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Journal of Information Engineering University

Analysis of LDPC's Loops

LI Shui-ping

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Small loops in the graphical representations of low density parity-check codes are hypothesised to be detrimental to the code's performance.This paper analyzes the essential properties of LDPC codes, and then presents a kind of method for removing such loops from the graphs.

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It is hypothesised that small loops in the graphical representations of low-density parity-check codes are detrimental to the code's performance. We demonstrate a procedure for removing such loops from the codes. An algorithm based on the code's adjacency matrix is used to locate unwanted loops, and then certain edges within the graph are exchanged to eliminate those loops (without simultaneously creating any others). This process can be repeated until there are no loops remaining with a size less than a particular limit. A comparison of some theoretical and experimental values for this limit is given.
In low-density parity-check(LDPC) codes,the small loops between low degree nodes are more detrimental to the decoding performance than those between high degree nodes.In order to reduce small loops,we propose a method of exchanging the edges between nodes.It first removes the small loops between low degree nodes as much as possible,and then removes the small loops from whole LDPC codes under the condition of ensuring the smallest loop between low degree nodes not to be changed.Finally,the simulation result of constructing LDPC codes by the method is compared with that by only removing the small loops from whole LDPC codes.
Low-density parity-check (LDPC) codes are a class of linear block codes which provide near-capacity performance on a large collection of data transmission and storage channels while simultaneously admitting implementable decoders. LDPC codes were first proposed by Gallager in his 1960 doctoral dissertation [1] and were scarcely considered in the 35 years that followed. One notable exception is the important work of Tanner in 1981 [2] in which Tanner generalized LDPC codes and introduced a graphical representation of LDPC codes, now called Tanner graphs. The study of LDPC codes was resurrected in the mid1990s with the work of MacKay, Luby, and others [3-5] who noticed, apparently independently of the work of Gallager, the advantages of linear block codes which possess sparse (low-density) parity-check matrices.