Polar Orbit Decoding: Universal Parallel Soft Decoding via Automorphism Orbits
Pin-Jing Li, Yu-Chih Huang
TL;DR
Polar Orbit Decoding (POD) addresses the lack of a single universal BLBC decoder by exploiting automorphism orbits within polar-transformed BLBCs to create multiple parallel, yet equivalent, polar subcodes with identical dynamic frozen constraints. The method employs a Base/Strong Generating Set (BSGS) representation and Schreier-Sims precomputation to enable polynomial-time orbit traversal, allowing $M$ parallel polar decoders to operate on the orbit members and then combine results. Simulations on extended BCH and extended Golay codes demonstrate near-ML performance with significantly reduced latency compared to conventional SCL decoding, validating POD as a scalable, code-agnostic solution for parallel decoding in BLBCs. This framework promises hardware-friendly, universal decoding across multi-code standards such as 5G NR, with potential extensions to enhanced polar transforms and nonbinary codes.
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.