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International Conference on Communications

Log-domain decoding of LDPC codes over GF(q)

Henk Wymeersch, Heidi Steendam, Marc Moeneclaey

Published Jan 1, 2004• 288 citations
Publisher

Abstract

This paper introduces a log-domain decoding scheme for LDPC codes over GF(q). While this scheme is mathematically equivalent to the conventional sum-product decoder, log-domain decoding has advantages in terms of implementation, computational complexity and numerical stability. Further, a suboptimal variant of the log-domain decoding algorithm is proposed, yielding a lower computational complexity. The proposed algorithms and the sum-product algorithm are compared both in terms of simulated BER performance and computational complexity.

DOI
10.1109/icc.2004.1312606

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This paper introduces a log-domain decoding scheme for LDPC codes over GF(q). While this scheme is mathematically equivalent to the conventional sum-product decoder, log-domain decoding has advantages in terms of implementation, computational complexity and numerical stability. Further, a suboptimal variant of the log-domain decoding algorithm is proposed, yielding a lower computational complexity. The proposed algorithms and the sum-product algorithm are compared both in terms of simulated BER performance and computational complexity.
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.
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.
Low-Density Parity-Check (LDPC) codes have gained significant popularity recently and have been recommended for various wireless standards of the future. Non-binary LDPC codes provide all the well-known advantages of binary LDPC codes but allow for much shorter block lengths. The sum-product decoding algorithm for non-binary LDPC codes is too complex for efficient implementation. Hence, we have represented the sum-product algorithm in a novel log-domain form in terms of operators defined earlier in literature. This form greatly simplifies the key step in the check-node processing and allows us to replace a max* operation in the decoder by a max operation. This leads to a sub-optimal decoding algorithm which we propose in this paper.
A simple,yet effective decoding algorithm for LDPC(low-density parity-check) codes over GF(q) is presented.By taking advantages of the first-term Taylor's series expansion to approximate the correction term of the Jacobian logarithm used in LLR-SPA(log-likelihood ratio sum-product algorithm),we propose an algorithm which significantly simplifies the check node update computation of the optimal LLR-SPA.Compared to the offset min-sum algorithm,the proposed algorithm achieves a gain of about 0.2dB at the BER of 10-4.Moreover,unlike the offset min-sum algorithm,parameters of this algorithm are independent of the order of the Galois Filed.