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International Conference on Ubiquitous and Future Networks

A Study of the Performance of LDPC Codes under Various Decoding Algorithms and Schedules

Sangwon Chae, Hyojeong Choi, Gangsan Kim, Hong‐Yeop Song, Jongsun Ahn

Published Jul 8, 2025• 1 citation
Publisher

Abstract

Low-Density Parity-Check (LDPC) codes have been widely used in modern communication standards due to their strong error correction capabilities. This paper presents an experimental evaluation of a (1200, 600) irregular LDPC code over an additive white Gaussian noise (AWGN) channel, systematically comparing three decoding algorithms (Sum-Product, Normalized Min-Sum, and Offset Min-Sum) with three scheduling methods (Flooding, Layered Belief Propagation, and Residual Belief Propagation). Parameter sweeps are performed to determine the optimal normalization factor ($\alpha$) for the Normalized Min-Sum and the offset factor ($\beta$) for the Offset Min-Sum. A comparative analysis is then performed on the frame error rate (FER) and convergence behavior of each algorithm and scheduling configuration, considering the maximum number of iterations set at 10 and 25. The results show that the Offset Min-Sum algorithm with$\beta=0.5$and Layered Belief Propagation scheduling provides an acceptable trade-off between complexity and error-correction performance, closely matching the Sum-Product algorithm but at a lower computational cost. Although Residual Belief Propagation converges quickly at lower signal-to-noise ratios, it exhibits a high error floor. These findings provide practical guidelines for selecting optimal decoding configurations in resource-constrained applications.

DOI
10.1109/icufn65838.2025.11170007

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Low-Density Parity-Check (LDPC) codes have been widely used in modern communication standards due to their strong error correction capabilities. This paper presents an experimental evaluation of a (1200, 600) irregular LDPC code over an additive white Gaussian noise (AWGN) channel, systematically comparing three decoding algorithms (Sum-Product, Normalized Min-Sum, and Offset Min-Sum) with three scheduling methods (Flooding, Layered Belief Propagation, and Residual Belief Propagation). Parameter sweeps are performed to determine the optimal normalization factor (α\alphaα) for the Normalized Min-Sum and the offset factor (β\betaβ) for the Offset Min-Sum. A comparative analysis is then performed on the frame error rate (FER) and convergence behavior of each algorithm and scheduling configuration, considering the maximum number of iterations set at 10 and 25. The results show that the Offset Min-Sum algorithm withβ=0.5\beta=0.5β=0.5and Layered Belief Propagation scheduling provides an acceptable trade-off between complexity and error-correction performance, closely matching the Sum-Product algorithm but at a lower computational cost. Although Residual Belief Propagation converges quickly at lower signal-to-noise ratios, it exhibits a high error floor. These findings provide practical guidelines for selecting optimal decoding configurations in resource-constrained applications.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
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This paper presents a low complexity Min-Sum algorithm for decoding irregular Low-Density Parity-Check (LDPC) codes. In the proposed algorithm, the significant improvement in the error correcting performance without enhancing the hardware complexity is achieved by employing adaptive and optimized normalization factors for both the extrinsic information and log-likelihood ratio data bits respectively. The experimental results demonstrate that the proposed algorithm with 6-bit non-uniform quantization achieves reasonable decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without increasing the hardware complexity by avoiding finite word length effects of soft information.
5G technology new radios (5G NR) require high-speed decoders that operate on highly irregular low-density parity-check (LDPC) codes.LDPC decoders have gained significant attention due to their excellent error correction performance.This study evaluates on different algorithms and scheduling techniques used for LDPC decoders.The analysis highlights that Min-Sum-based approaches can reduce the computational complexity compared to the basic sum-product algorithm, while the normalized and extended Min-Sum algorithms provide a better trade-off owing to their accurate value assumptions.Furthermore, different scheduling methods are implied for MS to improve speed and reduce latency.This study provides a comparative analysis of the algorithms and architectures that yield high throughputs without compromising performance efficiency.The LNMS algorithm with a data-level rescheduling technique resolves data dependency issues.This resolves the complexity of CN and VN and improves the throughput, making it suitable for 5G NR applications.The decoded throughput achieved with this scheduling is 7.0 Gbps.This throughput is achieved by maintaining the standard parameters and worst case parameters, such as four/eight iterations, BG1, and a code rate of 0.8/0.5.The evaluated architectures are implemented on Field Programmable Gate Array (FPGA) devices.This study aids in selecting the optimal architecture and scheduling techniques for LDPC decoders by considering various performance standards to deploy wireless networks in 5G and beyond.
The near-capacity performance and effective decoding algorithms of Low-Density Parity-Check (LDPC) codes have made them a mainstay of contemporary error correction. With an emphasis on iterative techniques like the Belief Propagation (BP) algorithm, the Min-Sum algorithm, and their variations, this paper offers a thorough analysis of decoding algorithms for LDPC codes. We investigate the trade-offs between various algorithmic techniques’ computational complexity, decoding latency, and error correction performance. Particular focus is placed on new methods and hardware-friendly algorithms that are tailored for next-generation communication systems, such 5 G and beyond.