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IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

An O(qlogq) log-domain decoder for non-binary LDPC over GF(q)

Chun-Hao Liao, Chien-Yi Wang, Chun-Hao Liu, Tzi‐Dar Chiueh

Published Nov 1, 2008• 6 citations
Publisher

Abstract

This paper presents a log-domain decoder for non-binary LDPC over GF(q). Comparing with the conventional O(q2) decoders, the proposed decoder can efficiently reduce the decoding complexity to O(qlogq) with only negligible degradation in BER. Comparisons on both simulated BER performance and computational complexity between the proposed and existing log-domain decoders are also provided.

DOI
10.1109/apccas.2008.4746352

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This paper presents a log-domain decoder for non-binary LDPC over GF(q). Comparing with the conventional O(q2) decoders, the proposed decoder can efficiently reduce the decoding complexity to O(qlogq) with only negligible degradation in BER. Comparisons on both simulated BER performance and computational complexity between the proposed and existing log-domain decoders are also provided.
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In this paper, we introduce a simplified log-domain decoding algorithm for LDPC codes over GF(q), named EMS. While this algorithm is a simplification of the conventional sum-product algorithm , the log-domain decoding has advantages in terms of implementation, computation complexity and numerical stability. Further, we propose some variants of implementation for the EMS algoritm, yielding a lower computational complexity. The different variants are compared with their binary homologous, the Min-Sum algorithm, both in terms of simulated FER performance and computational complexity.
An improved log domain decoding algorithm of Low density parity check (LDPC) codes over GF (q) using permutation to simplify the parity check equation is presented in this paper. This approach is different from the conventional log domain decoding algorithm of Low Density Parity Check (LDPC) codes over GF (q). The difference between improved log domain decoding and conventional log domain is that in improved log domain decoding permutation is applied in check node process where permutation is applied in between check node process and variable node process for conventional log domain decoding. Improved Log domain is mathematically equivalent to the conventional log domain decoding, however improved log-domain has advantages in terms of implementation, computational complexity and numerical stability. The proposed algorithm and the conventional log domain decoding algorithm are compared both in terms of memory requirement and simulated BER performance of (1008, 504) regular LDPC codes over GF (4) having row weight 3 & column weight 6, BPSK modulation.
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.
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.
This paper present a novel decoding scheme for low density parity check codes (LDPC) over GF(q). The scheme is a variation of the sum-product algorithm. The novel algorithm has a low complexity and reduces the number of look up table accesses necessary. Moreover, the algorithm does not compute division or multiplication, making it suitable for hardware implementation. The new algorithm has been compared with existing algorithms showing that both the BER performance and the speed of convergence are identical.