Parallel Decoding of Binary Linear Block Codes via Equivalent Polar Transformation Class

A parameterized universal decoding framework based on polar transformations was recently proposed to enable polar-style decoding of general binary linear block codes (BLBCs). However, existing parallelization methods for polar codes cannot be directly applied to this framework. The key obstacle is that these methods rely on static frozen-set structures, which are incompatible with the dynamic frozen constraints induced by polar transformations.
To address this challenge, we revisit code automorphisms from a new perspective: instead of applying them to the codeword space, we let them act on the transformation parameter itself. We show that the BLBC automorphism group induces equivalence polar transformation classes. Crucially, all transformations within an equivalence class share the same polar subcode structure, eliminating the need for separate decoder designs.
This insight enables a novel parallel decoding framework termed polar ensemble decoding (PED). By decoding multiple equivalent transformations simultaneously, PED exploits transformation diversity while maintaining decoder compatibility.
Simulation results on extended BCH and extended Golay codes demonstrate that PED achieves near maximum-likelihood performance while significantly reducing the decoding latency compared to successive cancellation list (SCL) decoding.