arXiv subjects

Guangwen Li

Publications and source records attributed to Guangwen Li.

12 recordsLinked to original sources

arXiv2026

Quasi-Belief Propagation and Neural-Network Check Node Processing for BCH Codes

This paper proposes a quasi-BP decoding scheme for BCH codes that preserves the parallelizable structure of belief propagation while exploiting code automorphisms and optimized redundant parity-check matrices. To eliminate the computationally expensive $\tanh$ and $\tanh^{-1}$ functions in check node updates, we further introduce a neural-network-based variant that replaces them with a lightweight convolutional neural network trained under a triple-constraint loss function enforcing non-negativity and order consistency. Simulation results for three BCH codes demonstrate that quasi-BP decoding achieves competitive frame error rate performance, with a gap within 0.25 decibels compared with belief propagation decoding of an LDPC code of similar blocklength. The neural-network-based variant incurs negligible performance loss while enabling stable deployment with arithmetic operations on hardware accelerators. Concatenation with an ordered statistics decoding variant further bridges the gap to the maximum-likelihood bound. Hence, the proposed schemes offer a viable path toward high-throughput, low-latency decoding of BCH codes in next-generation communication systems.

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arXiv2026

Quasi-BP for BCH Codes and its Optimization

This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their parity-check matrices--to enable efficient iterative decoding. We rigorously formalize this parallelizable decoder within an information-theoretic framework by tracking mutual information evolution through the constituent variable and check decoders, thereby validating the use of scattered EXIT charts as a tool for optimizing the decoder's parameters. At each iteration, an input dilation operation expands the set of messages, while a subsequent merging operation accelerates mutual information growth, ensuring rapid convergence. The proposed decoder achieves decoding performance approaching that of LDPC codes with comparable rate and blocklength, effectively pioneering the feasible deployment of BP-like decoding for high-density parity-check codes. The generality and robustness of the scheme are demonstrated through extensive simulations across codes of varying rates and blocklengths.

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arXiv2025

Neural-Model-Augmented Hybrid NMS-OSD Decoders for Near-ML in Short Block Codes

This paper presents a hybrid decoding architecture that serially couples a normalized min-sum (NMS) decoder with reinforced ordered statistics decoding (OSD) to achieve near-maximum likelihood (ML) performance for short linear block codes, including LDPC, BCH, and RS codes. The framework introduces several key innovations. A decoding information aggregation model based on a convolutional neural network refines bit-reliability estimates for OSD using the soft-output trajectory of the NMS decoder. An adaptive decoding path for OSD is initialized by the arranged list of the most a priori likely tests algorithm and dynamically updated with empirical data. A sliding-window assisted model enables early termination of test error pattern (TEP) traversal, reducing complexity with minimal performance loss. For short high-rate codes, an undetected error detector identifies erroneous NMS outputs that satisfy parity checks, ensuring they are forwarded to OSD for correction. Extensive simulations on LDPC, BCH, and RS codes demonstrate that the proposed hybrid decoder achieves a competitive trade-off: near-ML frame error rate performance while maintaining advantages in throughput, latency, and complexity over state-of-the-art alternatives. Complexity analysis shows that the average number of OSD TEPs is drastically reduced, and the architecture remains highly parallelizable. An optimization framework is also formulated to balance performance and complexity via parameter tuning.

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arXiv2024

Effective Application of Normalized Min-Sum Decoding for Short BCH Codes

This paper introduces an enhanced normalized min-sum decoder designed to address the performance and complexity challenges associated with developing parallelizable decoders for short BCH codes in high-throughput applications. The decoder optimizes the standard parity-check matrix using heuristic binary summation and random cyclic row shifts, resulting in a Tanner graph with low density, controlled redundancy, and minimized length-4 cycles. The impact of row redundancy and rank deficiency in the dual code's minimum-weight codewords on decoding performance is analyzed. To improve convergence, three random automorphisms are applied simultaneously to the inputs, with the resulting messages merged at the end of each iteration. Extensive simulations demonstrate that, for BCH codes with block lengths of 63 and 127, the enhanced normalized min-sum decoder achieves a 1-2 dB performance gain and 100X faster convergence compared to existing parallel and iterative decoders. Additionally, a hybrid decoding scheme is proposed, which selectively activates order statistics decoding when the enhanced normalized min-sum decoder fails. This hybrid approach is shown to approach maximum-likelihood performance while retaining the advantages of the normalized min-sum decoder across a broad SNR range.

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arXiv2024

Iterative decoding of short BCH codes and its post-processing

Effective iterative decoding of short BCH codes faces two primary challenges: identifying an appropriate parity-check matrix and accelerating decoder convergence. To address these issues, we propose a systematic scheme to derive an optimized parity-check matrix through a heuristic approach. This involves a series of binary sum and row shift operations, resulting in a low-density, quasi-regular column weight distribution with a reduced number of shortest cycles in the underlying redundant Tanner graph. For the revised normalized min-sum decoder, we concurrently integrate three types of random permutations into the alternated messages across iterations, leading to significantly faster convergence compared to existing methods. Furthermore, by utilizing the iterative trajectories of failed normalized min-sum decoding, we enhance the reliability measurement of codeword bits with the assistance of a neural network model from prior work, which accommodates more failures for the post-processing of ordered statistics decoding. Additionally, we report the types of undetected errors for the design of iterative decoders for short BCH codes, which potentially challenge efforts to approach the maximum likelihood limit. Extensive simulations demonstrate that the proposed hybrid framework achieves an attractive balance between performance, latency, and complexity.

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arXiv2024

Boosting Ordered Statistics Decoding of Short LDPC Codes with Simple Neural Network Models

Ordered statistics decoding has been instrumental in addressing decoding failures that persist after normalized min-sum decoding in short low-density parity-check codes. Despite its benefits, the high computational complexity of effective ordered statistics decoding has limited its application in complexity-sensitive scenarios. To mitigate this issue, we propose a novel variant of the ordered statistics decoder. This approach begins with the design of a neural network model that refines the measurement of codeword bits, utilizing iterative information from normalized min-sum decoding failures. Subsequently, a fixed decoding path is established, comprising a sequence of blocks, each featuring a variety of test error patterns. The introduction of a sliding window-assisted neural model facilitates early termination of the ordered statistics decoding process along this path, aiming to balance performance and computational complexity. Comprehensive simulations and complexity analyses demonstrate that the proposed hybrid method matches state-of-the-art approaches across various metrics, particularly excelling in reducing latency.

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arXiv2024

Deep learning based enhancement of ordered statistics decoding of short LDPC codes

In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum decoder, is enhanced by instilling three innovations. Firstly, soft information gathered at each step of the neural min-sum decoder is leveraged to forge a new reliability measure using a convolutional neural network. This measure aids in constructing the most reliable basis of ordered statistics decoding, bolstering the decoding process by excluding error-prone bits or concentrating them in a smaller area. Secondly, an adaptive ordered statistics decoding process is introduced, guided by a derived decoding path comprising prioritized blocks, each containing distinct test error patterns. The priority of these blocks is determined from the statistical data during the query phase. Furthermore, effective complexity management methods are devised by adjusting the decoding path's length or refining constraints on the involved blocks. Thirdly, a simple auxiliary criterion is introduced to reduce computational complexity by minimizing the number of candidate codewords before selecting the optimal estimate. Extensive experimental results and complexity analysis strongly support the proposed framework, demonstrating its advantages in terms of high throughput, low complexity, independence from noise variance, in addition to superior decoding performance.

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arXiv2024

The impact when neural min-sum variant meets ordered statistics decoding of LDPC codes

This paper introduces three key initiatives in the pursuit of a hybrid decoding framework characterized by superior decoding performance, high throughput, low complexity, and independence from channel noise variance. Firstly, adopting a graphical neural network perspective, we propose a design methodology for a family of neural min-sum variants. Our exploration delves into the frame error rates associated with different decoding variants and the consequential impact of decoding failures on subsequent ordered statistics decoding. Notably, these neural min-sum variants exhibit generally indistinguishable performance, hence the simplest member is chosen as the constituent of the hybrid decoding. Secondly, to address computational complexities arising from exhaustive searches for authentic error patterns in cases of decoding failure, two alternatives for ordered statistics decoding implementation are proposed. The first approach involves uniformly grouping test error patterns, while the second scheme dynamically generates qualified searching test error patterns with varied sizes for each group. In both methods, group priorities are determined empirically. Thirdly, iteration diversity is highlighted in the case of LDPC codes requiring high maximum iterations of decoding. This is achieved by segmenting the long iterative decoding trajectory of a decoding failure into shorter segments, which are then independently fed to small models to enhance the chances of acquiring the authentic error pattern. These ideas are substantiated through extensive simulation results covering the codes with block lengths ranging from one hundred to several hundreds.

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arXiv2022

A recipe of training neural network-based LDPC decoders

It is known belief propagation decoding variants of LDPC codes can be unrolled easily as neural networks after assigning differed weights to message passing edges flexibly. In this paper we focus on how to determine these weights, in the form of trainable paramters, within a framework of deep learning. Firstly, a new method is proposed to generate high-quality training data via exploiting an approximation to the targeted mixture density. Then the strong positive correlation between training loss and decoding metrics is fully exposed after tracing the training evolution curves. Lastly, for the purpose of facilitating training convergence and reducing decoding complexity, we highlight the necessity of slashing the number of trainable parameters while emphasizing the locations of these survived ones, which is justified in the extensive simulation.

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arXiv2009

Hybrid Decoding of Finite Geometry LDPC Codes

For finite geometry low-density parity-check codes, heavy row and column weights in their parity check matrix make the decoding with even Min-Sum (MS) variants computationally expensive. To alleviate it, we present a class of hybrid schemes by concatenating a parallel bit flipping (BF) variant with an Min-Sum (MS) variant. In most SNR region of interest, without compromising performance or convergence rate, simulation results show that the proposed hybrid schemes can save substantial computational complexity with respect to MS variant decoding alone. Specifically, the BF variant, with much less computational complexity, bears most decoding load before resorting to MS variant. Computational and hardware complexity is also elaborated to justify the feasibility of the hybrid schemes.

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arXiv2008

Generalized reliability-based syndrome decoding for LDPC codes

Aiming at bridging the gap between the maximum likelihood decoding (MLD) and the suboptimal iterative decodings for short or medium length LDPC codes, we present a generalized ordered statistic decoding (OSD) in the form of syndrome decoding, to cascade with the belief propagation (BP) or enhanced min-sum decoding. The OSD is invoked only when the decoding failures are obtained for the preceded iterative decoding method. With respect to the existing OSD which is based on the accumulated log-likelihood ratio (LLR) metric, we extend the accumulative metric to the situation where the BP decoding is in the probability domain. Moreover, after generalizing the accumulative metric to the context of the normalized or offset min-sum decoding, the OSD shows appealing tradeoff between performance and complexity. In the OSD implementation, when deciding the true error pattern among many candidates, an alternative proposed proves to be effective to reduce the number of real additions without performance loss. Simulation results demonstrate that the cascade connection of enhanced min-sum and OSD decodings outperforms the BP alone significantly, in terms of either performance or complexity.

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arXiv2007

Fast Reliability-based Algorithm of Finding Minimum-weight Codewords for LDPC Codes

Despite the NP hardness of acquiring minimum distance $d_m$ for linear codes theoretically, in this paper we propose one experimental method of finding minimum-weight codewords, the weight of which is equal to $d_m$ for LDPC codes. One existing syndrome decoding method, called serial belief propagation (BP) with ordered statistic decoding (OSD), is adapted to serve our purpose. We hold the conjecture that among many candidate error patterns in OSD reprocessing, modulo 2 addition of the lightest error pattern with one of the left error patterns may generate a light codeword. When the decoding syndrome changes to all-zero state, the lightest error pattern reduces to all-zero, the lightest non-zero error pattern is a valid codeword to update lightest codeword list. Given sufficient codewords sending, the survived lightest codewords are likely to be the target. Compared with existing techniques, our method demonstrates its efficiency in the simulation of several interested LDPC codes.

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