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IEEE International Symposium on Information Theory (ISIT)

A two-stage decoding algorithm for short nonbinary LDPC codes with Near-ML performance

Dixia Deng, Hengzhou Xu, Baoming Bai, Ji Zhang

Published Jun 1, 2017• 3 citations
Publisher

Abstract

This paper proposes a two-stage decoding algorithm (called BP-LED) for short nonbinary low-density parity-check (LDPC) codes. It consists of the classical belief propagation (BP) decoder and a list erasure decoder (LED). Simulation results show that, for the (16, 8) LDPC code over GF(256) in the CCSDS standard, our proposed BP-LED algorithm can achieve a coding gain of 0.6 dB with respect to the FFT-QSPA. By choosing the parameters suitable for the proposed algorithm, it has a negligible performance loss with lower decoding complexity compared with the BP-MRB (most reliable basis) algorithm in [10].

DOI
10.1109/isit.2017.8006719

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This paper proposes a two-stage decoding algorithm (called BP-LED) for short nonbinary low-density parity-check (LDPC) codes. It consists of the classical belief propagation (BP) decoder and a list erasure decoder (LED). Simulation results show that, for the (16, 8) LDPC code over GF(256) in the CCSDS standard, our proposed BP-LED algorithm can achieve a coding gain of 0.6 dB with respect to the FFT-QSPA. By choosing the parameters suitable for the proposed algorithm, it has a negligible performance loss with lower decoding complexity compared with the BP-MRB (most reliable basis) algorithm in [10].
A new method is presented for low-complexity near-maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over the additive white Gaussian noise channel. The proposed method termed belief-propagation-list erasure decoding (BP-LED) is based on erasing carefully chosen unreliable bits performed in case of BP decoding failure. A strategy of introducing erasures into the received vector and a new erasure decoding algorithm are proposed. The new erasure decoding algorithm, called list erasure decoding, combines ML decoding over the BEC with list decoding applied if the ML decoder fails to find a unique solution. The asymptotic exponent of the average list size for random regular LDPC codes from the Gallager ensemble is analyzed. Furthermore, a few examples of irregular quasi-cyclic LDPC as well as randomly constructed regular LDPC codes of short and moderate lengths are studied by simulations and their performance is compared to the tightened upper bound on the LDPC ensemble-average performance and the upper bound on the average performance of random linear codes under ML decoding. A comparison of the BP decoding and BP-LED performance of the WiMAX standard codes and performance of the near-ML BEAST decoding are presented. The new algorithm is applied to decoding a short nonbinary (NB) LDPC code over extensions of the binary Galois field. The obtained simulation results are compared to the tightened upper bound on the ensemble-average performance of the binary image of regular NB LDPC codes.
In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (LDPC) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative LDPC decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) ≈ 10-5. Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER ≈ 10-5with respect to BP decoding and MRB decoding used alone.
Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
Low-density parity-check (LDPC) codes have been widely used in practice due to their excellent error correction capabilities. However, the error correction performance of traditional decoding algorithms for LDPC codes is limited under short block lengths. To address this problem, this paper proposes an effective scheme that contains two stages for decoding short LDPC codes. In the first stage, the traditional belief propagation (BP) iterative algorithm is used to decode an LDPC code. The decoding process terminates if a codeword is obtained in this stage. Otherwise, the second stage decoding is invoked, in which the ordered reliability bits guessing random additive noise decoding (ORBGRAND) algorithm is applied. The accumulated log-likelihood ratios in the first stage are used to order the test error patterns in the ORBGRAND algorithm. Simulation results indicate that the proposed BP-ORBGRAND scheme can outperform the traditional BP iterative algorithm with relatively low additional complexity. Compared with the decoding scheme that concatenates the BP algorithm and the order statistics decoding (OSD) algorithm, the proposed decoding scheme has similar performance and the operations involved can be efficiently implemented in the hardware platform. All these indicate that the proposed scheme is desirable for practical purposes.
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.