Code-Weight Sphere Decoding
Yubeen Jo, Geon Choi, Yongjune Kim, Namyoon Lee
TL;DR
URLLC demands reliable decoding at finite blocklengths. The paper introduces a two-stage near-ML framework that first applies a low-complexity decoder and, upon CRC-triggered failure, refines the estimate with Code-Weight Sphere Decoding (WSD). WSD leverages pre-computed low-weight codewords and a correlation-based filtering to search within a code-weight sphere, performing iterative, monotonic refinements that converge toward ML performance with bounded latency. Simulations across CA-polar, CA-DP, and RM codes demonstrate near-ML performance with adaptively limited complexity, highlighting significant gains over conventional decoders and the universality of the approach.
Abstract
Ultra-reliable low-latency communications (URLLC) demand high-performance error-correcting codes and decoders in the finite blocklength regime. This letter introduces a novel two-stage near-maximum likelihood (near-ML) decoding framework applicable to any linear block code. Our approach first employs a low-complexity initial decoder. If this initial stage fails a cyclic redundancy check, it triggers a second stage: the proposed code-weight sphere decoding (WSD). WSD iteratively refines the codeword estimate by exploring a localized sphere of candidates constructed from pre-computed low-weight codewords. This strategy adaptively minimizes computational overhead at high signal-to-noise ratios while achieving near-ML performance, especially for low-rate codes. Extensive simulations demonstrate that our two-stage decoder provides an excellent trade-off between decoding reliability and complexity, establishing it as a promising solution for next-generation URLLC systems.