Polar Orbit Decoding: Universal Parallel Soft Decoding via Automorphism Orbits

2026-01-16

AI Summary

This work addresses the lack of a unified and parallelizable soft-decoding framework for binary linear block codes, which leads to high hardware complexity in multi-code scenarios. The paper proposes Polarized Orbit Decoding (POD), the first approach that integrates automorphism orbits with polar decoding by executing multiple equivalent decoding paths in parallel after a polarizing transformation, thereby achieving low-latency, high-performance universal soft decoding. Leveraging the Schreier–Sims algorithm, the method represents the automorphism group as a base and strong generating set (BSGS), enabling systematic offline computation in polynomial time and efficient orbit traversal without requiring refreezing or exhaustive search. Evaluated on extended BCH and Golay codes, POD attains maximum-likelihood performance while significantly outperforming conventional serial list decoding in terms of latency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Binary linear block codes
• Universal decoding
• Parallel decoding
• Polar transformations
• Decoding latency

Innovation

• Polar Orbit Decoding
• automorphism orbit
• universal decoding
• parallel soft decoding
• BSGS representation