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Genetic Algorithm-Optimized Adaptive Offset Min-Sum LDPC Decoder for 5G- NR Base Graph 2 Codes

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

Published Jan 28, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-8646460/v1

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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.
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.
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.
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.
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.
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.
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.