Code-Weight Sphere Decoding

TL;DR

This paper presents a two-stage decoding framework combining a low-complexity initial decoder with a code-weight sphere decoding method, achieving near-ML performance with reduced complexity for ultra-reliable low-latency communications.

Contribution

It introduces a novel two-stage decoding approach applicable to any linear block code, combining initial decoding with a localized sphere decoding to improve efficiency and reliability.

Findings

Achieves near-ML decoding performance with lower complexity.

Effectively balances reliability and computational cost.

Demonstrates promising results for next-generation URLLC systems.

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.