Polar Orbit Decoding: Universal Parallel Soft Decoding via Automorphism Orbits

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.