CN105375933A - Message passing-based LDPC circle search and circle enumeration algorithm - Google Patents

Abstract

The invention discloses a message passing-based LDPC circle search and circle enumeration algorithm. According to the algorithm, a check matrix is set, and a Tanner graph is determined; information is passed between a variable node and a check node through using a message passing algorithm; the number and respective paths of various kinds of length-defined circles are recorded; in a search process, paths with overlapped points or overlapped edges are deleted timely; and paths for constituting the circles are saved. With the message passing-based LDPC circle search and circle enumeration algorithm of the invention adopted, the circles can be counted, and the information of the circles, such as the position information, construction and length of the circles, can be fully mastered; since codes are influenced by graph dimensionality, after short circles are deleted, short circles are decreased, and constraint of graph dimensionality can be alleviated, and the improvement of the construction of code words can be benefitted.

Description

Message-passing-based LDPC (Low Density parity check) ring search and ring enumeration algorithm

Technical Field

The invention belongs to the information coding technology of non-cooperative communication, and particularly relates to an LDPC (Low Density parity check) ring search and ring enumeration algorithm based on message passing.

Background

The iterative message passing algorithm can obtain excellent performance in the aspect of LDPC code decoding with relatively low complexity, and with the rapid development of the iterative algorithm, the LDPC code which can approach to the channel capacity under a plurality of channel conditions is regenerated as a research hotspot. The Tanner graph is widely applied to the research of the LDPC code, and the low complexity of the LDPC code iterative decoding is just due to the sparsity of the Tanner graph. Furthermore, the dimension of the Tanner graph also affects the performance of the LDPC code. It is currently generally believed that the better the coding performance is to be obtained, the more the appearance of short loops in the corresponding Tanner graph should be circumvented.

In 2013, a scholars m.karimi, a.h.banihashemi, proposed an information transfer algorithm for counting short loops in a graph in "Message-passing algorithm for computing short loops" (ieee trans.commun, vol.61, No.2, feb.2013), but no algorithm processing was performed on invalid loops of repeated nodes, the coding was limited by the graph dimension, the loop information in the code graph was not effectively utilized, and the short loops affecting the codeword structure still existed objectively. The algorithm is more biased toward theoretical derivation and does not work further for learning important information for improving codeword construction.

Disclosure of Invention

The invention aims to provide an LDPC loop search and loop enumeration algorithm based on message passing, which solves the problem that the LDPC loop search and loop enumeration algorithm is easily limited by short loops and trapping sets in an iterative decoding process.

The technical solution for realizing the purpose of the invention is as follows: an LDPC ring search and ring enumeration algorithm based on message passing comprises the following steps:

step 1, setting an H matrix, determining a Tanner graph, obtaining the total node number n and connecting the node A with the node A_iNumbering in sequence, wherein i is the serial number of the node, and i is 1, 2,3, … and n; initialization i ═ 1, a_iFor the start node, determining the start node A_iThe maximum length of the ring is 2K, the total iteration times is K, and the step 2 is carried out.

Step 2, for the starting node A_iThe iteration number is K, K is 1, 2,3, … … K, and the initialization K is 1;

if K is less than or equal to K, starting node A_iCarrying out information transmission, and returning to the step 1 if no path remains in the information transmission process; otherwise, when the remaining path exists, recording and entering the step 3;

if K is larger than K, making i equal to i +1, and returning to the step 1 when i is less than or equal to n; when i > n, the output labels the node and its corresponding path.

Step 3, counting the rings in the information transmission process and removing the initial node A_iAnd in the outer residual paths, searching for a short ring containing the repeated nodes, sequentially outputting the data information and the position information of the repeated nodes according to the minimum serial number of the nodes, recording and deleting the ring path, and turning to the step 4.

Step 4, recording and storing the node A_iStep 2 is proceeded to, where the number of rings is the starting node and the length is 2k, and k is k + 1.

Further, in step 2, for the start node A_iAnd carrying out information transfer, wherein the information transfer process is as follows: will start node A_iThe information contained in the node and the external information are used as new external information to be transmitted to the adjacent nodes, the adjacent nodes transmit the information contained in the node and the new external information to the nodes adjacent to the adjacent nodes, and the information transmission is completed through iteration, wherein the node transmission is mutual transmission between the variable nodes and the detection nodes.

Further, in step 3, when counting the rings, it is determined that A is used_iThe number of rings with length of 2k as the starting node is given by the following formula:

$N_{2k}^{A_i}=\frac{1}{2}\underset{j=1}{\overset{d_{A_i}}{\mathrm{\Σ}}}\underset{i\≠j}{\overset{d_{A_i}}{\underset{i=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;e_i,e_j}-\underset{u_l\≠A_i}{\overset{n}{\underset{l=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;u_l}$

wherein,denotes the starting node as A_iAnd the number of rings of length 2 k.

Denotes the starting node as A_iThe initial path is e_iEnd path is e_jRing lengthNumber of rings of 2 k.

Denotes the starting node as A_iNumber of rings of length 2k, u_lDetermining a corresponding loop path for a repeated node which passes through the loop at least twice, namely a mark node; l represents its minimum sequence number, where l ═ 1, 2,3 …, n.

n represents the total number of nodes of the graph.

Compared with the prior art, the invention has the remarkable advantages that: (1) not only can the rings be counted, but also the ring information including the position information, the structure of the rings, and the length of the rings can be sufficiently grasped.

(2) Because the coding is influenced by the dimension of the graph, after the short ring is deleted, the short ring is reduced, the restriction of the dimension of the graph is relieved, and the method is favorable for improving the code word structure.

(3) The algorithm can be generalized to a general bipartite graph.

Drawings

FIG. 1 is a flow chart of the message passing-based LDPC ring search and ring enumeration algorithm of the present invention.

Fig. 2 is a simulation diagram of the message-passing-based LDPC ring search and ring enumeration algorithm of the present invention, wherein (a) is a codeword a: 252.252.3.252 variable node dimension graph; (b) for codeword B: 504.504.3.504 variable node dimension graph; (c) for codeword C: graph of the variable node dimension of PEGReg252x 504; (d) for codeword D: graph of the variable node dimension of PEGReg504x 1008.

FIG. 3 is a schematic view of a non-simple loop of the present invention, (a) being a first type; (b) is of a second type; (c) is a third type; (d) is the fourth.

Fig. 4 is a schematic diagram of U and W transmitting information according to a message transmission algorithm.

Detailed Description

The present invention is described in further detail below with reference to the attached drawing figures.

In order to better realize the LDPC code through hardware, a quasi-maximum likelihood algorithm such as iterative decoding based on a message passing mechanism is generally used for decoding. And determining a Tanner graph according to the check matrix, and transmitting information between the variable nodes and the check nodes by using a message transmission algorithm. However, since the existence of loops, especially short loops, can seriously affect the performance of the algorithm, the number of loops of various specified lengths and their respective paths are recorded during the execution of the algorithm. Meanwhile, in the searching process, paths with key points or heavy edges are deleted in time, and paths forming the rings are stored. And the algorithm proposed by the user is not limited by the self structure of the search object like other algorithms, and can search rings with any specified length. The loop information obtained by executing the algorithm can be used for changing the code word structure so as to improve the error correction performance or reduce the error floor. Moreover, the algorithm has generality and can be used for bipartite graphs without self-loops and heavy edges, even common graphs.

With reference to fig. 1, an LDPC ring search and ring enumeration algorithm based on message passing includes the following steps:

step 1, setting an H matrix, determining a Tanner graph, obtaining the total node number n and connecting the node A_iNumbering in sequence, wherein i is the serial number of the node, and i is 1, 2,3, … and n; initialization i ═ 1, a_iFor the start node, determining the start node A_iThe maximum length of the ring of (2) and the total number of iterations is K.

Step 2, for the starting node A_iThe iteration number is K, K is 1, 2,3, … … K, the initialization K is 1:

if K is less than or equal to K, starting node A_iCarrying out information transmission, and returning to the step 1 if no path remains in the information transmission process; otherwise, when the remaining path exists, recording and entering the step3。

If K is larger than K, making i equal to i +1, and returning to the step 1 when i is less than or equal to n; when i > n, the output labels the node and its corresponding path.

In the bipartite graph, an information code and a detection code of the LDPC code are defined as a corresponding information node and a corresponding detection node, and the bipartite graph is represented as:

G＝(V，E)(1)

wherein the bipartite graph G is defined as a node set of an information node U and a detection node W, andand a set of paths E representing paths between U and W, and { (U, W) | U ∈ U, W ∈ W }. take i ═ 0, i ═ i + 1.

The message passing algorithm is represented as:

u and W pass information according to a message passing algorithm, as in fig. 4.

In the process of information transfer, taking X, Y, Z as an example of three adjacent nodes, the information transfer between X and Y can be expressed as the following formula: i is_X→Y＝∑_z∈N(X)I_Z→X-I_Y→X+I_X＝∑_z∈N(X)-{Y}I_Z→X+I_X. Namely:

in the Tanner graph, a variable node (detection node) of LDPC coding transmits information contained in the variable node and external information as new external information to a detection node (variable node) adjacent to the variable node, and the node transmits the information contained in the subset and the new external information to the next adjacent node, so that the information transmission is completed through iteration. The serial number i of the initial node is less than n, and the initial node traverses all nodes.

The information transferred is related only to the node's extrinsic information from the information and neighboring nodes. However, when the message passing algorithm encounters special structures such as rings, independence of passed messages and the like cannot be guaranteed. That is, the existence of loops, especially short loops, can seriously affect the performance of iterative decoding. Therefore, it is necessary to search the ring by using a fast and efficient algorithm, which is very important for detecting the error correction performance of the existing LDPC code, further improving the error correction capability of the existing LDPC code, and designing an LDPC code with better error correction performance.

It is to be noted that the present invention contemplates the case of a simple ring;

if the nodes are different except for two end nodes in the ring, or a ring of length k, a corresponding non-repeating series of paths { e } may be used₁，e₂，L，e_kRepresents, then, is defined as a simple ring, and accordingly, there is a non-simple ring, as in fig. 3.

Step 3, counting the rings in the information transmission process, and removing the initial node A_iAnd in the outer residual paths, searching for a short ring containing the repeated nodes, sequentially outputting the data information and the position information of the repeated nodes according to the minimum serial number of the nodes, recording and deleting the ring path, and turning to the step 4.

When counting the ring, determine with node A_iThe number of rings with length of 2k as the starting node is given by the following formula:

$N_{2k}^{A_i}=\frac{1}{2}\underset{j=1}{\overset{d_{A_i}}{\mathrm{\Σ}}}\underset{i\≠j}{\overset{d_{A_i}}{\underset{i=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;e_i,e_j}-\underset{u_l\≠A_i}{\overset{n}{\underset{l=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;u_l}$

wherein,denotes the starting node as A_iAnd the number of rings of length 2 k;

denotes the starting node as A_iThe initial path is e_iEnd path is e_jThe number of rings with a ring length of 2 k;

denotes the starting node as A_iNumber of rings of length 2k, u_iAnd determining the corresponding loop path of the repeated node which passes through the loop at least twice, namely the mark node. l represents its minimum sequence number, where l ═ 1, 2,3 …, n };

n represents the total number of nodes of the graph.

Step 4, recording and storing by the node A_iStep 2 is proceeded to, where the number of rings is the starting node and the length is 2k, and k is k + 1. And ending until all the nodes are traversed.

Example 1

An LDPC ring search and ring enumeration algorithm based on message passing comprises the following steps:

step 1, the method comprises the following steps of http: html download codeword a: 252.252.3.252, B: 504.504.3.504, C: PEGReg252x504 and D: PEGReg504x1008 corresponding to the check matrix H_A(252，504)，H_B(504，1008)，H_C(252，504)，H_D(504, 1008), the coding rates are both 0.5, the weights of the A and B code word lines are 3, and the weights of the C and D code word lines are 4, and a Tanner graph is determined. Node A_iNumbering in sequence, wherein i is the serial number of the node, and i is 1, 2,3, … and n; initialization i ═ 1, a_iFor the start node, determining the start node A_iThe maximum length of the ring is 2K, and the total number of iterations is K; in Matlab, K is 3, 4, 5, 6, and 7, respectively, and the results are shown in table 1.

TABLE 1 number of rings of four codeword ring lengths 6 to 14

	Code A	Code B	Code C	Coding of D
					N6	169	165	0	0
N8	1312	1258	802	2
					N10	10052	10169	11279	11238
N12	83007	83489	86791	91101
					N14	699526	707468	723426	748343

Step 2, for the starting node A_iThe iteration number is K, K is 1, 2,3, … … K, the initialization K is 1:

if K is less than or equal to K, starting node A_iCarrying out information transmission, and returning to the step 1 if no path remains in the information transmission process; otherwise, when the remaining path exists, recording and entering the step 3.

If K is larger than K, making i equal to i +1, and returning to the step 1 when i is less than or equal to n; when i > n, the output labels the node and its corresponding path.

In the bipartite graph, an information code and a detection code of the LDPC code are defined as a corresponding information node and a corresponding detection node, and the bipartite graph is represented as:

G＝(V，E)(1)

wherein the bipartite graph G is defined as a node set of an information node U and a detection node W, andand a set of paths E representing paths between U and W, and { (U, W) | U ∈ U, W ∈ W }. take i ═ 0, i ═ i + 1.

The message passing algorithm is represented as:

u and W communicate information according to a message-passing algorithm (as shown in fig. 4).

In the process of information transfer, taking X, Y, Z as an example of three adjacent nodes, the information transfer between X and Y can be expressed as the following formula: i is_X→Y＝∑_z∈N(X)I_Z→X-I_Y→X+I_X＝∑_z∈N(X)-{Y}I_Z→X+I_X. Namely:

in the Tanner graph, a variable node (detection node) of LDPC coding transmits information contained in the variable node and external information as new external information to a detection node (variable node) adjacent to the variable node, and the node transmits the information contained in the subset and the new external information to the next adjacent node, so that the information transmission is completed through iteration. The serial number i of the initial node is less than n, and the initial node traverses all nodes.

It should be noted that the present invention contemplates a simple ring.

If the nodes are different except for two end nodes in the ring, or a ring of length k, a corresponding non-repeating series of paths { e } may be used₁，e₂，L，e_kRepresents, then, is defined as a simple ring, and accordingly, there is a non-simple ring, as in fig. 3.

Step 3, counting the rings in the information transmission process, and removing the initial node A_iIn the outer remaining paths, searching for a short ring containing the repeated nodes, sequentially outputting data information and position information of the repeated nodes according to the minimum serial number of the nodes, recording and deleting the ring path, and turning to the step 4;

when counting the ring, determine with node A_iThe number of rings with length of 2k as the starting node is given by the following formula:

$N_{2k}^{A_i}=\frac{1}{2}\underset{j=1}{\overset{d_{A_i}}{\mathrm{\Σ}}}\underset{i\≠j}{\overset{d_{A_i}}{\underset{i=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;e_i,e_j}-\underset{u_l\≠A_i}{\overset{n}{\underset{l=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;u_l}$

wherein,denotes the starting node as A_iAnd the number of rings of length 2 k;

denotes the starting node as A_iThe initial path is e_iEnd path is e_jRing length of 2kThe number of (2);

denotes the starting node as A_iNumber of rings of length 2k, u_lAnd determining the corresponding loop path of the repeated node which passes through the loop at least twice, namely the mark node. l represents its minimum sequence number, where l ═ 1, 2,3 …, n.

n represents the total number of nodes of the graph.

Step 4, recording and storing by the node A_iStep 2 is proceeded to, where the number of rings is the starting node and the length is 2k, and k is k + 1. And ending until all the nodes are traversed.

The Matlab simulation results are shown as follows, a dimension histogram of four codewords (shown in FIG. 2).

The corresponding dimension graphs of the four code words can be visually seen through the simulation graph, and the corresponding short ring number of the dimension graphs fully grasps the ring information in the LDPC coding and is used for improving the code word structure. The fast and efficient algorithm is used for searching the ring, which has very important significance for detecting the error correction performance of the existing LDPC code, further improving the error correction capability of the existing LDPC code and designing the LDPC code with better error correction performance.

Claims (3)

1. An LDPC ring search and ring enumeration algorithm based on message passing is characterized in that the method comprises the following steps:

step 1, setting an H matrix, determining a Tanner graph, obtaining the total node number n and connecting the node A with the node A_iNumbering in sequence, wherein i is the serial number of the node, and i is 1, 2,3, … and n; initialization i ═ 1, a_iFor the start node, determining the start node A_iThe maximum length of the ring is 2K, the total iteration times are K, and the step 2 is carried out;

step 2, for the starting node A_iThe iteration number is k, k is 1,2,3, … … K, initialization K ═ 1;

if K is less than or equal to K, starting node A_iCarrying out information transmission, and returning to the step 1 if no path remains in the information transmission process; otherwise, when the remaining path exists, recording and entering the step 3;

if K is larger than K, making i equal to i +1, and returning to the step 1 when i is less than or equal to n; when i is larger than n, outputting a marking node and a corresponding path thereof;

step 3, counting the rings in the information transmission process and removing the initial node A_iIn the outer remaining paths, searching for a short ring containing the repeated nodes, sequentially outputting data information and position information of the repeated nodes according to the minimum serial number of the nodes, recording and deleting the ring path, and turning to the step 4;

step 4, recording and storing the node A_iStep 2 is proceeded to, where the number of rings is the starting node and the length is 2k, and k is k + 1.

2. The message-passing based LDPC ring search and ring enumeration algorithm of claim 1, wherein: in step 2, the initial node A is paired_iAnd carrying out information transfer, wherein the information transfer process is as follows: will start node A_iThe information contained in the node and the external information are used as new external information to be transmitted to the adjacent nodes, the adjacent nodes transmit the information contained in the node and the new external information to the nodes adjacent to the adjacent nodes, and the information transmission is completed through iteration, wherein the node transmission is mutual transmission between the variable nodes and the detection nodes.

3. The message-passing based LDPC ring search and ring enumeration algorithm of claim 1, wherein: in step 3, when counting the rings, it is determined that A is used_iThe number of rings with length of 2k as the starting node is given by the following formula:

$N_{2k}^{A_i}=\frac{1}{2}\underset{j=1}{\overset{d_{A_i}}{\Σ}}\underset{i\≠j}{\overset{d_{A_i}}{\underset{i=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;e_i,e_j}-\underset{u_l\≠A_i}{\overset{n}{\underset{l=1}{\mathrm{\Σ}}}}{N}_{2k}^{A_i;u_l}$

wherein,denotes the starting node as A_iAnd the number of rings of length 2 k;

denotes the starting node as A_iThe initial path is e_iEnd path is e_jThe number of rings with a ring length of 2 k;

denotes the starting node as A_iNumber of rings of length 2k, u_lDetermining a corresponding loop path for a repeated node which passes through the loop at least twice, namely a mark node; l represents its minimum sequence number, where l ═ 1, 2,3 …, n };

n represents the total number of nodes of the graph.