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Hybrid Construction of LDPC Codes

Shu Lin, Jun Xu, Ivana Djurdjevic, Heng Tang

Published Oct 2, 2002• 0 citations
OpenAlex

Abstract

This paper presents a hybrid method for constructing low density parity check (LDPC) codes.Several classes of hybrid LDPC codes have been constructed.A special case of the hybrid construction gives a class of product LDPC codes.

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In this paper, a new class of low-density parity-check (LDPC) codes, named hybrid LDPC codes, is introduced. Hybrid LDPC codes are characterized by an irregular connectivity profile and heterogeneous orders of the symbols in the codeword. It is shown in particular that the class of hybrid LDPC codes can be asymptotically characterized and optimized using density evolution (DE) framework, and a technique to maximize the minimum distance of the code is presented. Numerical assessment of hybrid LDPC code performances is provided, by comparing them to protograph-based and multiedge-type (MET) LDPC codes. Hybrid LDPC codes are shown to allow to achieve an interesting tradeoff between good error-floor performance and good waterfall region with nonbinary coding techniques.
In this study, a new method for constructing low-density parity-check (LDPC) codes is presented. This construction is based on permutation matrices which come from a finite abstract group and hence the codes constructed in this manner are called group permutation low-density parity-check (GP-LDPC) codes. A necessary and sufficient condition under which a GP-LDPC code has a cycle is given and some properties of these codes are investigated. A class of flexible-rate GP-LDPC codes without cycles of length four is also introduced. Simulation results show that GP-LDPC codes perform very well with the iterative decoding and can outperform their random-like counterparts.
Low Density Parity Check(LDPC) codes is one of the high topics of the channel coding theory and has been paid more and more attention.This paper begins with a brief review of channel coding theories.Then the iterative decoding algorithm of LDPC codes,so-called as Sum-Product algorithm or Belief Propagation algorithm,is represented in detail.And the construction of LDPC codes by means of random bipartite graph and algebraic constructions,and the performance analysis by Density Evolution theory,Gaussian Approximation method and Extrinsic Information Transfer(EXIT) charts etc.,are respectively discussed.Finally,the latest study results of LDPC codes are presented and some open questions about LDPC codes are provided.