, the spatial complexity of the compiled code is reduced, and the decoding accuracy is improved.

It is to be understood that the application of the present invention is not limited to the above-described examples, and those skilled in the art can make modifications and changes in accordance with the above description, all of which are within the scope of the appended claims.

Claims

A segmented polarization code encoding and decoding method based on LSC-CRC decoding, characterized in that the method comprises the following steps:

A. Combining and splitting multiple independent channels to obtain a bit channel having the same number of independent channels, obtaining the capacity of each bit channel, and counting the number of fully polarized bit channels; wherein, the bit channel The capacity is greater than the preset capacity threshold and is a fully polarized bit channel;

B. The free information bit sequence to be transmitted is divided into corresponding sub-sequences according to the number of fully-polarized bit channels, and each sub-sequence is subjected to polarization code encoding, and the encoded information is sent to corresponding bits. In the channel;

C. After receiving the information at the receiving end, the information is decoded according to the LSC-CRC decoding algorithm, and finally the decoded subsequence obtained after decoding is spliced together to obtain a decoding sequence.
The segmentation polarization code encoding and decoding method based on LSC-CRC decoding according to claim 1, wherein the step A specifically includes:

A1. The n independent channels are recursively merged into a combined channel; where n is a positive integer;

A2. The combined channel is split according to the transition probability of the channel, and split into the same bit channel as the number of independent channels;

A3. Obtain a capacity of each bit channel according to a Monte Carlo method, a density evolution method, or a Gaussian approximation method;

A4. Statistics to obtain the number of fully polarized bit channels, which will be fully polarized bits. The number of channels is denoted by m; wherein, if the capacity of the bit channel is greater than 0.9, it is a fully polarized bit channel, m is a positive integer, and m ≤ n.
The segmentation polarization code encoding and decoding method based on LSC-CRC decoding according to claim 2, wherein the step B specifically includes:

B1, according to the information sequence (n, k) to be transmitted, obtain a free information bit sequence F=round(n×k) to be transmitted; where n is the code length and k is the code rate;

B2. The number of bit channels obtained and fully polarized is recorded as the power number M of the smallest difference of m, and it is determined whether F can be divisible by M;

B3, when F can be divisible by M, the free information bit sequence F to be transmitted is split into R sub-sequences; wherein R=F/M, and the length of each sub-sequence is M;

B4. When F cannot be divisible by M, the quotient of F divided by M is R, the remainder is denoted by Q, and the free information bit sequence F to be transmitted is split into R+1 subsequences; wherein R+1 The sub-sequences of the sub-sequences are filled with sub-sequences of F, and the first Q sub-sequences of the last sub-sequence of R+1 sub-sequences are filled with sub-sequences of F, and the last MQ bits are filled with 0;

B5. Perform polarization code encoding on each subsequence, and send the information after encoding to the corresponding bit channel.
The method of claim 3, wherein the step C includes:

C1, receiving the information after encoding at the receiving end, and performing segmentation according to the LSC-CRC decoding algorithm to obtain a decoding subsequence of the corresponding number of segments; wherein the corresponding formula of the LSC-CRC decoding algorithm is as follows:

among them,
Decoding a code likelihood ratio in which the code length is an N-bit sequence number of odd bits,
Indicates that the code length is N bits and the sequence number is even number is the decoding likelihood ratio.
Decoding a code likelihood ratio of a transmission channel by a code channel having a code length of N/2 and a bit channel being two bit channels, or combining channels,
The code length is N/2 and the bit channel is the decoding likelihood ratio of the channel corresponding to the pass bit after the XOR.
Representing a decoding likelihood ratio representing the i-th bit,
Decoding the decoded result of the ith bit;

C2: The decoding subsequences are spliced together to obtain a decoding sequence.
The segmented polarization code encoding and decoding method based on the LSC-CRC decoding according to claim 4, wherein the step C2 specifically includes:

C21, when the free information bit sequence F to be transmitted is split into R sub-sequences, the R decoding sub-sequences are spliced together to obtain a decoding sequence;

C22. When the free information bit sequence F to be transmitted is split into R+1 subsequences, the first R decoding subsequences and the first M-Q bits of the last decoding subsequence are concatenated to obtain a decoding sequence.
A piecewise polarization code encoding and decoding system based on LSC-CRC decoding, its characteristics The method includes: a channel processing and a calculation statistics module, configured to combine and split a plurality of independent channels to obtain a bit channel having the same number of independent channels, obtain a capacity of each bit channel, and obtain a fully polarized a number of bit channels; wherein, the capacity of the bit channel is greater than a preset capacity threshold; then a fully polarized bit channel; and a partitioning and coding module for using the free information bit sequence to be transmitted according to the fully polarized bit channel The number is divided into corresponding sub-sequences, each sub-sequence is subjected to polarization code encoding, and the encoded information is sent to the corresponding bit channel; the decoding splicing module is used after receiving the encoding at the receiving end The information is decoded according to the LSC-CRC decoding algorithm, and finally the decoded subsequence obtained by decoding is spliced together to obtain a decoding sequence.
The piecewise polarization code coding and decoding system based on LSC-CRC decoding according to claim 6, wherein the channel processing and calculation statistics module comprises: a recursive merging unit, configured to pass n independent channels Recursively merge into a merged channel; where n is a positive integer; a splitting unit is used to split the merged channel according to the transition probability of the channel, and split into the same bit channel as the number of independent channels; the capacity acquisition unit uses Obtaining the capacity of each bit channel according to Monte Carlo method, density evolution method or Gaussian approximation method;

a statistical unit, configured to obtain the number of fully polarized bit channels, and record the number of fully polarized bit channels as m; wherein, if the capacity of the bit channel is greater than 0.9, it is a fully polarized bit channel, where m is A positive integer and m ≤ n.
The piecewise polarization code encoding and decoding system based on the LSC-CRC decoding according to claim 7, wherein the dividing and encoding module comprises: a free information bit sequence acquiring unit, configured to use the information sequence to be transmitted. (n, k), obtaining a free information bit sequence F=round(n×k) to be transmitted; wherein n is a code length and k is a code rate;

The divisibility determining unit is configured to obtain a power order M of 2, which is the smallest difference between the number of the fully polarized bit channels and m, and determine whether F can be divisible by M;

a first splitting unit, configured to split the free information bit sequence F to be transmitted into R subsequences when F can be divisible by M; wherein R=F/M, and each subsequence has a length of M;

a second splitting unit, when F cannot be divisible by M, then the quotient of F divided by M is R, the remainder is denoted by Q, and the free information bit sequence F to be transmitted is split into R+1 sub- a sequence; wherein the first R subsequences of the R+1 subsequences are filled with sub-sequences of F, and the first Q sub-sequences of the last sub-sequence of the R+1 sub-sequences are filled with sub-sequences of F, followed by MQ bits Each is padded with 0; a polarization and transmission unit is configured to perform polarization code encoding on each subsequence, and transmit the information after encoding to the corresponding bit channel.
The segmented polarization code encoding and decoding system based on the LSC-CRC decoding according to claim 8, wherein the decoding and splicing module specifically comprises:

The decoding unit is configured to receive the information after the encoding at the receiving end, and perform segmentation according to the LSC-CRC decoding algorithm to obtain a decoding subsequence of the corresponding number of segments; wherein the corresponding formula of the LSC-CRC decoding algorithm is as follows:

among them,
Decoding a code likelihood ratio in which the code length is an N-bit sequence number of odd bits,
Indicates that the code length is N bits and the sequence number is even number is the decoding likelihood ratio.
Decoding a code likelihood ratio of a transmission channel by a code channel having a code length of N/2 and a bit channel being two bit channels, or combining channels,
The code length is N/2 and the bit channel is the decoding likelihood ratio of the channel corresponding to the pass bit after the XOR.
Representing a decoding likelihood ratio representing the i-th bit,
Representing the decoding result of the ith bit; a splicing unit for splicing the decoding subsequences to obtain a decoding sequence.
The segmented polarization code encoding and decoding system based on LSC-CRC decoding according to claim 9, wherein the splicing unit specifically comprises:

a first splicing sub-unit, configured to: when the free information bit sequence F to be transmitted is split into R sub-sequences, the R decoding sub-sequences are spliced together to obtain a decoding sequence;

a second splicing sub-unit, configured to: when the free information bit sequence F to be transmitted is split into R+1 sub-sequences, the first R decoding sub-sequences and the first M-bits of the last decoding sub-sequence are spliced Get the decoding sequence.