Parallelism has become a central concern in modern decoding frameworks aiming to meet stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that tests candidate Error Patterns (EPs) until a valid codeword is found. Among its variants, Soft GRAND (SGRAND) achieves maximum-likelihood (ML) decoding but relies on real-time generation and likelihood ordering of EPs, making parallel execution nontrivial under the ML optimality constraint. In this work, we introduce a unified binary tree representation of EPs, termed the EP tree, which formalizes the hierarchical structure underlying SGRAND and Ordered Reliability Bits (ORB) GRAND algorithms, enabling structured organization of EPs and algorithmic-level parallel exploration. Building upon this unified framework, we propose a parallel design of SGRAND that preserves ML optimality while significantly reducing decoding complexity through pruning strategies and tree-based computation. Furthermore, we develop an enhanced ORBGRAND algorithm based on the same EP tree representation, improving decoding performance toward ML while retaining parallel efficiency. Numerical experiments show that the proposed parallel SGRAND achieves a $3.96\times$ reduction in decoding latency compared with its serial counterpart, while the enhanced ORBGRAND achieves a $4.21\times$ speedup, demonstrating the effectiveness of the unified tree-based framework and its strong potential for future algorithmic and hardware optimizations.

翻译：并行化已成为现代译码框架追求高吞吐量与低延迟需求的核心关注点。猜测随机加性噪声译码（GRAND）是一种近期提出的译码范式，通过测试候选错误图样（EP）直至找到有效码字。在其变体中，软GRAND（SGRAND）能实现最大似然（ML）译码，但依赖实时生成与似然排序的EP，使得在ML最优约束下实现并行执行具有挑战性。本文引入一种统一的EP二叉树表示——EP树，该表示形式化了SGRAND与有序可靠性比特（ORB）GRAND算法中的层次结构，可支持EP的结构化组织与算法层面的并行探索。基于此统一框架，我们提出一种保持ML最优性的SGRAND并行设计方案，通过剪枝策略与基于树的运算显著降低译码复杂度。此外，我们基于相同EP树表示开发出一种增强型ORBGRAND算法，在保持并行效率的同时提升译码性能趋近ML。数值实验表明，与串行版本相比，所提出的并行SGRAND可降低$3.96\times$的译码延迟，而增强型ORBGRAND可实现$4.21\times$的加速比，验证了统一树形框架的有效性及其在未来算法与硬件优化中的巨大潜力。