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

DE-aided ANMSA with edge classification and its application for 5G-NR LDPC codes

Ziqi Zhou, Kewu Peng, Jian Song, Zhitong He

Published Aug 4, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1109/bmsb53066.2021.9547073

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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.
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.
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.
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.
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.
In this letter, we propose various low-complexity neural layered min-sum (NLMS) algorithms to improve the decoding performance of the fifth generation (5G) new radio (NR) low-density parity-check (LDPC) codes. Our proposals are based on the computationally-efficient normalized offset min-sum (NOMS) approach for the layered belief propagation (LBP). The main novelty of our proposals is a deep neural network (DNN) that implements the layered mode decoding and that additionally learns the normalization and the offset parameters of the NOMS scheme. The schemes that we propose use the DNN as well as adaptation and filtering for estimating the optimum values of these parameters. We show by simulation that our proposed decoders achieve a significant computational benefit compared to the standard (non-neural) LBP decoder without an appreciable performance penalty.
To offer commercial LDPC decoders with better performance, in this paper, multi-edge-type (MET) normalized scheme is proposed to improve the performance of traditional min-sum algorithm (MSA) and its modified versions. With respect to sum-product algorithm (SPA), we firstly analyze and find out that the degradations of convergence in different edge types are distinct in MSA theoretically. To compensate the different degradations above, proposed MET-normalized scheme is used in normalized min-sum algorithm (MET-NMSA). In addition, MET-based density evolution (MET-DE) is also presented to search optimized MET-scaling factors for MET-NMSA. To further verify the validity of MET-normalized scheme, Advanced Television Systems Committee (ATSC) 3.0 LDPC codes are used to evaluate MET-NMSA in comparison with the conventional algorithms, i.e., normalized min-sum algorithm (NMSA), offset min-sum algorithm (OMSA) and variable-scaling normalized min-sum algorithm (VS-NMSA). Extensive simulation results show that MET-NMSA for ATSC 3.0 LDPC decoders has at most 1.53dB, 0.21dB and 0.35dB gain over NMSA, OMSA and VS-NMSA respectively when frame error rate (FER) is at 10-4level over additive white Gaussian noise (AWGN) channels using QPSK modulation.