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IEEE International Conference on Anti-counterfeiting, Security, and Identification (ASID)

A Further Research on Two-phase Decoding for GC-LDPC Codes

Wei Zhou, Lijun Zhang, Qiang Sun

Published Nov 1, 2018• 1 citation
Publisher

Abstract

For GC-LDPC code, a targeted decoding scheme is the two-phase decoding scheme, i.e., the local decoding phase and the global decoding phase. For both the phases, we find the direct application of log-domin belief propagation (BP) algorithm will lead to error. Hence, we propose an improved log-domin BP algorithm and it will be used in the two-phase decoding scheme. Since the two-phase decoding scheme has a large gain loss, we present a modified two-phase decoding scheme in order to further accelerate the convergence rate. Simulation results show that the modified two-phase decoder has a gain of about 0.2 dB compared to the two-phase decoder. Moreover, it also can reduce complexity by 33.4% in high SNR compared with the whole decoder.

DOI
10.1109/icasid.2018.8693129

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For GC-LDPC code, a targeted decoding scheme is the two-phase decoding scheme, i.e., the local decoding phase and the global decoding phase. For both the phases, we find the direct application of log-domin belief propagation (BP) algorithm will lead to error. Hence, we propose an improved log-domin BP algorithm and it will be used in the two-phase decoding scheme. Since the two-phase decoding scheme has a large gain loss, we present a modified two-phase decoding scheme in order to further accelerate the convergence rate. Simulation results show that the modified two-phase decoder has a gain of about 0.2 dB compared to the two-phase decoder. Moreover, it also can reduce complexity by 33.4% in high SNR compared with the whole decoder.
A novel belief propagation(BP) decoding algorithm for convolutional low-density parity-check codes is proposed.The proposed algorithm raises the efficiency of updating the variable information by applying feedback information at each decoding iteration and employs the weighting factor to reduce the error propagation caused by the cycles in the Tanner graph,thus yielding a faster convergence of the decoding.Simulation results show that an error performance better than that of the existing belief propagation algorithm can be achieved,while the 5/8 decoding delay and the computation complexity are effectively reduced.Compared with the existing BP,the proposed algorithm achieves a gain of 0.16dB at the BER of 10-6 with the same number of iterations.
We present in this paper a new method for improving the decoding of the LDPC (low-density parity check) codes by optimising the log-SPA (sum-product algorithm). Currently, the LDPC codes give very good results with iterative decoding algorithm, log-SPA, based on the propagation confidence BP (belief propagation). To improve the existing log-SPA, we propose a decoding algorithm (log-SPA modified), which minimises the error decoding of words that could not be previously decoded. This algorithm is based on the dependency between the weight of the syndrome and the weight of the error sequence generated during iterations of decoding. Simulations illustrate the performance of our approach compared with classical LDPC code based on log-SPA.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
The fast decoding of low-density parity-check (LDPC) is crucial for its future applications. In this paper, we propose to use Early Termination (ET) and Force Convergence (FC) techniques to accelerate the decoding of two new local/global two-phases decoding algorithms to reduce the Globally Coupled (GC) LDPC codes. Specifically, ET is applied in the local decoding phase of two- phases decoding of GC-LDPC codes to skip the local decoding which is highly likely to fail and avoid the unnecessary iterations. FC is applied in global decoding phase where converged variable nodes are identified and removed from Tanner graph and the decoding can be speed up shrinking parity check matrices. Two variants are proposed for the ET operation in local decoding phase. ET-1 merely stops iteration if it meets the stopping criterion while in ET-1, the iteration number saved in local decoding is added up in global decoding to improve the decoding performance. The simulation results show that the ET-1-FC scheme can save up to 42% decoding time complexity in the low SNR region while keeping the error rate performance nearly unchanged, the ET-2-FC can improve the error rate performance by 0.18dB at bit error rate 0.001 or 0.23dB at frame error rate 0.1. In the waterfalling region of BER/FER curves, both schemes can save about 25% decoding time complexity.
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].
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.