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Dual Threshold Self-Corrected Minimum Sum Algorithm for 5G LDPC Decoders

Rong Chen, Lan Chen

Published Jul 7, 2020• 3 citations
Publisher

Abstract

Fifth generation (5G) is a new generation mobile communication system developed for the growing demand for mobile communication. Channel coding is an indispensable part of most modern digital communication systems, for it can improve the transmission reliability and anti-interference. In order to meet the requirements of 5G communication, a dual threshold self-corrected minimum sum (DT-SCMS) algorithm for low-density parity-check (LDPC) decoders is proposed in this paper. Besides, an architecture of LDPC decoders is designed. By setting thresholds to judge the reliability of messages, the DT-SCMS algorithm erases unreliable messages, improving the decoding performance and efficiency. Simulation results show that the performance of DT-SCMS is better than that of SCMS. When the code rate is 1/3, the performance of DT-SCMS has been improved by 0.2 dB at the bit error rate of 10 − 4 compared with SCMS. In terms of the convergence, when the code rate is 2/3, the number of iterations of DT-SCMS can be reduced by up to 20.46% compared with SCMS, and the average proportion of reduction is 18.68%.

DOI
10.3390/info11070355

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Fifth generation (5G) is a new generation mobile communication system developed for the growing demand for mobile communication. Channel coding is an indispensable part of most modern digital communication systems, for it can improve the transmission reliability and anti-interference. In order to meet the requirements of 5G communication, a dual threshold self-corrected minimum sum (DT-SCMS) algorithm for low-density parity-check (LDPC) decoders is proposed in this paper. Besides, an architecture of LDPC decoders is designed. By setting thresholds to judge the reliability of messages, the DT-SCMS algorithm erases unreliable messages, improving the decoding performance and efficiency. Simulation results show that the performance of DT-SCMS is better than that of SCMS. When the code rate is 1/3, the performance of DT-SCMS has been improved by 0.2 dB at the bit error rate of 10 − 4 compared with SCMS. In terms of the convergence, when the code rate is 2/3, the number of iterations of DT-SCMS can be reduced by up to 20.46% compared with SCMS, and the average proportion of reduction is 18.68%.
In order to improve the performance and reliability of Low-Density Parity-Check (LDPC) code decoding algorithms, this paper proposes a Self-Correcting Minimum Sum algorithm with Dual Reliability Determination (DRD-SCMS) to address the limitations of the Self-Correcting Minimum Sum (SCMS) algorithm in determining the reliability of variable nodes. Unlike the traditional SCMS algorithm, which relies solely on the symbols from the previous and current iterations to assess the reliability of variable nodes, the DRD-SCMS algorithm combines the number of connections between variable nodes and check nodes with check failures, along with the results of symbol iterations, to provide a more accurate reliability evaluation. By categorizing variable nodes into three groups and prioritizing the updating of the most unreliable nodes, the algorithm optimizes the iteration order in the decoding process. Simulation results demonstrate that the DRD-SCMS algorithm significantly reduces the number of iterations and improves decoding efficiency compared to the SCMS algorithm, offering better applicability and reliability.
Low-Density Parity-Check (LDPC) code is a linear block code approaching the Shannon limit. The improvement of the decoding performance of LDPC codes is a hot research direction today. To improve the decoding performance of the self-correcting min-sum (SCMS) algorithm, an improved self-correcting min-sum (ISCMS) algorithm is proposed based on this algorithm. In the iterative decoding process of the ISCMS algorithm, the update rule of the check node (CN) is optimized to the update rule of the CN of the IOMS algorithm, which improves the accuracy of decoding from the processing of the CN. Simulation results show that the proposed ISCMS algorithm has better error performance and convergence performance than the SCMS algorithm with a small increase in computational complexity.
The development of the Fifth Generation (5G) New Radio (NR) provides several significant advantages when compared to the fourth generation (4G) Long Term Evolution (LTE) in mobile communications. Due to the outstanding characteristics of Low-Density Parity-Check (LDPC) codes such as high decoding performance, high throughput, low complexity, they have been accepted as the standard codes for the 5G NR. In this paper, we propose two LDPC decoding algorithms: Hybrid Offset Min-Sum (HOMS) and Variable Offset Min-Sum (VOMS), which are aimed at improving the error correction performance. The main idea of the HOMS/VOMS algorithm is to apply modified factors to both variable-nodes and check-nodes updated processing in order to compensate the extrinsic messages overestimation of the MS-based algorithms and increase the protection ability for degree-1 variable-nodes. The simulation results show that at the Bit-Error-Rate (BER) of 10-5, the proposed HOMS/VOMS algorithm achieves the decoding gain up to 0.2 dB compared to the Offset Min-Sum (OMS) algorithm, with a slight increase in decoding complexity.
In this letter, a neural self-corrected min-sum (NSCMS) decoder is proposed for 5G new radio (NR) low-density parity-check (LDPC) codes. Training in real-time on a rapidly changing channel requires low latency and minimal resource utilization. Unfortunately, typical neural decoders for LDPC codes use large and deep neural networks proportional to the code length, leading to latency and resource problems. In the network of NSCMS similar to network model pruning, certain nodes meeting the self correction condition are deleted and excluded from learning. This reduces the computational complexity of learning, compared to conventional networks. Thus, the NSCMS decoder has high practicality in real-time training using machine learning. Furthermore, self-correction allows for more reliable message-based learning and significantly improves performance. Simulation results demonstrate that NSCMS decoders exhibit lower error rates than previously proposed min-sum decoders.
One of the most important units of Low-Density Parity-Check (LDPC) decoders is the Check-Node Unit.Its main task is to find the first two minimum values among incoming variable-to-check messages and return check-tovariable messages.This block significantly affects the decoding performance, as well as the hardware implementation complexity.In this paper, we first propose a modification to the check-node update rule by introducing two optimal offset factors applied to the check-to-variable messages.Then, we present the Check-Node Unit hardware architecture which performs the proposed algorithm.The main objective of this work aims to improve further the decoding performance for 5 th Generation (5G) LDPC codes.The simulation results show that the proposed algorithm achieves essential improvements in terms of error correction performance.More precisely, the error-floor does not appear within Bit-Error-Rate (BER) of 10 -8 , while the decoding gain increases up to 0.21 dB compared to the baseline Normalized Min-Sum, as well as several state-ofthe-art LDPC-based Min-Sum decoders.
The paper presents a detailed analysis of the minsum decoding algorithm as applied to low-density parity-check (LDPC) codes used in 5G new radio (NR) systems. With the increasing demand for higher data rates and improved reliability in next-generation wireless communications, LDPC codes have emerged as a pivotal component in 5G NR's coding strategy. The minsum algorithm, known for its simplicity and efficiency in message passing, is evaluated in the context of its performance and practical implementation for these codes. Minsum decoding reduces complexity by approximating the soft-decision values using the minimum of the incoming messages, rather than applying the more computationally expensive operations such as hyperbolic tangent functions. In the context of 5G NR, this approximation makes minsum decoding particularly attractive for hardware implementation, providing a good trade-off between error-correction performance and computational efficiency. The algorithm iteratively updates messages passed along the edges of the Tanner graph, leveraging the sparsity of LDPC codes. This abstract reviews the relevance of minsum decoding to 5G NR LDPC codes, emphasizing its role in balancing performance with low computational requirements, critical in mobile and high-throughput applications.