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International Conference on Electronics, Communications and Control

Design of nonbinary LDPC cycle codes based on cycle entropy

Yongqiang Yin, Xingcheng Liu, Chulong Liang

Published Sep 1, 2011• 2 citations
Publisher

Abstract

In this paper, we focus on the design of a type of low- density parity-check (LDPC) codes called cycle codes whose parity-check matrix have exactly weight-2 columns. An approach to design nonbinary LDPC cycle codes with good performance is presented based on cycle entropy defined here. This method can obtain an elegant distribution of the nonbinary elements over the Galois Field GF(q) among the cycles whose length is exactly equal to the girth. Simulation results demonstrate that the LDPC codes designed with the proposed algorithm perform better than the randomly-constructed nonbinary LDPC cycle codes.

DOI
10.1109/icecc.2011.6067586

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In this paper, we focus on the design of a type of low- density parity-check (LDPC) codes called cycle codes whose parity-check matrix have exactly weight-2 columns. An approach to design nonbinary LDPC cycle codes with good performance is presented based on cycle entropy defined here. This method can obtain an elegant distribution of the nonbinary elements over the Galois Field GF(q) among the cycles whose length is exactly equal to the girth. Simulation results demonstrate that the LDPC codes designed with the proposed algorithm perform better than the randomly-constructed nonbinary LDPC cycle codes.
A low-density parity-check (LDPC) code whose parity-check matrix consists of weight-2 columns is known as a cycle code. In this letter, we propose a construction of nonbinary quasi-cyclic (QC) LDPC cycle codes based on Singer perfect difference set. The Tanner graph has girth 12 and the code length achieves the Gallager lower bound. We further show that constructed codes have exactly a minimum symbol Hamming distance 6. Simulation results show that the proposed codes perform better than random nonbinary LDPC cycle codes.
In this paper, we study a class of nonbinary LDPC (NBLDPC) codes whose parity‐check matrices have column weight 2, called NBLDPC cycle codes. We propose a design framework of (2, ρ)‐regular binary quasi‐cyclic (QC) LDPC codes and then construct NBLDPC cycle codes of large girth based on circulants and finite fields by randomly choosing the nonzero field elements in their parity‐check matrices. For enlarging the girth values, our approach is twofold. First, we give an exhaustive search of circulants with column/row weight ρ and design a masking matrix with good cycle distribution based on the edge‐node relation in undirected graphs. Second, according to the designed masking matrix, we construct the exponent matrix based on finite fields. The iterative decoding performances of the constructed codes on the additive white Gaussian noise (AWGN) channel are finally provided.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
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Quasi-cyclic (QC) low-density parity-check (LDPC) codes have several appealing properties regarding decoding, storage requirements and encoding aspects. In this paper, we focus on the QC LDPC codes over GF(q) whose parity-check matrices have fixed column weight j=2. By investigating two subgraphs in the Tanner graphs of the corresponding base matrices, we derive two upper bounds on the minimum Hamming distance for this class of codes. In addition, a method is proposed to construct QC LDPC codes over GF(q), which have good Hamming distance distributions. Simulations show that our designed codes have good performance.
Low Density Parity Check (LDPC) codes over nonbinary Galois Fields GF(q) are a generalization of the industrial standard binary LDPC codes for forward error correction in communication and information systems.The nonbinary codes can achieve significantly better performance for short and moderate block lengths.A lot of works concerning "good" LDPC codes parity check matrix construction has been published so far.However, it is well known that efficient partially parallel hardware decoder architectures are allowed only for codes with blockwise partitioned structure of the parity check matrix, called structured codes.In this paper we present a versatile algorithm for construction of codes that are both nonbinary and structured.The proposed algorithm aims at optimizing the code graph (Tanner graph) by reducing the existence of small cycles with low external connectivity, while at the same time selecting appropriate nonzero coefficients from the Galois Field under interest.The algorithm can be used for code construction of any field order, block length and code rate.