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International Conference on Computer and Information Technology (ICCIT)

Improved log domain decoding algorithm for LDPC codes over GF (q)

Md Murad Hossain, Mohammad Rakibul Islam

Published Dec 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1109/iccitechn.2011.6164824

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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 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 propose the modified minsum decoding algorithm of LDPC(Low-Density Parity-Check) code in the simplified difference-domain on the basis of detailed analysis of LDPC decoding algorithm in difference-domain. The simulation indicates that the proposed decoding algorithm offers almost no performance degradation compared with the BP(Belief Propagation) decoding algorithm in log-domain and the decoding algorithm in difference-domain and offers better performance than minsum decoding algorithm in log-domain and greatly reduces the computation complexity in AWGN(Additive White Gaussian Noise) channel and under BPSK(Binary Phase Shift Keying) modulation.
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.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
As for the sum-product decoding algorithm of low density parity check(LDPC) codes,a difference-based decoding method is proposed.The main idea is shown as follows: the messages passed on the bipartite graph of LDPC are based on the probability differences,and the updates of both check nodes and message nodes are carried out on some special addition domain.As for the update of check nodes,only some lowest differences can be selected for reducing computational complexity.In contrast with the traditional log-likelyhood-ratio-based(LLR-based) decoding method,the proposed method has much lower complexity,while it has no obvious loss of performance and convergence.