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 (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.
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 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.
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.
This paper presents an adaptation of the Min-Sum decoders for the Low-Density Parity-Check (LDPC) used in the enhanced mobile broadband (eMBB) scenario in the 5th generation mobile networks (5G). Starting from the structure of the proposed LDPC codes for 5G where a significant part of the Variable Nodes (VNs) is with degree-1 and is sensitively to be erroneous in the traditional Offset Min-Sum decoder, we adapt the Min-Sum decoding principle to decode these 5G LDPC codes, targeting to improve the error correction performance. The proposed decoder, named Adapted Min-Sum (AMS), processes the core and the extension parts of the code differently using different offset factors. By doing that, the error probability of degree-1 VN is significantly depressed. We show through the simulation performance that the proposed decoder, with small number of quantization bits, can even surpass the floating-point counterpart and approaches the performance of the Sum-Product decoder for several 5G LDPC code lengths and code rates, with negligible additional complexity.
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.
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.