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IEEE Communications Letters

Approximated Box-Plus Decoding of LDPC Codes

Stylianos Papaharalabos, F. Lazarakis

Published Oct 20, 2015• 10 citations
Publisher

Abstract

The problem of how to approximate effectively the box-plus operation used in sum-product algorithm (SPA) decoding of low-density parity-check (LDPC) codes has been widely investigated over the past years of research. This letter deals, for the first time, with a totally different approach where a very simple, yet efficient, decoding algorithm for LDPC codes is proposed. The tremendous savings, in terms of required number of operations, offered by the proposed algorithm and its near optimal SPA performance are making it appealing in practical applications requiring very low complexity LDPC decoding architectures.

DOI
10.1109/lcomm.2015.2492965

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The problem of how to approximate effectively the box-plus operation used in sum-product algorithm (SPA) decoding of low-density parity-check (LDPC) codes has been widely investigated over the past years of research. This letter deals, for the first time, with a totally different approach where a very simple, yet efficient, decoding algorithm for LDPC codes is proposed. The tremendous savings, in terms of required number of operations, offered by the proposed algorithm and its near optimal SPA performance are making it appealing in practical applications requiring very low complexity LDPC decoding architectures.
This letter proposes a new algorithm for the check node update in the decoding of low-density parity-check (LDPC) codes. The proposed algorithm is based on a new approximation formula of standard sum-product algorithm (SPA) which can reduce the approximation error of min-sum algorithm (MSA) and has almost the same performance as sum-product algorithm (SPA) under both floating precision operation and fixed-point operation. Besides, the new approximation formula can be implemented in simple structures competitive with MSA.
Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.
Efficient implementations of the sum-product algorithm (SPA) are presented for decoding low-density parity-check (LDPC) codes using log-likelihood ratios (LLR) as messages between symbol and parity-check nodes. Various reduced-complexity derivatives of the LLR-SPA are proposed. Both serial and parallel implementations are investigated, leading to trellis and tree topologies, respectively. Furthermore, by exploiting the inherent robustness of LLRs, it is shown, via simulations, that coarse quantization tables are sufficient to implement complex core operations with negligible or no loss in performance. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate design point in high-speed applications from a performance, latency and computational complexity perspective.
Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.