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Applied Computational Intelligence and Soft Computing

Adaptive Offset Min‐Sum Decoder for 5G‐NR BG2 LDPC Codes Using Genetic Algorithm

Anwer Sabah Ahmed, Yousif Jawad Kadhim Nukhailawi, Heyam A. Marzog, Marwa Jaleel Mohsin

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This paper proposes a more efficient resource‐constrained decoding algorithm for Adaptive Offset Min‐Sum (A‐OMS) low‐density parity check (LDPC) optimized decoder parameters in fifth‐generation New Radio (5G‐NR) Base Graph 2 codes (BG2). To curb the challenge of observing the all‐time finest offset to use the irregular BG2 structure, a genetic algorithm (GA) is utilized to enhance the respective offset aspect in the updating of check nodes to achieve the required objective of creating a near‐optimal solution offset aspect. Depending on the GA, the bit error rate (BER) can achieve optimal performance over a wide range of signal‐to‐noise ratios (SNRs), which is a metaheuristic optimizer. These results of the simulation indicate that this proposed optimized decoder outperforms the conventional fixed‐offset OMS by 0.2–0.5 dB in terms of belief propagation (BP) decoding performance, coding gains, and a BER that are 0.3–0.6 dB and a BER of 4.6, respectively. The proposed method achieves BP at about 35 percent decoding computation. In the case of 5G‐NR next‐generation receivers, the suggested approach will provide a fair trade‐off between the implementation efficiency and performance.

DOI
10.1155/acis/4082392

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This paper proposes a more efficient resource‐constrained decoding algorithm for Adaptive Offset Min‐Sum (A‐OMS) low‐density parity check (LDPC) optimized decoder parameters in fifth‐generation New Radio (5G‐NR) Base Graph 2 codes (BG2). To curb the challenge of observing the all‐time finest offset to use the irregular BG2 structure, a genetic algorithm (GA) is utilized to enhance the respective offset aspect in the updating of check nodes to achieve the required objective of creating a near‐optimal solution offset aspect. Depending on the GA, the bit error rate (BER) can achieve optimal performance over a wide range of signal‐to‐noise ratios (SNRs), which is a metaheuristic optimizer. These results of the simulation indicate that this proposed optimized decoder outperforms the conventional fixed‐offset OMS by 0.2–0.5 dB in terms of belief propagation (BP) decoding performance, coding gains, and a BER that are 0.3–0.6 dB and a BER of 4.6, respectively. The proposed method achieves BP at about 35 percent decoding computation. In the case of 5G‐NR next‐generation receivers, the suggested approach will provide a fair trade‐off between the implementation efficiency and performance.
Abstract This paper proposes a resource-efficient Adaptive Offset Min-Sum (A-OMS) LDPC decoder for 5G-NR Base Graph 2 (BG2) codes. A Genetic Algorithm (GA) is employed to optimize the offset factor within the check-node update, addressing the difficulty of selecting a globally optimal offset for the irregular BG2 structure. The GA operates as a meta-heuristic optimizer that minimizes the bit-error rate (BER) over a wide range of signal-to-noise ratios (SNRs). Simulation results show that the proposed GA-optimized A-OMS decoder achieves performance within 0.2–0.4 dB of belief-propagation decoding, while providing coding gains of 0.3–0.6 dB and up to a 4.6× BER reduction compared with conventional fixed-offset OMS. These improvements are obtained with approximately 35% of the computational complexity of BP decoding. The proposed approach offers a practical balance between performance and implementation efficiency for next-generation 5G-NR receivers.
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.
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 Improved Offset Min-Sum (IOMS) algorithm for Low-Density Parity-Check (LDPC) decoders, used in 5thgeneration (5G) mobile communication. The proposed algorithm IOMS applies a multiplication factor to check-node update information messages. The simulation results show that the proposed IOMS algorithm offers a better error correction performance than the existing Min-Sum-based algorithms at the expense of a slight increase in complexity. At the BER of 10–5, the IOMS achieves a decoding gain of 0.1dB with respect to the OMS algorithm.
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.
Low-density parity check (LDPC) codes, are a family of error-correcting codes, their performances close to the Shannon limit make them very attractive solutions for digital communication systems. There are several algorithms for decoding LDPC codes that show great diversity in terms of performance related to error correction. Also, very recently, many research papers involved the genetic algorithm (GA) in coding theory, in particular, in the decoding linear block codes case, which has heavily contributed to reducing the bit error rate (BER). In this paper, an efficient method based on the GA is proposed and it is used to improve the power of correction in terms of BER and the frame error rate (FER) of LDPC codes. Subsequently, the proposed algorithm can independently decide the most suitable moment to stop the decoding process, moreover, it does not require channel information (CSI) making it adaptable for all types of channels with different noise or intensity. The simulations show that the proposed algorithm is more efficient in terms of BER compared to other LDPC code decoders.