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IEEE International Symposium on Circuits and Systems proceedings

An Adaptation of Min-Sum Decoder for 5G Low-Density Parity-Check Codes

Khoa Le, Fakhreddine Ghaffari, David Declercq

Published May 1, 2019• 22 citations
Publisher

Abstract

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.

DOI
10.1109/iscas.2019.8702344

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•Oct 31, 2015•2 citations
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.
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.
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.
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.
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.
Offset Min-Sum Algorithm (OMSA) and Normalized Min-Sum Algorithm (NMSA) are widely used in commercial LDPC decoders due to low complexity and reasonable performance. In this paper we proposes an Adaptive Layered Offset min- sum algorithm for the decoding of LDPC codes, which utilizes an adaptive offset factor to improve the accuracy of the soft information transferred during the iterative decoding process, and it provides good performance accordingly. The performed simulations showed that the layered offset min-sum decoding for LDPC codes can provide significant improvement compared to existing MS based algorithm, OMSA and NMSA.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.