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Systems Communications

Generalized Two-Magnitude Check Node Updating with Self Correction for 5G LDPC Codes Decoding

Wei Zhou, Michael Lentmaier

Published Jan 1, 2019• 7 citations
Publisher

Abstract

The min-sum (MS) and approximate-min* (a-min*) algorithms are alternatives of the belief propagation (BP) algorithm for decoding low-density parity-check (LDPC) codes. To lower the BP decoding complexity, both algorithms compute two magnitudes at each check node (CN) and pass them to the neighboring variable nodes (VNs).In this work we propose a new algorithm, ga-min*, that generalizes the MS and a-min* in terms of number of incoming messages to a CN.We analyze and demonstrate a condition to improve the performance when applying self-correction to the ga-min*. Simulations on 5G LDPC codes show that the proposed decoding algorithm yields comparable performance to the a-min* with a significant reduction in complexity, and it is robust against LLR mismatch.

DOI
10.30420/454862047

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IEEE International Symposium on Circuits and Systems proceedings•May 1, 2019•22 citations
The min-sum (MS) and approximate-min* (a-min*) algorithms are alternatives of the belief propagation (BP) algorithm for decoding low-density parity-check (LDPC) codes. To lower the BP decoding complexity, both algorithms compute two magnitudes at each check node (CN) and pass them to the neighboring variable nodes (VNs).In this work we propose a new algorithm, ga-min*, that generalizes the MS and a-min* in terms of number of incoming messages to a CN.We analyze and demonstrate a condition to improve the performance when applying self-correction to the ga-min*. Simulations on 5G LDPC codes show that the proposed decoding algorithm yields comparable performance to the a-min* with a significant reduction in complexity, and it is robust against LLR mismatch.
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.
This paper presents an Enhanced Offset Min-Sum (EOMS) decoder for Low-Density Parity-Check (LDPC) codes used in the 5th generation (5G) mobile communications. It is observed that a significant part of Variable Nodes (VNs) in the 5G LDPC codes are with degree-1 and are very sensitive to be erroneous, leading to the fact that the decoding performance is generally reduced. In the EOMS decoding, the core check nodes (CN) and extension CNs are processed with different update rules. A new CN -update criterion is also proposed by making use of the third minimum value. As a result, the offset factors are adaptively selected and the error probability of degree-1 VNs is significantly reduced. Simulation results show that the proposed EOMS decoder offers a much better error-correction performance than the state-of-the-art benchmarks for several 5G LDPC codes with a negligible complexity overhead.
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.
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.
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.
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.