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International Conference on Wireless Communications, Networking and Mobile Computing

Construction of Non-Binary LDPC Codes with Very Large Girth

Xiongfei Tao, Deyu Feng, Yan Zhang, Anguo Huang

Published Sep 1, 2012• 1 citation
Publisher

Abstract

A non-binary LDPC codes whose parity check matrix has uniform column weight 2 is constructed in this paper. The approach derives a non-binary LDPC codes from a column-weight 2 binary LDPC codes which is designed according to a all one (2, k) matrix, We proposed a search algorithm for constructing a (2, k) LDPC codes with desired girth, and in this paper, we use the search algorithm twice to obtain a code with larger girth. The simulation result shows that the proposed LDPC codes outperform the random codes.

DOI
10.1109/wicom.2012.6478463

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A non-binary LDPC codes whose parity check matrix has uniform column weight 2 is constructed in this paper. The approach derives a non-binary LDPC codes from a column-weight 2 binary LDPC codes which is designed according to a all one (2, k) matrix, We proposed a search algorithm for constructing a (2, k) LDPC codes with desired girth, and in this paper, we use the search algorithm twice to obtain a code with larger girth. The simulation result shows that the proposed LDPC codes outperform the random codes.
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An approach to construct column-weight-2 LDPC codes with high girth is presented. The approach derives a column-weight-2 LDPC code from the Tanner graph of a (k,k) QC-LDPC code. By the construction, the new LDPC codes double in girth. To construct the (k,k) QC-LDPC codes with desired girth, a search algorithm is proposed in this paper. The approach generates an example of a (2,3) LDPC code with a girth of 36, which is larger than the column-weight-2 LDPC codes constructed by the previously methods.
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.
In this paper, a method for constructing Low-Density Parity-Check (LDPC) codes of good performance in terms of Bit Error Rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A Modified Shortest-Path (MSP) Algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.
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.