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IEEE Internet of Things Journal

Trapping-Set-Assisted Decoding for Short-Length Low-Density Parity-Check Codes

Asif Ali Zamzami, Zhu-En Yu, Yuh-Tser Wu, Shih‐Chun Lin

Published Apr 24, 2025• 2 citations
Publisher

Abstract

To guarantee that every device in industrial Internet of Things (IoT) is reliable for fast data exchange, ultrareliable and low-latency communication (URLLC) technology from 5G is crucial. To reduce latency, typically, only up to 1000 code blocklength is allowed. Indeed, a block error rate (BLER) of less than$10^{-5}$and latency of less than 1 ms are achievable in 5G URLLC. The short code blocklength feature is also required in satellite IoT. Though low-density parity-check (LDPC) decoding via belief propagation (BP) shows promise for achieving low BLER with long blocklength, its BLER is high in short LDPC codes due to error-prone patterns, with the trapping set (TS) being one of the most significant patterns. To alleviate the damage of TS, which can be identified offline, we propose two decoding algorithms named dynamic TS-assisted reinforced BP (DTS-RBP) and TS-assisted relaxation for neural-network BP (TSR-NNBP), respectively. Compared with previous works, only proposed TS assisted decoders can meet URLLC requirements under 308 code blocklength at a 3 dB signal-to-noise ratio (SNR). Moreover, under 128 code blocklength for satellite IoT, our DTS-RBP decoder provides the best memory-performance tradeoff with approximately the same number of iterations as BP.

DOI
10.1109/jiot.2024.3516737

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To guarantee that every device in industrial Internet of Things (IoT) is reliable for fast data exchange, ultrareliable and low-latency communication (URLLC) technology from 5G is crucial. To reduce latency, typically, only up to 1000 code blocklength is allowed. Indeed, a block error rate (BLER) of less than10−510^{-5}10−5and latency of less than 1 ms are achievable in 5G URLLC. The short code blocklength feature is also required in satellite IoT. Though low-density parity-check (LDPC) decoding via belief propagation (BP) shows promise for achieving low BLER with long blocklength, its BLER is high in short LDPC codes due to error-prone patterns, with the trapping set (TS) being one of the most significant patterns. To alleviate the damage of TS, which can be identified offline, we propose two decoding algorithms named dynamic TS-assisted reinforced BP (DTS-RBP) and TS-assisted relaxation for neural-network BP (TSR-NNBP), respectively. Compared with previous works, only proposed TS assisted decoders can meet URLLC requirements under 308 code blocklength at a 3 dB signal-to-noise ratio (SNR). Moreover, under 128 code blocklength for satellite IoT, our DTS-RBP decoder provides the best memory-performance tradeoff with approximately the same number of iterations as BP.
The low-density parity-check (LDPC) code is chosen to be a channel coding scheme for ultra-reliable and low-latency communications (URLLC) in 5G. However, short LDPC compromises the belief propagation (BP) decoder because of the stopping set (SS) in the decoding graph. We propose to perform different node operations according to the SS. A dynamic SS selection according to the received sequence is further applied. In the length 308 5G LDPC, our decoders outperform prior work, improving BP and collaborative BP at block error probability (BLER) of3×10−53 \times 10^{-5}3×10−5by around 0.176 and 0.092 dB respectively, with almost the same number of iterations.
Abstract Meeting the latency and reliability requirements of 5G Ultra-Reliable Low-Latency Communications (URLLC) is enabled through the adoption of short-block Low-Density Parity-Check (LDPC) codes. Traditional decoding of short-block LDPC using Belief Propagation (BP) may fail due to trapping sets, resulting in degraded decoding performance. This paper proposes a three-stage decoding algorithm that combines low-iteration BP decoding, a perturbation-based rescue process, and Maximum Likelihood (ML) based candidate validation to improve decoding reliability. When the low-iteration BP decoding stage fails to converge, the rescue stage perturbs the least reliable bits to generate multiple decoding candidates, which are subsequently evaluated using an ML-based metric to select the most likely candidate and reduce miscorrections. The proposed algorithm was evaluated through MATLAB simulations with a short-block LDPC configuration for 5G URLLC systems. QAM modulation was used and two channel models were considered, Additive White Gaussian Noise and flat Rayleigh fading. The performance was investigated for different numbers of perturbed bits and different coding rates. The results show improved decoding performance compared to standard LDPC, achieving coding gains exceeding 1 dB at low bit error rates while reducing decoding failures caused by trapping sets.
This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10 −2 , the decoder outperforms reference shorter codes (K40, K64) with an E b /N o gain of up to 0.9 dB.
This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10−2, the decoder outperforms reference shorter codes (K40, K64) with an Eb/No gain of up to 0.9 dB.
The tremendous progress of 5G technology has transformed the landscape of the Internet of Things (IoT), allowing for fast data speeds, low delay, and widespread connection that is crucial for a variety of applications, including smart cities and industrial automation. In the context of 5G enabled IoT networks, colored noise introduces varying levels of interference across different frequency bands, which can significantly degrade the performance of 5G LDPC decoding. This paper presents a novel Deep learning approach for 5G channel LDPC code decoding tailored for next-generation IoT applications. The proposed method integrates an Iterative Normalized Min-Sum (NMS) algorithm with a Convolutional Neural Network (CNN) to enhance the performance of LDPC decoding in the presence of colored noise, a common interference in real-world communication channels. Through extensive simulations and analysis, our approach demonstrates a significant performance improvement, achieving a 3.8 dB enhancement at a Bit error rate of10−610^{-6}10−6. This is achieved by accurately estimating and mitigating channel noise, thereby ensuring reliable data transmission for critical IoT applications. The findings indicate that our approach to decoding technique not only enhances error correction capabilities but also adapts to varying channel conditions, optimizing IoT network performance and efficiency. This research contributes a robust solution to the challenges posed by colored noise in 5G-enabled IoT networks, promoting the deployment of more reliable and efficient IoT systems.
Belief-propagation (BP) decoding of short and moderate-length low-density parity-check (LDPC) codes is limited by finite-length graph effects: a single decoder trajectory can become trapped or oscillatory even when an alternative trajectory would decode the received word. Existing ensemble-BP decoders create the required diversity through multiple parity-check matrices, automorphisms, modified schedules, subcodes, or altered update rules. We introduce row-boosted ensemble (RBE) decoding as a minimal decoder-side diversity mechanism: all ensemble members share the same parity-check matrix and the same BP kernel, and differ only in a small set of parity-check rows whose outgoing messages are boosted. On the 5G~NR BG1 (144,96)(144,96)(144,96) code, RBE with 323232 members lowers the frame-error rate of BP with 202020 iterations (BP-20) from 1.6×10−21.6\times10^{-2}1.6×10−2 to 1.6×10−31.6\times10^{-3}1.6×10−3 at Eb/N0=4.0 dBE_\mathrm{b}/N_0=4.0\,\mathrm{dB}Eb​/N0​=4.0dB, outperforming saturated-min-sum and affine subcode ensembles of equal size. Increasing the ensemble size yields additional gains, indicating that RBE provides a scalable performance-complexity tradeoff. The gains transfer across 5G~NR block lengths and rates, to non-5G short LDPC codes, and across flooding and layered schedules.