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International Conference on Communications and Networking in China (ChinaCom)

Hybrid decoding for one class of low-density parity-check codes

Guangwen Li, Xuelan Zou, Xin Wang

Published Jan 1, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1109/chinacom.2008.4685036

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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.
To enhance the performance of short low-density parity-check (LDPC) codes, we introduce an innovative hybrid decoder that seamlessly integrates belief propagation (BP) with ordered statistics decoding (OSD). This hybrid approach initially employs BP to decode received vectors until successful or upon reaching specified conditions, either a maximum iteration limit or a trapping iteration threshold, indicating the stagnation of BP’s hard output. Upon these conditions, the decoder transitions to a pre-configured error pattern (PEP) OSD. The PEPOSD phase then pursues a valid result, flexibly utilizing either the received vectors or the soft values of BP as input, contingent upon the signal-to-noise ratio (SNR). Given the minimal error overlap between BP and OSD, simulations reveal that this hybrid decoder achieves a notable gain of 1.5dB over BP and 0.3-0.6dB over PEPOSD, while maintaining comparable complexity to BP alone.
Abstract- Low Density Parity Check (LDPC) codes can be decoded in various ways, namely the Bit-Flipping (BF) algorithm, the Weighted BF algorithm (WBF) ， the Belief Propagation (BP) algorithm and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. In this paper, a novel self-reliability-based weighted bit-flipping decoding scheme for low-density parity-check codes is proposed. Improvement in performance is observed in comparison with the modified weighted bit-flipping decoding scheme, and the decoding complexity can be significantly reduced as well. Key-Words:- Low-density parity-check (LDPC) codes, decoding algorithm, bit flipping, self reliability
A hybrid belief propagation (BP) decoding algorithm for low-density parity-check code is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. The hybrid scheme is presented by integrating the BP algorithm with the bit-flipping function which is used as adaptive weighted factor in the BP iteration decoding. The adaptive weighting factor is based on the average weighted reliability measure of the hard output of decoder. The proposed hybrid adaptive weighted iteration scheme can efficiently increase the convergence speed of the belief propagation decoding and therefore improve the error performance. Simulation results show that the proposed algorithm can significantly reduce the decoding complexity and achieve better error performances as compared with the sum-product algorithm.
In this paper, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.5dB coding gain improvement at BER = 5×10−6while reducing up to 48% iterations for decoding and maintaining low decoding complexity, compared with the conventional weighted BF algorithm.
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 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.