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

TL;DR

The paper tackles the challenge of achieving ML-like decoding for short LDPC codes by relaying neural MS failures into an enhanced OSD stage. It introduces DIA, a CNN-based method to fuse the entire NMS decoding trajectory into a robust bit reliability metric, and pairs it with a path-guided adaptive OSD that processes prioritized blocks of test error patterns, plus an auxiliary candidate-downsizing criterion. Experimental results across multiple short LDPC codes show near-ML performance with high throughput and modest complexity, and independence from noise variance, though longer codes remain more challenging. Overall, the framework offers a practical, parallelizable post-processing approach that significantly narrows the gap to ML decoding for short codes and provides a flexible mechanism to trade off performance and complexity. The work also discusses limitations on longer codes and BCH cases, and points to future research directions in time-series models and broader code families.

Abstract

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.

Figures (15)

• Figure 1: CNN implementation of the DIA model for CCSDS LDPC (128,64) code
• Figure 2: Comparison of cross-entropy and BER evaluation per decoding iteration for NMS ($\alpha=0.78$) decoding failures of LDPC (128,64) code with $T=12$. The plot includes the outputs of the DIA model, trained at SNR = 2.7dB and applied to all SNR points.
• Figure 3: Ratios and cumulative distribution functions (CDFs) of the number of erroneous bits $\delta$ in the MRB of NMS decoding failures for LDPC (128,64) code (the cases of $\delta\ge6$ merged into $\delta=6$ for convenience of plotting)
• Figure 4: Flow chart depicting the acquisition of the decoding path and its role in OSD decoding, illustrated through a toy example
• Figure 5: The relative frequency (RF) and CDF of counts of swapping between the MRB and the LRB when reducing $\mathbf{H}$ to its systematic form for decoding failures of $(128,64)$ code at SNR = $2.8, 3.5$dB