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IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB)

Adaptive Quantized and Normalized MSA and Its Application for DTMB-A LDPC Codes

Xia An, Chao Zhang, Kewu Peng, Zhitong He, Jian Song

Published Jun 14, 2023• 4 citations
Publisher

Abstract

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.

DOI
10.1109/bmsb58369.2023.10211558

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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.
5G new radio (5G-NR) enhanced Mobile Broadband (eMBB) scenario demands a high data throughput of up to 20Gb/s, leading to an urgent need for low complexity and high throughput decoding algorithms for 5G-NR low-density parity-check (LDPC) codes, the coding scheme of 5G eMBB data channel. Quantization of input and intermediate signals enables the data throughput enhancement and the computation and storage overhead reduction of LDPC decoder, but confronts the problem of performance degradation. In addition, conventional analysis tools show limitation on the accurate asymptotic performance prediction of quantized and normalized LDPC decoding algorithms. In this paper, we first introduce modified multi-edge type density evolution (MET-DE) to the asymptotic performance prediction of quantized and adaptive normalized min-sum algorithm (ANMSA). Then we adopt adaptive asymmetric quantization strategy for MET LDPC codes, combine it with conventional adaptive normalization technique, and further propose adaptive quantized and normalized min-sum algorithm (AQNMSA), which significantly alleviates the performance degradation of fixed quantized and normalized min-sum algorithm (NMSA) with negligible increment of computational complexity. Concurrently, we provide a novel look-up table design algorithm for AQNMSA based on the analysis tool of modified MET-DE. Finally, we apply AQNMSA to 5G-NR LDPC codes with a very low quantization bit-width of 4 bits for intermediate signals, and observe a comparable or superior decoding performance compared with its float-point non-adaptive counterparts under multiple code rates.
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.
In this paper, we present adaptive quantization schemes in the normalized min-sum decoding algorithm considering scaling effects to improve the performance of irregular low-density parity-check (LDPC) decoder for WirelessMAN (IEEE 802.16e) applications. We discuss the finite precision effects on the performance of irregular LDPC codes and develop optimal finite word lengths of variables over an SNR. For floating point simulation, it is known that in the normalized min-sum or offset min-sum algorithms the performance of a min-sum based decoder is not sensitive to scaling in the log-likelihood ratio (LLR) values. However, when considering the finite precision for hardware implementation, the scaling affects the dynamic range of the LLR values. The proposed adaptive quantization approach provides the optimal performance in selecting suitable input LLR values to the decoder as far as the tradeoffs between error performance and hardware complexity are concerned.
It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.
For decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs), i.e., in the “waterfall region” of the bit error rate curve. This paper demonstrates that, for quantized decoders, MSA actually outperforms AMSA and OMSA in the “error floor” region, and that all three algorithms suffer from a relatively high error floor. This motivates the introduction of a modified MSA that is designed to outperform MSA, AMSA, and OMSA across all SNRs. The new algorithm is based on the assumption that trapping sets are the major cause of the error floor for quantized LDPC decoders. A performance estimation tool based on trapping sets is used to verify the effectiveness of the new algorithm and also to guide parameter selection. We also show that the implementation complexity of the new algorithm is only slightly higher than that of AMSA or OMSA. Finally, the simulated performance of the new algorithm, using several classes of LDPC codes (including spatially coupled LDPC codes), is shown to outperform MSA, AMSA, and OMSA across all SNRs.
In this paper, we propose an improvement of the normalized min-sum (MS) decoding algorithm and novel MS decoder architectures with reduced word length using nonuniform quantization schemes for low-density parity-check (LDPC) codes. The proposed normalized MS algorithm introduces a more exact adjustment with two optimized correction factors for check-node-updating computations, while the conventional normalized MS algorithm applies only one correction factor. The proposed algorithm provides a significant performance gain without any additional computation or hardware complexity. The finite word-length analysis in implementing an LDPC decoder is a very important factor since it directly impacts the size of memory to store the intrinsic and extrinsic messages and the overall hardware area in the partially parallel LDPC decoder. The proposed nonuniform quantization scheme can reduce the finite word length while achieving similar performances compared to a conventional quantization scheme. From simulation results, it is shown that the proposed 4-bit nonuniform quantization scheme achieves an acceptable decoding performance, unlike the conventional 4-bit uniform quantization scheme. Finally, the proposed MS decoder architectures by the nonuniform quantization scheme provide significant reductions of 20% and up to 8% for the memory area and combinational logic area, respectively, compared to the conventional 5-bit ones.