CN106059596B - Using binary BCH code as the grouping markov supercomposed coding method and its interpretation method of composition code - Google Patents

Abstract

The invention belongs to the fields of digital communication and digital storage, and discloses an encoding method and a decoding method of a component code using a binary BCH code as a grouped Markov superposition encoding method, comprising: taking the code length as n and the information bit length as A binary BCH code of k and error correction capability t _min encodes a binary information sequence u of length K=kBL into a codeword c of length N=nB(L+m) as a component code. The present invention also proposes a soft iterative decoding method suitable for the block Markov superposition coding method with binary BCH code as the component code, including generating a flip pattern according to a tree structure, and using the unreliability lower bound of the potential legal error pattern to determine whether to terminate Test process and calculate soft information output, etc. The block Markov superposition coding method and its decoding method proposed by the present invention can take the value of {1, 2, 3} with the coding memory length m, and can achieve a bit error rate performance as low as ^10-10 to ^10-15 orders of magnitude. Provides a net coding gain higher than 10dB, and can be used in communication systems with low bit error rate requirements such as optical fiber communication.

Description

Block Markov Superposition Coding Method Using Binary BCH Code as Component Code and Its Decoding code method

technical field

The invention belongs to the field of digital communication and digital storage, and particularly relates to a block Markov superposition coding method and a decoding method using binary BCH codes as component codes.

Background technique

In optical communication systems, BCH codes with high code rates (generally higher than 0.8) are often used as component codes for concatenated/product error correction coding to obtain high information transmission rates and extremely low bit error rates (BER) (generally on the order of ^10-10 to ^10-15 ). For example, in the International Telegraph Union Telecommunication Standardization Sector (ITU-T) standard G.975.1, a BCH-BCH product code with an overhead of 6.7% can provide a net coding gain of 9.24dB at an output bit error rate of ^10-15 (net coding gain, NCG). Under the condition of using the same overhead, the staircase code (staircase code) can obtain a net coding gain of 9.41dB at the same bit error rate. However, in the design process, under a given code rate requirement, the ladder code needs to use a brute force search method to obtain design parameters that meet the performance requirements, which greatly increases the complexity and workload of the design process.

Block Markov Superposition Coding (Sun Yat-Sen University, A Block Markov Superposition Coding Method [P]: CN105152060A) is a coding method for constructing large convolutional codes from short codes, wherein the short codes are called basic codes. The performance lower bound of block Markov superposition coding can be defined by the performance of the basic code and its memory length m. For block Markov superposition coding with code memory m, its bit error rate performance is relative to that of the basic code. A gain of up to 10log ₁₀ (m+1)dB is possible. When designing a system that requires a bit error rate performance of the order of 10 ^-10 to 10 ^-15 , if short single parity check code and short repetition code are used as component codes, the system is required to set up to several tens of memory lengths. The larger the memory length, the higher the complexity of the decoding method, which makes this scheme unsuitable for some systems with high delay requirements.

The block Markov superposition coding method can be decoded by a windowing iterative algorithm based on soft information or a two-stage decoding algorithm (Sun Yat-sen University, a two-stage decoding algorithm for block Markov superposition coding [P]: CN103944590A) code. When a soft iterative decoding method is involved in the decoding method, the basic code is required to provide a soft-in and soft-out decoding method to realize the soft iterative decoding process. When the binary BCH code is used to form the basic code of the block Markov superposition coding method, the binary BCH code as the component code also needs to provide a soft-in and soft-out decoding method. At present, when binary BCH codes are used as component codes, two commonly used soft-in and soft-out decoding methods are based on trellis and based on Chase-II decoding. The trellis-based decoding method is an optimal method, which can establish state transition according to the structure of binary BCH code and obtain soft information output through BCJR algorithm, but this method is only suitable for short codes with small error correction ability. The general binary BCH code is too complex to be suitable for practical systems. The decoding method based on Chase-II is often used in the soft iterative decoding of the block Turbo code. Using this method often requires multiple attempts to select the correction factor.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a grouped Markov superposition coding method with binary BCH code as the component code, which is simple in steps, convenient in implementation and low in complexity, aiming at the deficiencies in the above-mentioned prior art. Aiming at the shortcomings of the current soft-in and soft-out decoding methods of binary BCH codes, the present invention provides a soft-in and soft-out decoding method when binary BCH codes with early termination conditions are used as component codes. The invention selects the Cartesian product of the binary BCH code that meets the requirements as the basic code, and only requires the encoding memory m=1 when the bit error rate of the order of ^10-15 reaches the 11dB order of net coding gain required by the optical communication system. 2,3, can reduce the coding and decoding delay. The invention provides a soft-in and soft-out decoding method when a binary BCH code with an early termination condition is used as a component code, which can adjust the calculation resource allocation at each stage in the process of soft iterative decoding, thereby simplifying the design process and reducing decoding. Code complexity, that is: increasing computing resources in the early stage of iteration to improve the accuracy of soft output, reducing computing resources in the later stage of iteration to save expenses, and improving decoding performance under the condition of limited delay without using correction factors .

The technical scheme adopted in the present invention is: a block Markov superposition coding method using binary BCH code as component code, characterized in that: the code length is n, the information bit length is k and the error correction capability is t _min The binary BCH code is a component code, which is used to encode the binary information sequence u of length K=kBL into a codeword c of length N=nB(L+m). The encoding method includes the following steps:

(1.1) Divide the information sequence u of length K=kBL into L equal-length packets u = ( u ⁽⁰⁾ , u ⁽¹⁾ ,... u ^(L-1) ), each packet length is kB; for t =-1,-2,...,-(m-1),-m, initialize the sequence v ^(t) with length nB; m is the length of the coding memory, which is a positive integer greater than or equal to 1; B is a positive integer;

(1.1) At t=0,1,...,L-1, the sequence of length kB is Divide into B groups for [n, k] binary BCH code encoding, and obtain a coding sequence of length nB And combine v ^(t-1) , v ^{(t -2)} ,... v ^(tm) to calculate the t-th subsequence c ^(t) of the codeword c . The v (t) is combined with v (t-1), v (t-2),..., v (tm) to calculate the t (t≥0) subsequence c (t) of the codeword c according to the following steps :

First, for 1≤i≤m, the sequence v (ti) is sent to the interleaver Π _i to obtain a sequence w (i) with a length of nB after interleaving;

Then, v (t) and w (1), w (2),..., w (m) are fed into the symbol-by-symbol aliaser S to obtain a sequence c (t) of length nB.

In the coding method of the present invention, the information sequence u is a binary sequence, and the symbol-by-symbol aliaser S is a bit-by-bit modulo-2 sum operator. Encoder C can be any type of encoder. The interleaver Π _i can be any type of interleaver, 1≤i≤m.

A block Markov superposition coding method using binary BCH code as a component code proposed by the present invention is suitable for the above-mentioned coding method. The decoding method can use a soft iterative decoding method, such as a windowed decoding method. Two-stage decoding method for soft iterative process, etc. The decoding algorithm consists of a flip pattern priority queue The hard-decision decoder is composed of the legal error pattern set ε, including the following steps:

(2.1) Configure the maximum number of tests T, where T is a positive integer.

(2.2) Input soft information; obtain hard decision sequence z and unreliability sequence λ from the input soft information.

The input soft information refers to the iterative information transmitted in the soft iterative decoding algorithm, that is, the log-likelihood ratio of each bit of the BCH codeword:

where P _a (c _j =0) and P _a (c _j =1) represent the prior probabilities that the codeword bits are 0 and 1, respectively.

Each component in the hard-decision sequence z = (z ₀ , z ₁ , . . . , z _n-1 ) is calculated as follows,

Each component in the unreliability sequence λ = (λ ₀ ,λ ₁ ,...,λ _n-1 ) is calculate.

(2.3) Initialization: set the test count τ=0; sort λ to get an ascending sequence and calculate The corresponding position ^index sequence a in λ of each component in Initialize an empty queue and put an all-zero pattern into it middle. The position index sequence a = (a ₀ ,a ₁ ,...,a _n-1 ) obtained in the step (2.3) should satisfy The calculation method of the unreliability of the legal error pattern is as follows: given an error pattern e = (e ₀ , e ₁ , . . . , e _n-1 ), its unreliability is equal to

(2.4) Perform the following iterations until τ ≥ T, or is empty, or The lower bound corresponding to the first element of is not less than λ ^* : in , call the hard-decision decoder to perform test decoding according to the flip pattern provided by the team leader, and add 1 to τ. If the decoding is successful, put the obtained legal error pattern into ε, and calculate the unreliability. If the reliability is less than λ ^* , assign it to λ ^* ; assign The team leader is assigned to f and dequeued, and a new flip pattern is generated based on the tree structure according to f, and the unreliability lower bound of the corresponding potential legal error pattern is calculated for each flip pattern obtained, and the priority queue Use the Nether as the size relationship and place the flip pattern with the smallest Nether at the head of the team.

(2.5) Finally, the soft information is calculated according to the obtained ε and output. output soft information Calculated as follows:

(2.5.1) From the legal error pattern set ε, calculate the codeword set according to the following method

(2.5.2) Output soft information Calculated as follows:

if

if but

in, and

In particular, the test decoding method in the step (2.4) is described as follows: given a flip pattern f=(f ₀ , f ₁ , . . . , f _n-1 ), at the position {a _j |f _j =1, Flip z at 0≤j≤n-1} to get the flipped version of z Using a hard-decision decoder pair to decode. The hard-decision decoder may use hard-decision decoding algorithms including but not limited to Berlekamp-Massey (BM) algorithm, Euclidean algorithm, Welch-Berlekamp (WB) algorithm, and the like.

And, the tree structure-based flip pattern generation method is described as follows: given flip pattern f=(f ₀ , f ₁ ,..., f _n-1 ), define the order of f as

If R(f)≥nt _min , no new flip pattern is generated; otherwise, its left son f _↓ and right brother f _→ are generated. The left son f _↓ is obtained by flipping f at position R(f)+1. Right sibling f _→ is obtained by flipping f at positions R(f) and R(f)+1.

And, the calculation method of the unreliability lower bound B(f) of the potential legal error pattern is: given the flip pattern f=(f ₀ ,f ₁ ,...,f _n-1 ),

Compared with the prior art, the present invention has the following advantages:

1. The present invention uses binary BCH code as the component code of the block Markov superposition coding method. Compared with other codes suitable for optical communication based on product codes, it has the advantages of maintaining the basic code rate and simple design process.

2. Compared with the block Markov superposition coding method based on the short repetition code and the short parity check code, the present invention selects the required binary BCH code as the component code of the block Markov superposition coding method ^. Under the requirement of bit error rate of ¹⁰ to 10 ^-15 orders of magnitude, the required coding memory is m=1, 2, 3, which can reduce the coding and decoding delay and complexity.

3. The present invention proposes a soft-in and soft-out decoding method for binary BCH component codes of the grouped Markov superposition coding method using binary BCH codes as component codes, which can be used for windowing decoding methods, involving Among the decoding methods such as the two-stage decoding method of the soft iterative process. The bit error rate performance can reach the theoretical lower bound of the block Markov superposition coding method. Compared with the traditional trellis-based and Chase-II-based soft-in and soft-out decoding methods, it has the advantages of low complexity, no need to set a correction factor, and can provide a phased adjustment strategy for computing resources to optimize performance. Whether using the windowed decoding method or the two-stage decoding method involving the soft iterative process, compared with using the soft-in and soft-out decoding method based on Chase-II, using the method proposed in the present invention, in the waterfall region and the decoding level layers have better performance.

To sum up, the present invention proposes a block Markov superposition coding method using binary BCH code as a component code and a decoding method, which can achieve the matching of optical communication systems with coding memory m=1, 2, 3. Performance requirements for forward error correction coding to reduce latency and reduce complexity.

Description of drawings

Fig. 1 is a flow chart of a soft-in soft-out decoding method using binary BCH code as a component code.

Fig. 2 is a performance diagram when the block Markov superposition coding method using binary BCH code as the component code uses the windowed decoding method.

FIG. 3 is a performance diagram when a two-stage decoding method is used in the block Markov superposition coding method with binary BCH code as the component code.

Detailed ways

Two specific embodiments are described below to supplement the implementation steps and advantages of the present invention.

Example 1

This specific embodiment uses the windowed decoding method, and compares with the soft-in and soft-out decoding method using Chase-II to illustrate the effectiveness of the binary BCH code soft-in and soft-out decoding method proposed by the present invention. details as follows:

Use BCH[31,16] as the component code of the block Markov superposition coding method, and configure B=160. In the windowed decoding method, the decoding window size is set to (d+1)nBbits, where d=3m, and the Chase-II soft-in and soft-out decoding method and the soft-in and soft-out decoding method of the binary BCH code proposed by the present invention are used respectively. The Monte Carlo simulation experiment of the additive white Gaussian noise channel based on binary phase shift keying is carried out according to the decoding method (configuring the maximum number of tests T=256). From FIG. 2, it can be seen that compared with using the Chase-II soft-in and soft-out decoding method, the soft-in and soft-out decoding method using the binary BCH code proposed by the present invention has better bit errors in the waterfall area and the error leveling layer. rate performance. Using the soft-in and soft-out decoding method of the binary BCH code proposed by the present invention, the average test times at 2.5dB and 3.0dB obtained by statistics are 5.484020 and 3.315167 respectively, which are both lower than the required test times of Chase-II 8 times .

Example 2

This specific embodiment uses a two-stage decoding method to provide a coding and decoding scheme that meets the performance requirements of forward error correction coding in an optical communication system. details as follows:

Design a packet Markov superposition coding method that meets the requirements of optical communication systems and provides a net coding gain of the order of 11dB at a bit error rate of ^10-15 , using a two-stage decoding method for decoding, based on binary phase shift keying. The additive white Gaussian noise channel is subjected to Monte Carlo simulation experiments and performance analysis. The first stage of the two-stage decoding uses a windowed decoding method with a limited sliding window length (the decoding window size is (d+1)nB bits, where d=m). Using BCH[127,106] as the component code, configure B=50. Using the soft-in and soft-out decoding method of binary BCH code proposed by the present invention, the maximum number of tests T=256 is configured. From the theoretical lower bound of the block Markov superposition coding method, the required coding memory length m=2 can be obtained, so d=m=2 is set. The simulation results are shown in Figure 3. It can be seen from Figure 3 that when the bit error rate is ^10-15 , the net coding gain that can be achieved using the heuristic upper bound prediction provided by the two-stage decoding is 11.3dB, which meets the performance requirements of the optical communication system for forward error correction coding. .

The above are only preferred embodiments of the present invention, and do not limit the present invention. Any simple modifications and changes made to the above embodiments according to the technical essence of the present invention have equivalent structural changes, and they still belong to the present invention. within the scope of protection of the technical scheme.

Claims (5)

1. a grouping Markov superposition decoding method with binary BCH code as component code, is characterized in that: described decoding method is applicable to following coding method: Taking the binary BCH code with the code length as n, the information bit length as k and the error correction capability as t _min as the component code, it is used to encode the binary information sequence u of length K=kBL into length N=nB(L+m ) codeword c , its encoding method comprises the following steps: (1.1) Divide the information sequence u of length K=kBL into L equal-length packets u = ( u ⁽⁰⁾ , u ⁽¹⁾ ,... u ^(L-1) ), each packet length is kB; for t ＝-1,-2,...,-(m-1),-m, initialize the sequence v ^(t) of length nB; where m is the length of the coding memory, which is a positive integer greater than or equal to 1; B is a positive integer integer; (1.2) At time t=0,1,...,L-1, the sequence of length kB is Divide into B groups for [n, k] binary BCH code encoding, and obtain a coding sequence of length nB And combine v ^(t-1) , v ^(t-2) ,... v ^(tm) to calculate the t-th subsequence c ^(t) of the codeword c ; the v ^{(t) is} combined with v ^(t-1) , v ^(t-2) ,..., v ^(tm) calculates the t (t≥0) th subsequence c ^(t) of the codeword c as follows: First, for 1≤i≤m, the sequence v ^{(ti) is} sent into the interleaver Π _i to obtain a sequence w ⁽ⁱ⁾ with a length of nB after interleaving; Then, send v ^(t) and w ⁽¹⁾ , w ⁽²⁾ ,..., w ^(m) to the symbol-by-symbol aliaser S to obtain a sequence c ^(t) of length nB; The decoding method consists of flipping pattern priority queues The hard-decision decoder is composed of the legal error pattern set ε, including the following steps: (2.1) Configure the maximum number of tests T, where T is a positive integer; (2.2) Input soft information; obtain hard decision sequence z and unreliability sequence λ from the input soft information; The input soft information is the log-likelihood ratio of each bit of the BCH codeword where P _a (c _j =0) and P _a (c _j =1) represent the prior probability that the codeword bits are 0 and 1, respectively; Each component in the hard-decision sequence z = (z ₀ , z ₁ , . . . , z _n-1 ) is calculated as follows, Each component in the unreliability sequence λ = (λ ₀ ,λ ₁ ,...,λ _n-1 ) is calculate; (2.3) Initialization: set the test count τ=0; sort λ to get an ascending sequence and calculate The corresponding position ^index sequence a in λ of each component in Initialize an empty queue and put an all-zero pattern into it in; the position index sequence a = (a ₀ , a ₁ ,..., a _n-1 ) satisfies The calculation method of the unreliability of the legal error pattern is as follows: given an error pattern e = (e ₀ , e ₁ , . . . , e _n-1 ), its unreliability is equal to (2.4) Perform the following iterations until τ ≥ T, or is empty, or The lower bound corresponding to the first element of is not less than λ ^* : in , call the hard-decision decoder to perform test decoding according to the flip pattern provided by the team leader, and add 1 to τ. If the decoding is successful, put the obtained legal error pattern into ε, and calculate the unreliability. If the reliability is less than λ ^* , assign it to λ ^* ; assign The team leader assigns the flip pattern f=(f ₀ , f ₁ ,...,f _n-1 ) and dequeues, generates a new flip pattern based on the tree structure according to f, and calculates the corresponding potential legality for each flip pattern obtained Error pattern unreliability lower bound, priority queue According to the Nether as the size relationship, and place the flip pattern with the smallest Nether at the head of the team; (2.5) Finally, calculate and output soft information according to the obtained ε and output; the output soft information Calculated as follows: (2.5.1) From the legal error pattern set ε, calculate the codeword set according to the following method (2.5.2) Output soft information Calculated as follows: if if but in, and 2. a kind of grouped Markov superposition decoding method according to claim 1, is characterized in that: the test decoding method in step (2.4) is described as follows: Given flip pattern f=(f ₀ , f ₁ , ...,f _n-1 ), flip z at position {a _j | f _j =1,0≤j≤n-1} to get the flipped version of z Using a hard-decision decoder pair to decode. 3. a kind of grouped Markov superposition decoding method according to claim 1 is characterized in that: described hard-decision decoder use comprises Berlekamp-Massey (BM) algorithm, Euclidean algorithm, Welch-Berlekamp (WB) algorithm. 4. a kind of grouped Markov superposition decoding method according to claim 1 is characterized in that: in step (2.4), the method for generating flip pattern based on tree structure is described as follows: given flip pattern f=(f ₀ , f ₁ ,…,f _n-1 ), the order of f is defined as If R(f)≥nt _min , no new flip pattern is generated; otherwise, its left son f _↓ and right brother f _→ are generated; the left son f _↓ is at position R(f)+1 by the f Obtained by flipping; the right brother f _→ is obtained by flipping the f at positions R(f) and R(f)+1. 5. a kind of grouped Markov superposition decoding method according to claim 1, is characterized in that: the calculation method of the unreliability lower bound B (f) of potential legal error pattern in step (2.4) is: given flip pattern f=(f ₀ ,f ₁ ,...,f _n-1 ),