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International Symposium on Communications, Control and Signal Processing

Simulation-Based Validation of Improved BP-Based Decoding Algorithms of LDPC codes

Manel Abdelhedi, Fethi Tlili, Larbi Ben Hadj Slama

Published Mar 1, 2008• 4 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes deliver very good performance when decoded with the BP algorithm. Unfortunately, this algorithm has the disadvantage to be complex for implementation. In this paper, we investigate the BP algorithm and its simplifications (BP-Based, normalized BP-Based, offset BP-Based). Previous works on normalized and offset BP-Based proposed theoretical values for the offset and normalization factors, we perform simulations which allow to validate these theoretical results.

DOI
10.1109/isccsp.2008.4537192

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Low-density parity-check (LDPC) codes deliver very good performance when decoded with the BP algorithm. Unfortunately, this algorithm has the disadvantage to be complex for implementation. In this paper, we investigate the BP algorithm and its simplifications (BP-Based, normalized BP-Based, offset BP-Based). Previous works on normalized and offset BP-Based proposed theoretical values for the offset and normalization factors, we perform simulations which allow to validate these theoretical results.
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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 representations 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 performance, latency, computational-complexity, and memory-requirement perspectives.
In this paper, we analyze the performance of two improved BP-based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization. Finite quantization effects on the BP-based and the offset BP-based decoding algorithms are evaluated.
In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.
In this letter, we analyze the performance of two improved belief propagation (BP) based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization.