Hierarchical Subcode Ensemble Decoding of Polar Codes

2026-02-09

AI Summary

This work addresses the susceptibility of conventional polar code iterative decoding to stopping sets and the challenge of scaling existing subcode ensemble methods while preserving linear coverage. To overcome these limitations, the authors propose a hierarchical subcode ensemble decoding framework that recursively constructs layered parity-check constraints from subcodes, enabling large-scale integration strictly under the linear coverage condition. The approach introduces, for the first time, a hierarchical subcode construction mechanism that jointly exploits diversity gain and maintains manageable decoding complexity. Experimental results demonstrate that, under identical decoding latency, the proposed scheme significantly outperforms standard belief propagation and conventional ensemble decoding in terms of block error rate reduction.

Technology Category

• Machine Learning: Ensemble Methods
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Subcode-ensemble decoders improve iterative decoding by running multiple decoders in parallel over carefully chosen subcodes, increasing the likelihood that at least one decoder avoids the dominant trapping structures. Achieving strong diversity gains, however, requires constructing many subcodes that satisfy a linear covering property-yet existing approaches lack a systematic way to scale the ensemble size while preserving this property. This paper introduces hierarchical subcode ensemble decoding (HSCED), a new ensemble decoding framework that expands the number of constituent decoders while still guaranteeing linear covering. The key idea is to recursively generate subcode parity constraints in a hierarchical structure so that coverage is maintained at every level, enabling large ensembles with controlled complexity. To demonstrate its effectiveness, we apply HSCED to belief propagation (BP) decoding of polar codes, where dense parity-check matrices induce severe stopping-set effects that limit conventional BP. Simulations confirm that HSCED delivers significant block-error-rate improvements over standard BP and conventional subcode-ensemble decoding under the same decoding-latency constraint.

Problem

• subcode ensemble
• linear covering
• polar codes
• iterative decoding
• diversity gain

Innovation

• hierarchical subcode ensemble decoding
• polar codes
• belief propagation
• linear covering property
• stopping-set mitigation