阅读说明：本技术 一种基于部分叠加的递归分组马尔可夫叠加编码方法 (Recursive grouping Markov superposition coding method based on partial superposition ) 是由 赵山程 温金明 马啸 于 2019-09-27 设计创作，主要内容包括：本发明公开的一种基于部分叠加的递归分组马尔可夫叠加编码方法,以码长为n,信息为长度k的码C[n,k]作为基本码,将长度为kL的信息序列<U>u</U>编码成长度为n(L+T)的码字<U>c</U>,其中,L为耦合长度,代表长度为k的等长分组的数量,T为结尾长度；L,T为取值为非负的整数；编码方法包括以下步骤：将长度为kL的信息序列<U>u</U>划分为L个等长分组<U>u</U>＝(<U>u</U><Sup>(0)</Sup>,<U>u</U><Sup>(1)</Sup>,…,<U>u</U><Sup>(L-1)</Sup>),每个分组长度为k；对于时刻t＝-1,-2,…,-m,把长度为n的序列<U>w</U><Sup>(t)</Sup>初始化设置为全零序列；在t＝0,1,…,L-1时刻,将长度为k的序列<Image he="77" wi="460" file="DDA0002217696690000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>送入基本码的编码器ENC进行编码,得到长度为n的编码序列<Image he="80" wi="480" file="DDA0002217696690000012.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>并结合序列<U>w</U><Sup>(t-1)</Sup>,<U>w</U><Sup>(t-2)</Sup>,…,<U>w</U><Sup>(t-m)</Sup>计算码字<U>c</U>的第t个子序列<U>c</U><Sup>(t)</Sup>；本发明具有编码简单、译码复杂度低、构造灵活、可逼近信道容量等优点,与传统的分组马尔可夫叠加编码方法相比,适用于性能较好的基本码,拥有更低的编译码复杂度。(The invention discloses a recursive grouping Markov superposition coding method based on partial superposition, which takes a code C [ n, k ] with the code length n and the information length k as a code length]As basic code, information sequence with length of kL u Encoding into codewords of length n (L + T) c Wherein, L is a coupling length representing the number of equal-length packets with a length of k, and T is an ending length; l and T are integers with non-negative values; the encoding method comprises the following steps: information sequence with length of kL u Dividing into L equal-length packets u ＝( u (0) , u (1) ,…, u (L‑1) ) Each packet length is k; for time t-1, -2, …, -m, sequences of length n are applied w (t) Initializing and setting the sequence to be an all-zero sequence; at time t-0, 1, …, L-1, a sequence of length k is added Sending the code into a coder ENC of a basic code for coding to obtain a coded sequence with the length of n And binding sequences w (t‑1) ， w (t‑2) ，…， w (t‑m) Calculating code words c Of the tth sub-sequence c (t) (ii) a The invention has the advantages of simple coding, low decoding complexity, flexible construction, capability of approaching to the channel capacity and the like, is suitable for basic codes with better performance and has lower coding and decoding complexity compared with the traditional packet Markov superposition coding method.)

1. A recursive block Markov superposition coding method based on partial superposition is characterized in that a code C [ n, k ] with a code length n and information length k is used]As basic code, information sequence with length of kLuEncoding into codewords of length n (L + T)cWherein, L is a coupling length representing the number of equal-length packets with a length of k, and T is an ending length; l and T are integers with non-negative values; m is an integer with a non-negative value; for 1. ltoreq. i.ltoreq.m, p_iIs an integer with a non-negative value; the encoding method includes the steps of:

step one, information sequence with length of kLuDividing into L equal-length packetsu＝(u ⁽⁰⁾,u ⁽¹⁾,…,u ^(L-1)) Each packet length is k; for time t-1, -2, …, -m, sequences of length n are appliedw ^(t)Initializing and setting the sequence to be an all-zero sequence; wherein m is the code memory length, and the value of m is a non-negative integer;

step two, int is 0,1, …, time L-1, sequence with length k

first, for 1. ltoreq. i.ltoreq.m, the sequencew ^(t-i)Is sent into an interleaver II_iObtaining the sequence with length n after interweavingz ^(t-i)；

Then, for 1. ltoreq. i.ltoreq.m, the sequencez ^(t-i)Is sent into a mask M_iMask device M_iWill be sequencedz ^(t-i)P of (a)_iThe individual components are forced to be set to 0, resulting in a sequence of length nx ^(t-i)；

Finally, the sequence is sequencedv ^(t)And sequencex ^(t-1)，x ^(t-2)，…，x ^(t-m)Sent to a symbol-by-symbol aliasing device S to obtain a sequence with the length of nw ^(t)Andc ^(t)whereinc ^(t)＝w ^(t)；

Step three, at the time T being L, L +1, … and L + T-1, all-zero sequence with the length of k is processedu ^(t)＝0Sending the coded sequence into an encoder ENC of a basic code to obtain an all-zero sequence with the length of nv ^(t)And are combined withw ^(t-i)Calculating code wordscOf the tth sub-sequencec ^(t)Said binding sequencew ^(t-1)，w ^(t-2)，…，w ^(t-m)Calculating code wordscOf the tth sub-sequencec ^(t)According to the method described in the second stepv ^(t)Binding sequencesw ^(t-1)，w ^(t-2)，…，w ^(t-m)Calculating code wordscOf the tth sub-sequencec ^(t)"step (c)" is carried out.

2. A method for recursive packet markov superposition coding based on partial superposition according to claim 1, characterized in that said information sequence is a sequence of informationuIs a binary sequence or a multiple sequence.

3. A recursive grouped markov superposition coding method based on partial superposition according to claim 1, characterised in that said encoder ENC is an arbitrary type of encoder.

4. The method of claim 1, wherein the interleaver Π is configured to perform a recursive markov superposition coding process based on partial superposition_iIs an interleaver of any type.

5. Method for recursive Markov superposition coding based on partial superposition, according to claim 1, characterized in that said mask M is a mask_iWill input the sequencez ^(t-i)The component of (c) is set to zero.

6. A recursive packet Markov superposition coding method based on partial superposition, according to claim 5, characterized in that said mask M is a mask_iCan select to input sequencez ^(t-i)Any of p_iA component is set to zero, where p_iIs a non-negative integer less than or equal to n.

7. A method for recursive packet markov superposition coding based on partial superposition, according to claim 1, characterized in that said sequence is a sequence of partial superpositionv ^(t)Andw ^(t-1)，w ^(t-2)，…，w ^(t-m)is a sequence of length n over a finite field, the symbol-by-symbol aliasing means S is a symbol-by-symbol finite field weight sum operator; the symbol-by-symbol finite field weighted sum operator S functions as follows: outputting sequences of length nw ^(t)Andc ^(t)，w ^(t)andc ^(t)the jth component of

8. The method of claim 1, wherein the code word is encoded by a coding method based on a recursive Markov superpositionc＝(c ⁽⁰⁾,c ⁽¹⁾,…,c ^(L+T-1)) Modulated and sent to channel, and the vector received by receiving endy＝(y ⁽⁰⁾,y ⁽¹⁾,…,y ^(L+T-1)) Whereiny ^(t)For corresponding code word sub-sequencesc ^(t)According to the received vectoryAnd channel characteristics, decoding and obtaining a transmission sequenceuIs estimated by

Technical Field

The invention relates to the research field of digital communication and digital storage, in particular to a recursive packet Markov superposition coding method based on partial superposition.

Background

With the advent of the big data age, the demand of individuals in data transmission and data storage is increasing. As the devices and components have entered the ten nanometer era, the uncertainty of transmission links and storage media has increased, and the error rate has also increased. Channel coding is one of the important means to ensure the data reliability of these information systems. Therefore, it is of great practical significance to design high performance error correction coding techniques. Shannon proposed channel capacity and demonstrated the channel coding theorem in 1948. Since then, researchers have been working on constructing good codes that can approximate the channel capacity. Berrou et al, 1993, proposed iterative decoding-based Turbo codes, and since then opened a new era for modern coding. Later, more good codes that can approach the channel capacity were investigated, including Low-Density Parity-Check codes (LDPC codes), polar codes, and spatially-coupled LDPC codes.

Group Markov superposition coding is a class of numbers with approximable capacity proposed in 2015 by Marmowl, see (Zhongshan university, a group Markov superposition coding method [ P ]: CN 103152060A). The block markov superposition coding method may construct a large convolutional code from a short code. Packet markov superposition coding has a simple coding algorithm. When the repetition code and the parity check code are used as the basic codes, the block Markov superposition coding can realize the coding of multiple code rates by time division (Zhongshan university, a multi-code-rate code coding method [ P ] based on the time division block Markov superposition coding: CN 104410428A). The block Markov superposition coding may be decoded using a soft information based sliding window iterative decoding algorithm.

The above mentioned packet markov superposition coding method is non-recursive, which has a number of advantages. However, the non-recursive packet markov superposition coding method requires a large coding memory length m to effectively approach the channel capacity, and the larger the memory length m is, the larger the required decoding delay d is, and the higher the corresponding decoding complexity and decoding delay are. In 2017, Matsunami et al proposed a recursive packet Markov superposition coding method (Zhongshan university, a recursive packet Markov superposition coding method [ P ]: CN106972865A), which can effectively reduce the memory length m and the decoding delay d.

The above mentioned packet markov superposition coding methods all use the full superposition mode. The recursive packet markov superposition coding method using full superposition has the following problems: when the basic code is a code with better performance, the performance of the recursive packet Markov superposition coding adopting full superposition is poorer, performance gain cannot be brought, and the complexity of coding and decoding is increased.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a Markov superposition coding method based on partial superposition, on one hand, the coding method provided by the invention has the advantages of simple coding, capability of approaching the channel capacity and the like, and on the other hand, the coding method provided by the invention is suitable for basic codes with better performance, such as LDPC codes, and the required memory length is only 1 at the moment, so that the coding method has lower coding code complexity.

The purpose of the invention is realized by the following technical scheme:

a Markov superposition coding method based on partial superposition is characterized in that a code C [ n, k ] with a code length n and information length k is used]As basic code, information sequence with length of kLuEncoding into codewords of length n (L + T)cWherein L is a couplerThe total length represents the number of equal-length groups with the length of k, and T is the tail length; l and T are integers with non-negative values; m is an integer with a non-negative value; for 1. ltoreq. i.ltoreq.m, p_iIs an integer with a non-negative value; the encoding method includes the steps of:

step one, information sequence with length of kLuDividing into L equal-length packetsu＝(u ⁽⁰⁾,u ⁽¹⁾,…,u ^(L-1)) Each packet length is k; for time t-1, -2, …, -m, sequences of length n are appliedw ^(t)Initializing and setting the sequence to be an all-zero sequence; wherein m is the code memory length, and the value of m is a non-negative integer;

step two, at the time t is 0,1, … and L-1, a sequence with the length of k is added

Sending the code into a coder ENC of a basic code for coding to obtain a coded sequence with the length of n

And binding sequencesw ^(t-1)，w ^(t-2)，…，w ^(t-m)Calculating code wordscOf the tth sub-sequencec ^(t)(ii) a The above-mentionedv ^(t)Binding sequencesw ^(t-1)，w ^(t-2)，…，w ^(t-m)Calculating code wordscOf the tth sub-sequencec ^(t)The method comprises the following steps:

first, for 1. ltoreq. i.ltoreq.m, the sequencew ^(t-i)Is sent into an interleaver II_iObtaining the sequence with length n after interweavingz ^(t-i)；

Then, for 1. ltoreq. i.ltoreq.m, the sequencez ^(t-i)Is sent into a mask M_iMask device M_iWill be sequencedz ^(t-i)P of (a)_iThe individual components are forced to be set to 0, resulting in a sequence of length nx ^(t-i)；

Finally, the sequence is sequencedv ^(t)And sequencex ^(t-1)，x ^(t-2)，…，x ^(t-m)Sent to a symbol-by-symbol aliasing device S to obtain a sequence with the length of nw ^(t)Andc ^(t)whereinc ^(t)＝w ^(t)；

Step three, at the time T being L, L +1, … and L + T-1, all-zero sequence with the length of k is processedu ^(t)＝0Sending the coded sequence into an encoder ENC of a basic code to obtain an all-zero sequence with the length of nv ^(t)And are combined withw ^(t-i)Calculating code wordscOf the tth sub-sequencec ^(t)Said binding sequencew ^(t-1)，w ^(t-2)，…，w ^(t-m)Calculating code wordscOf the tth sub-sequencec ^(t)According to the method described in the second stepv ^(t)Binding sequencesw ^(t-1)，w ^(t-2)，…，w ^(t-m)Calculating code wordscOf the tth sub-sequencec ^(t)"step (c)" is carried out.

Further, the information sequenceuIs a binary sequence or a multiple sequence.

Further, the encoder ENC is an arbitrary type of encoder.

Further, the interleaver Π_iIs an interleaver of any type.

Further, the mask M_iIs to input a sequencez ^(t-i)Is set to zero.

Further, the mask M_iCan select to input sequencez ^(t-i)Any of p_iA component is set to zero, where p_iIs a non-negative integer less than or equal to n.

Further, the sequencev ^(t)Andw ^(t-1)，w ^(t-2)，…，w ^(t-m)is a sequence of length n over a finite field, the symbol-by-symbol aliasing means S is a symbol-by-symbol finite field weight sum operator; the symbol-by-symbol finite field weighted sum operator S functions as follows: outputting sequences of length nw ^(t)Andc ^(t)，w ^(t)andc ^(t)the jth component of

Wherein the content of the first and second substances,

and

are respectivelyv ^(t)Andx ^(t-i)the (j) th component of (a),

is m +1 field elements from finite field, and is binary or multivariate symbol, and is added

Sum multiplicationAnd (4) operating according to a finite field algorithm.

Furthermore, the code word obtained after the coding of the coding methodc＝(c ⁽⁰⁾,c ⁽¹⁾,…,c ^(L+T-1)) Modulated and sent to channel, and the vector received by receiving endy＝(y ⁽⁰⁾,y ⁽¹⁾,…,y ^(L+T-1)) Whereiny ^(t)For corresponding code word sub-sequencesc ^(t)According to the received vectoryAnd channel characteristics, decoding and obtaining a transmission sequenceuIs estimated by

Further, in the decoding method of the present invention, the transmitted and processed message is the probability distribution of the variable or other quantity equivalent to the probability distribution. Each codeword subsequencec ^(t)There are L + T decoding layers corresponding to one decoding layer. The decoding layer includes ═ nodes and ^ pi_i"node," S "node," M_i"node and5 types of nodes, the "C" node. Setting a decoding sliding window d and a maximum iteration number I_max. When the receiving end receivesy ^(t),y ^(t+1),…,y ^(t+d-1)(t is 0,1, …, L-1), start decoding and get the sending messageu ^(t)Is estimated by

The method comprises the following specific steps:

(Y1) for j ≦ T, T +1, …, T + d-1, if j ≦ L + T-1, based on the received vectory ^(j)And channel characteristic calculationc ^(j)A posterior probability distribution of (d); initializing an iteration number counter I to be 0;

(Y2) for j ═ T, T +1, …, T + d-1, if j ≦ L + T-1, process the j-th layer message, passing the j-th layer message to the j +1, j +2, …, j + m layer; otherwise, performing step (Y3);

(Y3) for j ═ T + d-1, T + d-2, …, T +1, if j ≦ L + T-1, processing the j-th layer message, passing the j-th layer message to the j-1, j-2, …, j-m layer; otherwise, performing step (Y4);

(Y4) setting I ═ I + 1; if the decoding reaches the maximum iteration number I ═ I_maxStopping iteration, obtaining the transmitted message by hard decisionu ^(t)Is estimated by

Otherwise, go to step (Y2).

In the decoding method of the present invention, the processing of the j-th layer message is performed according to the following steps_max：

(S1) at the ═ node, process and pass to ═ Π_iThe external information of the node and the S node, wherein i is more than or equal to 1 and less than or equal to m;

(S2) at ` pi_i"a node, processing and passing extrinsic information from or to node" S ", where 1 ≦ i ≦ m;

(S3) at the "S" node, processing and passing to the "M_i"node and" ═ node extrinsic information;

(S4) at the "C" node, updating extrinsic information to the "S" node using soft-input soft-output decoding, and updating decoded output information of the decoder.

Compared with the prior art, the invention has the following advantages and beneficial effects:

1. the recursive packet Markov superposition coding method based on partial superposition has the advantages of simple coding, low decoding complexity, flexible construction, capability of approaching channel capacity and the like.

2. Compared with the traditional packet Markov superposition coding method, the recursive packet Markov superposition coding method based on partial superposition is suitable for basic codes with better performance.

Drawings

FIG. 1 is a coding block diagram of a recursive block Markov superposition coding method based on partial superposition according to the present invention;

FIG. 2 is a decoding block diagram of a recursive block Markov superposition coding method based on partial superposition according to the present invention;

fig. 3 is a schematic diagram of a bit error rate performance curve of the recursive packet markov superposition coding method based on partial superposition over the BPSK-AWGN channel according to the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.