Hierarchical Subcode Ensemble Decoding of Polar Codes

TL;DR

This paper introduces hierarchical subcode ensemble decoding (HSCED), a scalable framework that improves polar code decoding by maintaining linear covering properties through recursive subcode generation, leading to better error performance.

Contribution

HSCED provides a systematic method to scale subcode ensembles while preserving linear covering, enhancing decoding diversity and performance for polar codes.

Findings

HSCED significantly improves block-error-rate over standard BP decoding.

HSCED maintains linear covering with large ensembles, enabling better decoding diversity.

Simulations show HSCED outperforms conventional methods under same latency constraints.

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.