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Journal of Nanjing University of Posts and Telecommunications

Combination of Belief Propagation and Beam Search Algorithms for the Decoding of LDPC Codes

Feng Guang-zeng

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

For short low-density parity-check codes,due to the message dependency,there exists a performance gap between the belief propagation (BP) and the maximum likelihood decoding (MLD) algorithms.Aiming at bridging the gap at the cost of some complexity,we put forward a beam search (BS) postprocessing scheme,based on the fact that LDPC codes commonly have sparsely distributed codewords and only a small portion of the codeword bits are erroneous in a BP decoding failure.In the implementation of BS to search for the error pattern,when evaluating the intermediate individuals given a limited beam width,we take advantage of the information about the decoding syndrome and the reliability metric of each bit fully.Simulation results show that the proposed method achieves a good tradeoff between performance and complexity.

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For short low-density parity-check codes,due to the message dependency,there exists a performance gap between the belief propagation (BP) and the maximum likelihood decoding (MLD) algorithms.Aiming at bridging the gap at the cost of some complexity,we put forward a beam search (BS) postprocessing scheme,based on the fact that LDPC codes commonly have sparsely distributed codewords and only a small portion of the codeword bits are erroneous in a BP decoding failure.In the implementation of BS to search for the error pattern,when evaluating the intermediate individuals given a limited beam width,we take advantage of the information about the decoding syndrome and the reliability metric of each bit fully.Simulation results show that the proposed method achieves a good tradeoff between performance and complexity.
In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.
In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.
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.
For high rate LDPC codes with light column weight and few redundant checks in their parity check matrix, the belief propagation (BP) decodings yield good error performance at the cost of high complexity. Aiming at seeking a effective decoder with good performance versus complexity tradeoff for this kind of LDPC codes, we present a new decoding framework which cascades a bit flipping (BF) variant with the ordered statistic decoding (OSD). During the iterative decoding of BF variant, the flipping value for each codeword bit is summed. The summation for each bit will be utilized as the reliability input for the OSD postprocessing, if no valid codeword is found after the maximum number of iterations for the BF variant is reached. With respect to the BP, simulation results show that the proposed BF-OSD achieves comparable performance with much less 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.