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Generalization of "Algorithm E" for Decoding LDPC Codes Over GF(q)

M Kurkoski Brian, Kazuhiko Yamaguchi, Kingo Kobayashi

Published May 18, 2006• 2 citations
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Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
We consider decoding of LDPC codes over GF(q) with a harddecision low-complexity majority algorithm, which is a generalization of the bit-flipping algorithm for binary LDPC codes. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new algorithm is derived. The estimate is shown to be better than the estimate for a single threshold majority decoder. At the same time, introducing multiple thresholds does not affect the order of decoding complexity.