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.

翻译：超可靠低延迟通信（URLLC）采用短数据包传输，其中有限块长效应使得近似最大似然（近似ML）解码成为理想选择，但通常计算成本过高。本文提出一种适用于任何线性分组码的两阶段近似ML解码框架。在第一阶段，运行低复杂度解码器生成候选码字和循环冗余校验。若此阶段成功，则立即终止解码。若失败，则调用第二阶段解码器——多码重球面解码（MP-WSD）。MP-WSD的核心思想是将ML搜索集中在关键区域：预先计算一组低码重码字，并利用它们对当前估计值生成结构化局部扰动。从第一阶段输出开始，MP-WSD通过叠加选定的低码重码字，迭代探索由候选码字构成的欧几里得小球面，并在发现更优候选时收缩搜索区域。该设计保持较低的平均复杂度：在高信噪比下，第一阶段以高概率成功，第二阶段极少激活；当第二阶段被激活时，搜索仍保持局部化。仿真结果表明，所提出的解码器在保持低解码延迟的同时，对短块长、低码率编码实现了近似ML性能。