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Electronics Letters

Simplified sum-product algorithm for decoding LDPC codes with optimal performance

Stylianos Papaharalabos, P. Takis Mathiopoulos

Published Jan 13, 2009• 31 citations
Publisher

Abstract

A simple, yet effective decoding algorithm is proposed for low-density parity-check (LDPC) codes, which significantly simplifies the check node update computation of the optimal sum-product algorithm. It achieves essentially optimal performance by applying scaling in the decoder's extrinsic information. If no such scaling is applied, then the proposed algorithm has small performance degradation, e.g. in the order of 0.1 to 0.2 dB, depending on the coded block size.

DOI
10.1049/el:20092323

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A simple, yet effective decoding algorithm is proposed for low-density parity-check (LDPC) codes, which significantly simplifies the check node update computation of the optimal sum-product algorithm. It achieves essentially optimal performance by applying scaling in the decoder's extrinsic information. If no such scaling is applied, then the proposed algorithm has small performance degradation, e.g. in the order of 0.1 to 0.2 dB, depending on the coded block size.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low Density Parity Check (LDPC) approaches Shannon -limit performance for binary field and long code lengths. However performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding, while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
A computationally efficient algorithm for the decoding of low-density parity check codes is introduced. Instead of updating all bit and check nodes at each decoding iteration, the developed algorithm only updates unreliable check and bit nodes. A simple reliability criteria is developed to determine the active bit and check nodes per decoding iteration. Based on the developed technique, significant computation reductions are achieved with very little or no loss in the BER performance of the LDPC codes. The proposed method can be implemented with a slight modification to the sum–product algorithm with negligible additional hardware complexity.
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.