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Applied Mechanics and Materials

An Improved Construction for Yielding Nonbinary LDPC Codes

Li Sheng Zhang, Zhipeng Huang, Fanxin Zeng

Published May 1, 2014• 0 citations
Publisher

Abstract

In this paper, we investigate construction methods for producing nonbinary LDPC codes, and a family of nonbinary LDPC codes over is presented and its properties are derived. Compared to the second method presented by Ref. [5], simulation results show that the proposed LDPC codes perform well over the AWGN channel under belief propagation decoding algorithm and have an almost same BER curve as the ones in Ref. [5]. However, the resultant construction method is simpler than the latter’s.

DOI
10.4028/www.scientific.net/amm.556-562.6307

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In this paper, we investigate construction methods for producing nonbinary LDPC codes, and a family of nonbinary LDPC codes over is presented and its properties are derived. Compared to the second method presented by Ref. [5], simulation results show that the proposed LDPC codes perform well over the AWGN channel under belief propagation decoding algorithm and have an almost same BER curve as the ones in Ref. [5]. However, the resultant construction method is simpler than the latter’s.
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A new method is presented for low-complexity near-maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over the additive white Gaussian noise channel. The proposed method termed belief-propagation-list erasure decoding (BP-LED) is based on erasing carefully chosen unreliable bits performed in case of BP decoding failure. A strategy of introducing erasures into the received vector and a new erasure decoding algorithm are proposed. The new erasure decoding algorithm, called list erasure decoding, combines ML decoding over the BEC with list decoding applied if the ML decoder fails to find a unique solution. The asymptotic exponent of the average list size for random regular LDPC codes from the Gallager ensemble is analyzed. Furthermore, a few examples of irregular quasi-cyclic LDPC as well as randomly constructed regular LDPC codes of short and moderate lengths are studied by simulations and their performance is compared to the tightened upper bound on the LDPC ensemble-average performance and the upper bound on the average performance of random linear codes under ML decoding. A comparison of the BP decoding and BP-LED performance of the WiMAX standard codes and performance of the near-ML BEAST decoding are presented. The new algorithm is applied to decoding a short nonbinary (NB) LDPC code over extensions of the binary Galois field. The obtained simulation results are compared to the tightened upper bound on the ensemble-average performance of the binary image of regular NB LDPC codes.
To solve the problem of high computational complexity and inconvenient for hardware implementation in original decoding algorithm for non-binary LDPC codes,two simplified decoding algorithms are introduced for nonbinary LDPC codes: the fast Fourier transform belief propagation(FFT-BP) decoding algorithm and the Log-domain belief propagation(Log-BP) decoding algorithm. The performance comparison between two different decoding algorithms for LDPC Codes over GF(q) is investigated at high code rates(1/2~1) over AWGN channel.The performance curves show that by the decreasing of code rate,both coding gains and the distances from Shannon limit increase with the two algorithms,which means that non-binary LDPC Codes are suit for applications at high rates.Meanwhile it is shown that Log-BP decoding algorithm may contribute a considerable improvement in computational complexity at the cost of sacrificing some performance, which is important for Log-BP decoding algorithm to be applied in hardware implementation.