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Conditional termination check min-sum algorithm for efficient LDPC decoders

Keol Cho, Ki‐Seok Chung

Published Jan 1, 2015• 3 citations
Publisher

Abstract

Conditional termination check min-sum algorithm (MSA) using the difference of the first two minima is proposed for faster decoding speed and lower power consumption of low-density parity-check (LDPC) code decoders. Judging from the size of the difference in LDPC decoding scheduling, the proposed method dynamically decides whether the termination checking steps will be skipped or not. The simulation results show that the decoding speed is improved up to 7%, and the power consumption is reduced by up to 16.43% without any loss of error correcting performance. Also, the additional hardware cost of the proposed method is negligible compared to conventional LDPC decoders.

DOI
10.1587/elex.12.20150738

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•May 20, 2009•1 citation
Conditional termination check min-sum algorithm (MSA) using the difference of the first two minima is proposed for faster decoding speed and lower power consumption of low-density parity-check (LDPC) code decoders. Judging from the size of the difference in LDPC decoding scheduling, the proposed method dynamically decides whether the termination checking steps will be skipped or not. The simulation results show that the decoding speed is improved up to 7%, and the power consumption is reduced by up to 16.43% without any loss of error correcting performance. Also, the additional hardware cost of the proposed method is negligible compared to conventional LDPC decoders.
Low-density parity-check (LDPC) codes have attracted tremendous attention for their excellent error-correction performance and inherent fitness for high-parallelism implementation. With great complexity reduction and friendly for hardware implementation, the min-sum (MS) decoding algorithm for LDPC codes gains widespread applications in practical. In the MS decoding algorithm, finding the first two minima among input variable-to-check messages is the most complex part. To further reduce the complexity of the MS decoding algorithm, an efficient single-minimum (single-min) based layered MS decoding for quasi-cyclic LDPC (QC-LDPC) codes is proposed in this paper. It is found that statistically the difference between the first minimum and second minimum increases as the decoding becomes more convergent. Accordingly, in the proposed single-min scheme, the second minimum is approximately derived based on the first minimum and an index indicating the convergence degree. Besides, some other metrics that are easily obtained are used to refine the second minimum. Simulation results show that the proposed method can significantly improve the error-correction performance and lower the average number of iterations, compared with the state-of-the-art single-min based MS decoding algorithms.
Compared with the sum-product algorithm (SPA) with high decoding complexity for low-density parity-check (LDPC) codes, its approximated version, the min-sum algorithm (MSA), reduces the computational complexity at the cost of slight performance degradation. In order to compensate the oversized check-node messages in the MSA, the effect of clipping on variable-node messages is investigated under two-bit resolution. Our results show that the performance of clipped MSA degrades at the high bit error rate (BER) and increases at the low BER as clipping threshold enlarges. Based on these results, we propose a modified quantized MS decoding algorithm where the adaptive clipping threshold is applied on the variable-node messages according to the number of unsatisfied checks per-iteration. The adaptive rule is designed for easy hardware implementations. Numerical results show that the proposed algorithm has considerable improvement in performance compared with the MSA under two-bit precision. And it can achieve the performance near the SPA for some short-length LDPC codes.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.
Entering the 5G era, the hardware design of low-density parity-check (LDPC) codes under the new standard has increasingly higher requirements on throughput. According to the geometric characteristics of the check matrices of the quasi-cyclicQC) LDCP codes under the CCSDS standard, this paper designs a layered dynamic normalized minimum sum algorithm(LDNMSA) under the pre-termination decoding based on de-layering scheme. The check matrix structure of this code is easy for hardware design and the storage resource consumption is low. The approximate replacement of the minimum sum algorithm(MSA) reduces the computational complexity of the check node update process. The determination of correction factors and inter-layer deletion thresholds through computer simulation improves the decoding performance and the speed of a single iteration, and adopt the layered scheduling scheme with optimized update order reduces the number of iterations required for decoding. Experimental results show that when the bit error rate(BER) is 10-5, the designed algorithm has a gain of approximately 0.5 dB compared to the MSA. The speed and calculation amounts to a single iteration are much lower than the log-likelihood-ratio(LLR) belief propagation(BP) algorithm and the performance is only less than 0.1dB.
The Minimum Sum (MS) algorithm is a standard Low-Density Parity-Check Codes (LDPC) decoding algorithm. Compared with traditional algorithms, it uses approximate calculations to reduce the computational complexity of the algorithm when calculating parity nodes, resulting in performance loss issues. To improve the LDPC decoding performance, the LDPC decoding algorithm of Multi-parameter Compensated Min-Sum (MCMS) is proposed. This algorithm introduces relevant information, such as channel and code length, into calculating update verification nodes. Introducing multiplication and correction factors to reduce errors in validation node calculations through multi-parameter compensation. Simulation results show that the MCMS algorithm has superior error rate performance compared with the MS algorithm.