Iterative Threshold Decoding Of High Rates Quasi-Cyclic OSMLD Codes

Karim Rkizat,Mohammed Lahmer,Mostafa Belkasmi,Anouar Yatribi

doi:10.14569/ijacsa.2016.070468

Karim Rkizat, Mohammed Lahmer + Show 2 more

Open Access

https://doi.org/10.14569/ijacsa.2016.070468

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Abstract

Majority logic decoding (MLD) codes are very powerful thanks to the simplicity of the decoder. Nevertheless, to find constructive families of these codes has been recognized to be a hard job. Also, the majority of known MLD codes are cyclic which are limited in the range of the rates. In this paper a new adaptation of the Iterative threshold decoding algorithm is considered, for decoding Quasi-Cyclic One Step Majority logic codes (QC-OSMLD) codes of high rates. We present the construction of QC-OSMLD codes based on Singer difference sets of rate 1/2, and codes of high rates based on Steiner triple system which allows to have a large choice of codes with different lengths and rates. The performances of this algorithm for decoding these codes on both Additive White Gaussian Noise (AWGN) channel and Rayleigh fading channel, to check its applicability in wireless environment, is investigated.

Highlights

Today Low Density Parity Check (LDPC) codes [1] are present in most Telecom standards like DVB-S2 and WiMAX [2]
Chen Zhi and al[6] had given a mathematical formulation for the construction of QCOSMLD codes with high rates, these codes are based on Steiner Triple system (STS)
Gaussian Noise (AWGN) channel [7]. the purpose of this paper is to investigate the performance of iterative threshold decoding of codes of rate n0 −1 n0 constructed from

Summary

Introduction

Today LDPC codes [1] are present in most Telecom standards like DVB-S2 and WiMAX [2]. The decoding of these codes remain algorithmically complex and in situations such as the DVB-S2 [3] are often concatenated with codes such as Reed Solomon to improve performances. The cyclic OSMLD codes can be decoded iteratively by an extension of the Massey algorithm [4] which is less complex than the believe propagation algorithm but almost with the same performances. The studied subject is QC-OSMLD codes which, unlike the cyclic OSMLD codes, offer a wide range of rates equivalent to that used in the standards. Chen Zhi and al[6] had given a mathematical formulation for the construction of QCOSMLD codes with high rates, these codes are based on Steiner Triple system (STS)

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