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Journal of Nanjing University of Posts and Telecommunications

Improved Syndrome-Based Ordered Statistic Decoding Algorithm

Feng Guang-zeng

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

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Aiming at bridge gap between maximum likelihood decoding (MLD) and belief propagation (BP) decoding for short or medium LDPC codes, we present one modified ordered statistics decoding (OSD) reprocessing method, which is serially concatenated with standard BP. Meanwhile, two novel points in implementation are addressed. For one thing, the new definition of bit reliability proposed enhances error-correcting performance via centralizing more decoding errors of standard BP within the scope of order-p OSD where p ≤ 2. For another, one way of reducing computational complexity is put forward in selecting optimal error pattern among all candidates. Simulation results demonstrate our approach could achieve good tradeoff between reprocessing performance and computational complexity. Techniques on further improvement are also discussed briefly. Reliability-based syndrome decoding of LDPC codes 1 I.

•Jan 1, 2007•0 citations
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.
Aiming at bridging the gap between the maximum likelihood decoding (MLD) and the suboptimal iterative decodings for short or medium length LDPC codes, we present a generalized ordered statistic decoding (OSD) in the form of syndrome decoding, to cascade with the belief propagation (BP) or enhanced min-sum decoding. The OSD is invoked only when the decoding failures are obtained for the preceded iterative decoding method. With respect to the existing OSD which is based on the accumulated log-likelihood ratio (LLR) metric, we extend the accumulative metric to the situation where the BP decoding is in the probability domain. Moreover, after generalizing the accumulative metric to the context of the normalized or offset min-sum decoding, the OSD shows appealing tradeoff between performance and complexity. In the OSD implementation, when deciding the true error pattern among many candidates, an alternative proposed proves to be effective to reduce the number of real additions without performance loss. Simulation results demonstrate that the cascade connection of enhanced min-sum and OSD decodings outperforms the BP alone significantly, in terms of either performance or complexity.
Abstract Aimed at bridging the gap between the maximum likelihood and the suboptimal decoding schemes for short or medium LDPC codes, a generalised ordered statistic decoding (OSD), in the form of syndrome decoding, is presented in the paper. The OSD is invoked once when a nonzero decoding syndrome is returned for the preceded belief propagation (BP) or min‐sum (MS) variants. With respect to the OSD with an accumulative reliability metric for the BP in the logarithmic likelihood ratio (LLR) domain, we extend the metric to the BP in the probability domain. Furthermore, the OSD with the metric specific for the MS variants, shows an appealing trade‐off between performance and complexity. Meanwhile, when determining the optimal error pattern estimation, an alternative designed to reduce the number of the required real additions proves to be effective. Copyright © 2008 John Wiley & Sons, Ltd.
In this work, we present an improvement on low complexity serial concatenation of belief propagation (BP) - order statistic decoding (OSD) algorithm for low-density parity-check (LDPC) codes. We introduce a more reliable method to reconstruct ordered information sequence in terms of the accumulated log-likelihood ratio (LLR) transitions of variable nodes. We give a general expression for both the existing BP-OSD algorithm and our proposed new method according to a structure similar to an infinite impulse response (IIR) filter. This improved algorithm achieves noticeable performance gains with only modest increase in computation complexity.
Aiming at bridge gap between maximum likelihood decoding (MLD) and belief propagation (BP) decoding for short or medium LDPC codes, we present one modified ordered statistics decoding (OSD) reprocessing method, which is serially concatenated with standard BP. Meanwhile, two novel points in implementation are addressed. For one thing, the new definition of bit reliability proposed enhances error-correcting performance via centralizing more decoding errors of standard BP within the scope of order-p OSD where p ≤ 2. For another, one way of reducing computational complexity is put forward in selecting optimal error pattern among all candidates. Simulation results demonstrate our approach could achieve good tradeoff between reprocessing performance and computational complexity. Techniques on further improvement are also discussed briefly. Reliability-based syndrome decoding of LDPC codes 1 I.