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IEEE International Conference on Communication Systems (ICCS)

A simple algorithm to design irregular LDPC codes for finite length

Mehrdad Taki, Mahdi Orooji

Published Jan 1, 2006• 1 citation
Publisher

Abstract

A simple and practical algorithm to design an irregular low density parity check (LDPC) codes for finite length applications is introduced. The simulation result will be proved the advantages of designed codes in compare with conventional regular and irregular finite length LDPC codes. Due to the semi-random structure of proposed codes, it will be encoded simpler than the other LDPC codes. Finally, a modified extended bit filling (EBF) is proposed to control rows weight

DOI
10.1109/iccs.2006.301433

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A simple and practical algorithm to design an irregular low density parity check (LDPC) codes for finite length applications is introduced. The simulation result will be proved the advantages of designed codes in compare with conventional regular and irregular finite length LDPC codes. Due to the semi-random structure of proposed codes, it will be encoded simpler than the other LDPC codes. Finally, a modified extended bit filling (EBF) is proposed to control rows weight
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In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over additive white Gaussian noise (AWGN) channels. We present the iterative decoding algorithm of LDPC codes, and we also discuss the encoding methods and the bipartite graph representation of LDPC codes ensemble. Finite-length LDPC code performances are investigated, and the influence of cycle is pointed out. Simulation results show that irregular LDPC codes with variable and check node degree distribution optimized for infinite-length codes are not optimal for finite-length LDPC codes, and the error patterns of both regular and irregular codes are investigated as an effort to improve the performance and design methodology of finite-length LDPC codes.
The main influence for the performance of finite length Low-Density Parity-Check(LDPC) codes is analyzed. According to optimum choice for degree distribution, a check matrix is constructed with improved Progressive-Edge-Growth (PEG) algorithm. A practical efficient encoding algorithm is proposed to optimize the check matrix. A finite length irregular LDPC code with low error-floor performance and approximate linear encoding complexity is obtained. This optimization method can be easily extended to general communication channels.
Low density parity check codes are a popular class of linear block codes for forward error correction in communication channels. Recent years have seen a lot of work towards the hardware-oriented constructions for LDPC codes which have comparable error-correcting performance to random construction codes. This paper proposes a novel method called Iterative-filled (IF) to construct LDPC codes and a new kind of LDPC codes named IF-LDPC codes. Based on the properties of the method proved in this paper, we present a design of regular and quasi-regular IF-LDPC encoders which have linear encoding complexity, simple construction, low memory requirement and are suitable for partly parallel decoding. These advantages make them easy to hardware implementation. The IF-LDPC codes exhibit good performance in computer simulations and some even better than MacKay codes.
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In this paper, low density parity check (LDPC) codes are considered. Design techniques are examined and new LDPC codes with improved error performance are proposed for irregular LDPC codes. Especially for BPSK modulation and AWGN channel, superior LDPC codes are successfully designed for R = 0.5 and N = 1000. For the designed superior irregular codes, it can be said that not only the performance of the codes is good when the code block length goes to infinity, but also they approach to the channel capacity and for code rate R = 0.5, they perform better than their counterparts given in the literature, when the code block length is finite (N = 1000). For irregular codes, when the degree of the bit node that possess the maximum number of branches is large, then that code approaches to the channel capacity. During the optimization of the encoder and decoder blocks, a combination of differential evolution technique, bit filling and message passing algorithms are considered to reach superior codes. The best superior code proposed in the paper is an irregular LDPC code with rate R = 0.5 which is only 0.02 dB away from the channel capacity.