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European Transactions on Telecommunications

Generalised reliability‐based syndrome decoding of LDPC codes

Guangwen Li, Guangzeng Feng

Published Aug 5, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.1002/ett.1319

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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.
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.
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.
This article deals with Ordered Statistics Decoding (OSD) applied to the soft outputs of the Belief Propagation (BP) algorithm. We first model the weighted sum of the a posteriori LLRs across BP decoding iterations into a neuron. The neuron is then trained with the focal loss to compute for each BP decoding failure a set of accumulated Log Likelihood Ratios (LLRs) suited for OSD post-processing. Then, we propose a recursive selection procedure of LLRs sets, for multiple OSD post-processing. This selection is carried out from the sets of a posteriori LLRs calculated at each BP iteration, and from the accumulated LLRs optimized for the OSD, based on their joint probabilities of failure with OSD post-processing. An OSD is then applied to each set of LLRs belonging to the selection. In addition, we propose to reduce the OSD post-processing decoding complexity without significantly degrading its performance. Our results show that this new decoding method provides an effective way to bridge the gap to maximum likelihood decoding for short and long Low Density Parity Check (LDPC) codes.
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.
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.