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.

翻译：二进制线性分组码构成现代通信系统的基础，然而没有任何单一码族能够同时优化所有性能指标。这导致标准中广泛采用多码架构，由于每台设备需要配备多个译码器，硬件复杂度显著增加。近期提出的基于极化变换的通用译码框架旨在将二进制线性分组码译码统一于极化式译码器之下，但其并行化方案尚未得到讨论。本工作提出极轨解码——一种适用于二进制线性分组码的通用并行译码框架。我们发现二进制线性分组码的自同构群会生成置换轨道，这些置换在极化变换后产生具有相同动态冻结约束的多样化译码轨迹。通过在该自同构轨道上并行执行译码，POD 能够在无需重新适配冻结集或进行额外穷举置换搜索的情况下，实现显著的延迟-性能权衡。此外，为实现高效的轨道遍历，我们采用 Schreier-Sims 算法将自同构群表示为基强生成集形式，使得离线系统计算可在多项式时间内完成。在扩展 BCH 码与扩展 Golay 码上的仿真结果表明，与传统连续取消列表译码相比，POD 能够在实现最大似然性能的同时显著降低译码延迟。