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International ICST Conference on Communications and Networking in China

Iterative symbol-by-symbol decoding of LDPC codes and constellation mapping for multilevel modulation

Hongtao Jiang, Zhongfeng Wang, Huaping Liu

Published Jan 1, 2010• 0 citations
Publisher

Abstract

Iterative probabilistic decoding of binary low-density parity-check (LDPC) codes have been studied extensively. Non-binary LDPC codes have recently attracted an increasing attention. Most of the existing non-binary codes are built over GF(2^q), and decoding methods developed for binary LDPC codes ca
DOI
10.4108/chinacom.2010.7

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The paper studies symbol-by-symbol maximum a posteriori (MAP) decoding algorithms for non binary codes over an extension field GF(q). This decoding rule minimizes the probability of symbol error over a time-discrete memory less channel by employing the dual code. It is shown that these algorithms meet all requirements needed for iterative decoding as the output of the decoder can be split into three independent estimates: soft channel value, a priori term and extrinsic value. It represents a better form of coding for the q-ary LDPC codes, which have been shown to outperform binary LDPC codes and Reed-Solomon codes on the AWGN channel and it gives us a new fast and reduced-complexity decoding algorithm. The complexity of this rule varies inversely with code rate, making the technique particularly attractive for high rate codes. Finally, we see that complexity is reduced by using the dual code, and the algorithm is accelerated by using the fast Hadamard transform (FHT). Examples are given for both single parity check (non iterative case) and LDPC (iterative case) non binary codes