The decoding performance of conventional belief propagation decoders is seriously confined by the existence of message dependence in the code structure for short or moderate LDPC codes. In spite of the similarity of the external performance, we found the corresponding decoding failures of varied decoders, symbolized by the cross-entropy metric, will leave differed room for improvement for the postprocessing of ordered statistical decoding. Bearing in mind the postprocessor of higher order ensures better performance and incurs more expensive complexity, we propose a dynamic assignment of searching scope with respect to each decoding pattern for the order statistical decoding. Furthermore, the segmentation of decoding patterns, determined on the fly by the number of swaps in reducing the code check matrix into its systematic form via Gaussian elimination operation. will also benefit reducing complexity. Compared with the existing methods, our adapted strategy is justified by saving most memory consumption and inefficient searching of code-word candidates in extensive simulation especially for longer codes, at the cost of marginal performance loss.
The decoding performance of conventional belief propagation decoders is seriously confined by the existence of message dependence in the code structure for short or moderate LDPC codes. In spite of the similarity of the external performance, we found the corresponding decoding failures of varied decoders, symbolized by the cross-entropy metric, will leave differed room for improvement for the postprocessing of ordered statistical decoding. Bearing in mind the postprocessor of higher order ensures better performance and incurs more expensive complexity, we propose a dynamic assignment of searching scope with respect to each decoding pattern for the order statistical decoding. Furthermore, the segmentation of decoding patterns, determined on the fly by the number of swaps in reducing the code check matrix into its systematic form via Gaussian elimination operation. will also benefit reducing complexity. Compared with the existing methods, our adapted strategy is justified by saving most memory consumption and inefficient searching of code-word candidates in extensive simulation especially for longer codes, at the cost of marginal performance loss.
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.
For short low-density parity-check codes,due to the message dependency,there exists a performance gap between the belief propagation (BP) and the maximum likelihood decoding (MLD) algorithms.Aiming at bridging the gap at the cost of some complexity,we put forward a beam search (BS) postprocessing scheme,based on the fact that LDPC codes commonly have sparsely distributed codewords and only a small portion of the codeword bits are erroneous in a BP decoding failure.In the implementation of BS to search for the error pattern,when evaluating the intermediate individuals given a limited beam width,we take advantage of the information about the decoding syndrome and the reliability metric of each bit fully.Simulation results show that the proposed method achieves a good tradeoff between performance and complexity.
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.
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.
The min-sum (MS) decoding for low-density parity-check codes, though less complex than the sum–product algorithm, suffers from worse error-correcting performance. For enhancement, neural MS decoders leveraging deep learning have recently been introduced, but how to train them has not been sufficiently discussed. In this paper, we propose a novel dataset construction method and also propose systematic learning strategies by finding a good combination of dataset composition, loss functions, weight sharing, weight assignment , and weight update method. Simulations demonstrate that the proposed method achieves better error-correcting performance than other works, especially in the error floor region, within a limited number of iterations.