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IEEE/CIC International Conference on Communications in China (ICCC)

A New Low-Resolution Min-Sum Decoder Based on Dynamic Clipping for LDPC Codes

Huanyu He, Lei Chu, Robert C. Qiu

Published Aug 1, 2019• 5 citations
Publisher

Abstract

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.

DOI
10.1109/iccchina.2019.8855823

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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.
The bit-error-rate (BER) performance of an LDPC decoding algorithm will be seriously degraded when the algorithm is realized with fixed-point implementation in practical applications, due to the introduced quantization errors and rounding errors. To remedy the problem, this paper proposes an improved min-sum algorithm (MSA), called CMVP algorithm. It achieves better performances than the popular min-sum algorithm (MSA), under the condition of the same fixed-point precision. Besides, the hardware overhead of the new algorithm over conventional MSA is small. On the other hand, under the condition of comparable performances, MSA algorithm needs a higher fixed-point precision and hardware costs than the new CMVP algorithm, according to the simulations and hardware synthesis results. The new algorithm also works well in a wide range of code rates and code lengths.
This letter proposes a new algorithm for the check node update in the decoding of low-density parity-check (LDPC) codes. The proposed algorithm is based on a new approximation formula of standard sum-product algorithm (SPA) which can reduce the approximation error of min-sum algorithm (MSA) and has almost the same performance as sum-product algorithm (SPA) under both floating precision operation and fixed-point operation. Besides, the new approximation formula can be implemented in simple structures competitive with MSA.
The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly outperform, the ideal belief-propagation algorithm at observed error rates.
A modified Min-Sum algorithm for low-density parity check codes is proposed in this paper. The inaccurate check node messages of the Min-Sum algorithm compared to the belief propagation (BP) algorithm are compensated by modified variable node messages, which is different from the normalized Min-Sum algorithm. The modified factor is obtained before decoding program and only one extra multiplication is needed in one cycle. So the increased complexity is fairly low. The simulation results show that the bit error rate (BER) and average number of iteration of the modified Min-Sum algorithm are very close to the BP algorithm, the modified algorithm can improve the BER performance compared to the Min-Sum algorithm while added complexity slightly.
In practical implementation, the input and intermediate signals of Low-Density Parity-Check (LDPC) message passing decoders are quantized into fixed-point messages with finite bit-width. The quantization operation with limited bit-width enhances the data throughput and reduces the computation and storage overhead of LDPC decoder, but confronts the problem of performance degradation. Existing improved algorithms of min-sum algorithm (MSA) generally do not consider the effect of quantization, and thus lack the optimization of the quantization strategy. To fill this gap, we first propose adaptive asymmetric quantization strategy. Then, based on the proposed quantization strategy, combined with conventional adaptive normalization technique, we propose adaptive quantized and normalized MSA (AQNMSA), which significantly alleviates the performance degradation of fixed quantized and normalized MSA (NMSA) with negligible increment of computational complexity. Concurrently, we provide a novel look-up table design algorithm for AQNMSA based on the tool of multi-edge-type density evolution (MET-DE). Finally, we apply AQNMSA to DTMB-A LDPC codes with a very low quantization bit-width of 4 bits, and observe a superior threshold performance and lower error floor compared with its non-adaptive float-point counterparts.
This paper is concerned with the implementation issues of the so-called min-sum algorithm (also referred to as max-sum or max-product) for the decoding of low-density parity-check (LDPC) codes. The effects of clipping threshold and the number of quantization bits on the performance of the min-sum algorithm at short and intermediate block lengths are studied. It is shown that min-sum is robust against quantization effects, and in many cases, only four quantization bits suffices to obtain close to ideal performance. We also propose modifications to the min-sum algorithm that improve the performance by a few tenths of a dB with just a small increase in decoding complexity.