Polar Orbit Decoding: Universal Parallel Soft Decoding via Automorphism Orbits

TL;DR

This paper introduces Polar Orbit Decoding (POD), a universal parallel decoding framework for binary linear block codes that reduces latency while maintaining maximum-likelihood performance by leveraging automorphism orbits.

Contribution

The work proposes a novel parallel decoding method using automorphism orbits and efficient group representation, enabling universal decoding for BLBCs with reduced latency.

Findings

Achieves maximum-likelihood performance on extended BCH and Golay codes.

Significantly reduces decoding latency compared to traditional methods.

Provides a polynomial-time systematic computation of automorphism groups.

Abstract

Binary linear block codes (BLBCs) form the foundation of modern communication systems, yet no single code family simultaneously optimizes all performance aspects. This leads to the widely used multi-code architecture in the standard, significantly increasing the hardware complexity since multiple decoders are required in each piece of equipment. A universal decoding framework based on polar transformations has recently been proposed to unify BLBC decoding under polar-style decoders, but its parallelization has not yet been discussed. In this work, we propose Polar Orbit Decoding (POD), a universal parallel decoding framework for BLBCs. We identify that the automorphisms of BLBCs generate an orbit of permutations that induce diverse decoding trajectories with identical dynamic-frozen constraints after the polar transformations. By decoding over this automorphism orbit in parallel, POD achieves substantial latency-performance tradeoffs without requiring frozen-set readaptation or extra exhaustive permutation searches. Moreover, to enable efficient orbit traversal in the implementation, we represent the automorphism group in a base and strong generating set (BSGS) form using Schreier-Sims algorithms, making offline systematic computation accessible in polynomial time. Simulation results on extended BCH and extended Golay codes demonstrate that POD can achieve maximum-likelihood performance while significantly reducing the decoding latency compared to conventional successive cancellation list decoding.