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.
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.
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.
Abstract This paper introduces 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. The framework incorporates several key innovations: a decoding information aggregation model that employs a convolutional neural network to refine bit reliability estimates for OSD using the soft-output trajectory of the NMS decoder; an adaptive decoding path for OSD, initialized by the arranged list of the most a priori likely tests algorithm and dynamically updated with empirical data; and a sliding window assisted model that enables early termination of test error patterns’ traversal, curbing complexity with minimal performance loss. For short high-rate codes, a dedicated undetected error detector identifies erroneous NMS outcomes 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 delivers a competitive trade-off, achieving near-ML frame error rate performance while maintaining advantages in throughput, latency, and complexity over state-of-the-art alternatives.
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.
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.
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with the codelength, thus they can only support short to moderate codelengths. From the point view of practicality, we propose a high-performance neural min-sum (MS) decoding method that makes full use of the lifting structure of protograph low-density parity-check (LDPC) codes. By this means, the size of the parameter array of each layer in the neural decoder only equals the number of edge-types for arbitrary codelengths. In particular, for protograph LDPC codes, the proposed neural MS decoder is constructed in a special way such that identical parameters are shared by a bundle of edges derived from the same edge-type. To reduce the complexity and overcome the vanishing gradient problem in training the proposed neural MS decoder, an iteration-by-iteration (i.e., layer-by-layer in neural networks) greedy training method is proposed. With this, the proposed neural MS decoder tends to be optimized with faster convergence, which is aligned with the early termination mechanism widely used in practice. To further enhance the generalization ability of the proposed neural MS decoder, a codelength/rate compatible training method is proposed, which randomly selects samples from a set of codes lifted from the same base code. As a theoretical performance evaluation tool, a trajectory-based extrinsic information transfer (T-EXIT) chart is developed for various decoders. Both T-EXIT and simulation results show that the optimized MS decoding can provide faster convergence and up to 1dB gain compared with the plain MS decoding and its variants with only slightly increased complexity. In addition, it can even outperform the sum-product algorithm for some short codes.
Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.