Multipoint Code-Weight Sphere Decoding: Parallel Near-ML Decoding for Short-Blocklength Codes

TL;DR

This paper introduces a two-stage decoding framework for short-blocklength codes in URLLC, combining a low-complexity initial decoding with a localized sphere decoding to achieve near-ML performance efficiently.

Contribution

It proposes multipoint code-weight sphere decoding (MP-WSD), a novel localized search method that improves decoding efficiency for short codes by focusing on promising candidate regions.

Findings

Achieves near-ML decoding performance for short, low-rate codes.

Maintains low average decoding complexity at high SNR.

Effective in reducing latency for URLLC applications.

Abstract

Ultra-reliable low-latency communications (URLLC) operate with short packets, where finite-blocklength effects make near-maximum-likelihood (near-ML) decoding desirable but often too costly. This paper proposes a two-stage near-ML decoding framework that applies to any linear block code. In the first stage, we run a low-complexity decoder to produce a candidate codeword and a cyclic redundancy check. When this stage succeeds, we terminate immediately. When it fails, we invoke a second-stage decoder, termed multipoint code-weight sphere decoding (MP-WSD). The central idea behind {MP-WSD} is to concentrate the ML search where it matters. We pre-compute a set of low-weight codewords and use them to generate structured local perturbations of the current estimate. Starting from the first-stage output, MP-WSD iteratively explores a small Euclidean sphere of candidate codewords formed by adding selected low-weight codewords, tightening the search region as better candidates are found. This design keeps the average complexity low: at high signal-to-noise ratio, the first stage succeeds with high probability and the second stage is rarely activated; when it is activated, the search remains localized. Simulation results show that the proposed decoder attains near-ML performance for short-blocklength, low-rate codes while maintaining low decoding latency.