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Advanced materials research

Parallel Decoding Scheme Based on OSD and KNIH Algorithms

Guo Lei Qiao

Published Jan 3, 2012• 1 citation
Publisher

Abstract

In this contribution, KNIH algorithm and Ordered Statistic Decoding (OSD) algorithm are investigated, based on which, a novel KNIH-OSD parallel decoding scheme for LDPC codes is proposed. KNIH decoding algorithm processes certain LRPs of a received sequence, while OSD algorithm processes certain MRIPs of a received sequence. If there are too many errors in MRIPs, the OSD algorithm will fail, on the contrary, if there are too many errors in LRPs, the KNIH algorithm will fail. This contribution proposes a parallel decoding scheme based on the complementary characteristic of these two algorithms. Simulation results show that the proposed scheme is feasible and effective. Compared with OSD and KNIH algorithm, the decoding performance is improved.

DOI
10.4028/www.scientific.net/amr.433-440.4813

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In this contribution, KNIH algorithm and Ordered Statistic Decoding (OSD) algorithm are investigated, based on which, a novel KNIH-OSD parallel decoding scheme for LDPC codes is proposed. KNIH decoding algorithm processes certain LRPs of a received sequence, while OSD algorithm processes certain MRIPs of a received sequence. If there are too many errors in MRIPs, the OSD algorithm will fail, on the contrary, if there are too many errors in LRPs, the KNIH algorithm will fail. This contribution proposes a parallel decoding scheme based on the complementary characteristic of these two algorithms. Simulation results show that the proposed scheme is feasible and effective. Compared with OSD and KNIH algorithm, the decoding performance is improved.
Ordered Statistic Decoding(OSD) algorithm and Chase algorithm are investigated in this paper,based on which,a new Chase-OSD parallel decoding algorithm for medium and short lengths Low Density Parity-Check(LDPC) codes is proposed.Chasetype decoding algorithm is based on processing certain LRPs of a received sequence,while OSD algorithm is based on processing certain MRIPs of a received sequence.If there are too many errors in MRIPs,the OSD algorithm will fail,while there are too much errors in LRPs,the Chase-type algorithm will fail.A parallel concatenation decoding algorithm is proposed based on that complementary characteristic.The simulation results show that the proposed algorithm is effective.The decoding performance is improved compared with BP-OSD and BP-Chase algorithm.
According to the error-correcting capability complementarity of Chase decoding algorithm and Ordered Statistic Decoding(OSD) algorithm,a new Chase-OSD parallel decoding algorithm for RM codes is proposed,in which,OSD algorithm processes certain MRIPs of a received sequence,while Chase-type decoding algorithm processes certain LRPs of a received sequence.If there are at least i+1 MRIPs of the ordered received sequence in error,OSD algorithm will fail.On the other hand,if the number of errors in the LRPs is large,the Chase-type algorithm will fail.A parallel decoding algorithm based on complementary characteristic is proposed.Simulation experimental results show this algorithm can achieve better decoding performance.
A syndrome-based ordered statistics decoding(SOSD) algorithm for LDPC codes is proposed based on ordered statistics decoding(OSD) algorithm and syndrome-based decoding algorithm.The indexed systematic form of parity check matrix is obtained based on the least reliable independent positions(LRIPs) by performing Gaussian eliminations,which leads to that candidate codes are generated in the SOSD processing by using several binary vector additions,instead of using the re-encoding process,computation complexity in thereby reduced.A block accumulated log-likelihood ratio(LLR) strategy is further proposed to reconstruct the ordered information sequence,which can reduce the sensitivity of accumulated parameter selection to performance fluctuation.
Ordered statistics decoding (OSD) algorithm and syndrome-based decoding algorithm are investigated in this work, based on which, a syndrome-based ordered statistics decoding (SOSD) algorithm for LDPC codes is proposed. The indexed systematic form of parity check matrix is obtained based on the least reliable independent positions (LRIPs) by performing Gaussian eliminations, which promises that the SOSD processing need not the re-encoding process, but only several binary vector additions, therefore achieves noticeable computation complexity reduction.
It is well-known that the Sum-Product Algorithm (SPA) is an efficient algorithm for decoding Low Density Parity Check (LDPC) codes. In spite of this, for LDPC codes with medium length which are now attracting interests for the application to fifth generation systems, it is known that decoding error rate is much inferior to that of Maximum Likelihood Decoding (MLD). In this paper, we improve bit error rate of SPA with so called Ordered Statistic Decoding (OSD) method by Fossorier [1]D Especially, we improve stopping condition of combinatorial search in OSD method and demonstrate by simulation that the proposal stopping condition is more efficient compared to Fossorier (IEEE J. Sel. Areas Commun., 19, 2001). For that purpose, we introduce a conception “coincidence rate” which plays an important role.
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and ordered statistics decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order- (m -1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.