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International Wireless Communications and Mobile Computing Conference (IWCMC)

Check-ratio-aided Layer-based Rescaling ANMSA and Its Application for 5G-NR LDPC Codes

Ziqi Zhou, Kewu Peng, Zhitong He

Published May 30, 2022• 1 citation
Publisher

Abstract

As a kind of iterative decoding algorithms based on belief propagation (BP), sum-product algorithm (SPA) is capacity-approaching but scale-variant. Currently, however, excellent performance and great stability are still incompatible for min-sum algorithm (MSA) and its improvements. To remedy above problems, we firstly introduce the concept of rescaling, and disclose the causes of the performance loss of MSA. Then introduce the asymptotic optimal decoding algorithm, as well as the suboptimal one. Finally, a more practicable algorithm is proposed, called check-ratio-aided layer-based rescaling adaptive normalized MSA (CL-RANMSA). Compared with the first two algorithms, CL-RANMSA is both capacity-approaching and characteristically robust. In particular, the practicably optimal factors for base graph 2 in 5G new radio low-density parity check (5G-NR LDPC) codes are provided. Simulations are also carried out whose results depict its scale-invariance and excellent performance.

DOI
10.1109/iwcmc55113.2022.9824284

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As a kind of iterative decoding algorithms based on belief propagation (BP), sum-product algorithm (SPA) is capacity-approaching but scale-variant. Currently, however, excellent performance and great stability are still incompatible for min-sum algorithm (MSA) and its improvements. To remedy above problems, we firstly introduce the concept of rescaling, and disclose the causes of the performance loss of MSA. Then introduce the asymptotic optimal decoding algorithm, as well as the suboptimal one. Finally, a more practicable algorithm is proposed, called check-ratio-aided layer-based rescaling adaptive normalized MSA (CL-RANMSA). Compared with the first two algorithms, CL-RANMSA is both capacity-approaching and characteristically robust. In particular, the practicably optimal factors for base graph 2 in 5G new radio low-density parity check (5G-NR LDPC) codes are provided. Simulations are also carried out whose results depict its scale-invariance and excellent performance.
Belief propagation (BP) provides the basis for the design of 5G new radio low density parity check (5G-NR LDPC) codes, which in turn require a BP-based decoding algorithm. The min-sum algorithm (MSA), the simplification of sum-product algorithm (SPA), should hardly be regarded as a BP-based decoding algorithm because of its minimization. To remedy this, this paper adopts the multi-edge-type density evolution (MET-DE) as the main analysis tool, and introduces the concept of Kullback-Leibler divergence. Then the least Kullback-Leibler divergence criterion is proposed to identify the optimal normalization factors. Finally, Density-Evolution-aided Adaptive Normalization Min-Sum Algorithm (DE-aided ANMSA) with edge classification is further proposed for the decoding implementation of 5G-NR LDPC codes. Simulation results demonstrate that the proposed decoding algorithm can achieve excellent performance, while the greatest advantage is that its factors could be obtained more flexibly and accurately than traditional training methods. In addition, the optimal factors for base graph 2 in 5G-NR LDPC codes are provided as well.
5G new radio low density parity check (5G-NR LDPC) codes specified by the 3rd generation partnership project (3GPP), a representative class of multi-edge-type, quasi-cyclic and raptor-like LDPC codes with rate-compatible and length-scalable capability, could meet with high-throughput demands. The corresponding decoding algorithm and implementation should support low complexity, high performance and scaleinvariance to channel variations and receiver imperfections. Flooding scheduling is usually used for the prevalent decoding algorithms and architecture of LDPC codes, but it is inefficient and inflexible compared with layered scheduling. This paper proposes a new simplification method where the sub-groups with similar fitting functions of normalization factors are incorporated into the same type, and enhanced adaptive normalized min-sum algorithm (enhanced ANMSA) for layered scheduling is further proposed for the implementation of 5G-NR LDPC codes. Based on the new simplification method, the proposed algorithm defines three types of check nodes for base graph 2 (BG2) in 5G-NR LDPC codes, and then obtains three look-up tables for BG2 by training. Simulation results demonstrate that the proposed algorithm can achieve excellent performance for 5G-NR LDPC codes of different rates and lengths over Binary-input AWGN channel and Rayleigh channel.
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.
Two methods are proposed to reduce the complexity of the belief propagation (BP) decoding for low-density parity-check (LDPC) codes, with the focus on the layered decoding for quasi-cyclic LDPC (QC-LDPC) codes. The two methods can be separately incorporated into the layered decoding procedures and combined seamlessly to provide the two-fold complexity reduction. In the first method, the message updates regarding a subset of variable nodes are omitted. To construct the subset, the most reliable bit-level channels, derived fromM-ary input channels, are identified. Then, we select the variable nodes with initial log-likelihood ratios (LLRs) exceeding a threshold among the ones assigned to the most reliable bit-level channels to form the subset. The threshold is designed and adjusted based on characteristics of the most reliable bit-level channels. Our numerical results demonstrate that the first method significantly reduces the complexity with negligibly impacting the error-correcting performance. In the second method, each layer of base graphs of QC-LDPC codes uses either sum-product algorithm (SPA) or min-sum algorithm (MSA) to update LLRs. A degree-based algorithm is presented to determine the layers employing either SPA or MSA. We compare with two intuitive methods: 1) applying SPA to randomly selected layers and MSA to the remaining layers, and 2) applying SPA to the core layers of 5G NR LDPC codes and MSA to the remaining layers. According to the numerical results, the degree-based algorithm maximally reduces the complexity while maintaining the same performance. To evaluate the joint method, the first method is applied on top of the second method. Further complexity reduction is achieved without degrading the performance of the second method.
Low-density parity-check(LDPC) code has been selected as the channel coding method by 5G NR because of its excellent error-correcting performance. To further improve the performance of LDPC decoding, this paper proposes a neural normalized min-sum(NNMS) algorithm based on multi-edge-type(MET). Based on the LLR convergence analysis of the protograph matrix of 5G NR, the base matrix is divided into several independent regions. Each part is assigned a unique scaling factor at different iterations. To verify the effectiveness of the proposed algorithm, We use two parity-check matrixes(PCM) derived from different base graphs in simulations. The results show that the proposed algorithm performs at most 0.45dB better than BP, 0.37dB better than NMS, and 0.25dB better than OMS, respectively, when the frame error rate (FER) is at 10−50^{-5}0−5 level over additive white Gaussian noise (AWGN) channels using BPSK modulation.
Layered Normalised Min-Sum algorithm is a widely used message passing algorithm for decoding Low Density Parity Check codes. The decoding performance heavily depends on the normalisation factor. Firstly, we leverage the bit structure present in 5G transport blocks to develop an improved decoding algorithm for 5G. Secondly, we determine the optimal normalisation factors of the proposed algorithm using a Deep Neural Network. Performance evaluations show an improvement of 0.3-1.9 dB, with no extra cost on multiplier resources on hardware. Hence, the proposed method is highly attractive for practical 5G decoder implementations.