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

TL;DR

This work introduces a hybrid LDPC decoding framework that fuses neural min-sum (NMS) variants with ordered statistics decoding (OSD) to achieve near-ML performance with high throughput and low complexity, while remaining invariant to channel noise variance. It advances three key ideas: a GNN-guided, low-complexity NMS design (favoring NMS-1), two adaptive OSD strategies for efficient test error pattern organization, and iteration-diversity to exploit long NMS failure trajectories through multiple small post-processors. The framework is validated on short-to-moderate LDPC codes, showing substantial reductions in OSD search space (TEPs) and competitive FER performance, approaching ML within a small gap even for longer codes. Practically, this approach enables high-rate, low-latency decoding suitable for systems like 5G and IoT, with scalable complexity managed by dynamic TEP partitioning and DIA-driven bit reliabilities.

Abstract

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.

Figures (8)

• Figure 1: Diagram of OSD procedures
• Figure 2: Hierarchical structure of decoding path
• Figure 3: FER comparison for various NMS variants and corresponding OSD with support of DIA, auxiliary criterion and iteration diversity for LDPC (128,64) code
• Figure 4: Statistics about the error rates of all MRB bits before and after GE calling are compared for LDPC (128,64) code at SNR=2.8, 3.4dB. Suppose the starting MRB index is 64; after some oscillation, it is found that the diverging curves will re-converge at some index 88.
• Figure 5: Block diagram of the approach to achieve diversity gain through iteration splitting for training DIA models. In this illustration, the decoding trajectory of length $T=13$ is split into 2 groups per decoding failure.