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International Journal of Geomate

MESSAGE PASSINGAND LOOPS SOLUTION ALGORITHM BASED ON CUT-NODE TREE

Huanming Zhang

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes are forward error-correction and linear block codes. An LDPC code can be described by a bipartite graph called Tanner graph(1). Loops, especially short loops in tanner graph, degrade the performance of LDPC decoder, because they affect the independence of the extrinsic information exchanged in the iterative decoding. In this paper, based on graph theory and Tanner graph, the loop structure in LDPC codes are studied carefully, a new notion, cut-node tree, is proposed to describe LDPC codes. Cut-node tree has full information of Tanner graph. So all loop features in LDPCs can be calculated relatively easy by a computer. Traditional message passing in graph is improved to avoid repeated iteration of information, a new decoding schemes for LDPC codes is proposed and can suppress repeated iteration of information in SPA. The results help to further research on related field.

DOI
10.21660/2016.27.1272

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Low-density parity-check (LDPC) codes are forward error-correction and linear block codes. An LDPC code can be described by a bipartite graph called Tanner graph(1). Loops, especially short loops in tanner graph, degrade the performance of LDPC decoder, because they affect the independence of the extrinsic information exchanged in the iterative decoding. In this paper, based on graph theory and Tanner graph, the loop structure in LDPC codes are studied carefully, a new notion, cut-node tree, is proposed to describe LDPC codes. Cut-node tree has full information of Tanner graph. So all loop features in LDPCs can be calculated relatively easy by a computer. Traditional message passing in graph is improved to avoid repeated iteration of information, a new decoding schemes for LDPC codes is proposed and can suppress repeated iteration of information in SPA. The results help to further research on related field.
LDPC codes are finding increasing use in applications requiring reliable and highly efficient information transfer over bandwidth. An LDPC code is defined by a sparse parity-check matrix and can be described by a bipartite graph called Tanner graph. Loops in Tanner graph prevent the sum-product algorithm from converging. Further, loops, especially short loops, degrade the performance of LDPC decoder, because they affect the independence of the extrinsic information exchanged in the iterative decoding. This paper, by graph theory, deduces cut-node tree graph of LDPC code, and depicts it with matrix. On the basis of tree matrix algorithm, whole depictions of loops can be figured out, providing of foundation for further research of relations between loops and LDPC codes’ performance.
The Tanner graph of long LDPC codes usually has no loops and LLR BP algorithm is the best soft-decision decoding algorithm.But the Tanner graph of short LDPC codes usually has loops,so information within variable nodes doesn't satisfy the condition of independent identical distribution and the decoding performance of LLR BP algorithm will decrease.In this paper,a modified LLR BP algorithm is proposed,which can reduce the relativity of information within variable nodes by adjusting the iterative process of variable nodes information.Simulation results show that the LDPC decoding performance of the modified LLR BP algorithm is more effective than that of LLR BP algorithm,Normalized BP algorithm and offset BP algorithm.
The best known practical algorithm for the decoding of low-density parity-check (LDPC) codes is the iterative sum-product or belief propagation algorithm, operating on a Tanner graph (TG) of the code. Conventionally, in each iteration, all the symbol nodes and subsequently all the check nodes in the TG pass new messages to their neighbors (the so-called "flooding schedule"). We propose a new message-passing schedule, called "probabilistic schedule". Unlike flooding, the probabilistic schedule operation is based on the structure of the TG, and probabilistically balances the frequency at which different symbol nodes update their outgoing messages in accordance with their girths. Our results show that, particularly for short block lengths, the new schedule offers a much better performance/complexity trade-off. For a particular example of a (1268, 456) code, at no cost in complexity, the probabilistic schedule not only decreases both the bit and message error rates by an order of magnitude, but also reduces the number of undetected errors considerably. This work shows the importance of scheduling in the performance of iterative decoding algorithms and suggests that a schedule which matches the structure of the TG can substantially improve the performance/complexity trade-off in the decoding of short LDPC codes.
Introduction In this chapter we introduce low-density parity-check (LDPC) codes, a class of error correction codes proposed by Gallager in his 1962 PhD thesis 12 years after error correction codes were first introduced by Hamming (published in 1950). Both Hamming codes and LDPC codes are block codes: the messages are broken up into blocks to be encoded at the transmitter and similarly decoded as separate blocks at the receiver. While Hamming codes are short and very structured with a known, fixed, error correction ability, LDPC codes are the opposite, usually long and often constructed pseudo-randomly with only a probabilistic notion of their expected error correction performance. The chapter begins by presenting parity bits as a means to detect and, when more than one is employed, to correct errors in digital data. Block error correction codes are described as a linear combination of parity-check equations and thus defined by their parity-check matrix representation. The graphical representation of codes by Tanner graphs is presented and the necessary graph theoretic concepts introduced. In Section 2.4 iterative decoding algorithms are introduced using a hard decision algorithm (bit flipping), so that the topic is developed first without reference to probability theory. Subsequently the sum–product decoding algorithm is presented. This chapter serves as a self-contained introduction to LDPC codes and their decoding. It is intended that the material presented here will enable the reader to implement LDPC encoders and iterative decoders.
The best known practical algorithm for the decoding of low-density parity-check (LDPC) codes is the iterative sum-product or belief propagation algorithm, operating on a Tanner graph (TG) of the code. Conventionally, in each iteration, all the symbol nodes and subsequently all the check nodes in the TG pass new messages to their neighbors (the so-called "flooding schedule"). We propose a new message-passing schedule, called "probabilistic schedule." Unlike flooding, the probabilistic schedule operates based on the structure of the TG, and probabilistically balances the frequency at which different symbol nodes update their outgoing messages in accordance with their girths. Our results show that, particularly for short block lengths, the new schedule offers a much better performance/complexity trade-off. For a particular example of a (1268,456) code, at no cost in complexity, the probabilistic schedule not only decreases both the bit and message error rates by an order of magnitude, but also reduces the number of undetected errors considerably. This work shows the importance of scheduling in the performance of iterative decoding algorithms and suggests that a schedule which matches the structure of the TG can substantially improve the performance/complexity trade-off in the decoding of short LDPC codes.