Fourier Domain Decoding Algorithm of Non-binary LDPC Codes for Parallel Implementation

Kenta KASAI
Kohichi SAKANIWA

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.11    pp.1949-1957
Publication Date: 2010/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.1949
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
Keyword: 
LDPC code,  non-binary LDPC codes,  belief propagation,  Galois field,  iterative decoding,  

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Summary: 
For decoding non-binary low-density parity-check (LDPC) codes, logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing quantization effects of SP algorithm in conjunction with FFT. Since FFT is not applicable in the logarithm domain, the computations required at check nodes in the Log-SP algorithms are computationally intensive. What is worth, check nodes usually have higher degree than variable nodes. As a result, most of the time for decoding is used for check node computations, which leads to a bottleneck effect. In this paper, we propose a Log-SP algorithm in the Fourier domain. With this algorithm, the role of variable nodes and check nodes are switched. The intensive computations are spread over lower-degree variable nodes, which can be efficiently calculated in parallel. Furthermore, we develop a fast calculation method for the estimated bits and syndromes in the Fourier domain.