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中满足严格吞吐量和延迟要求的核心关注点。猜测随机加性噪声译码（GRAND）是一种新近提出的译码范式，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，但依赖于错误图样的实时生成和似然排序，在ML最优性约束下使得并行执行具有挑战性。本文提出了一种统一的错误图样二叉树表示——EP树，形式化描述了SGRAND与有序可靠比特（ORB）GRAND算法的层次化结构，从而支持错误图样的结构化组织与算法层面的并行探索。基于该统一框架，我们设计了保留ML最优性的SGRAND并行方案，通过剪枝策略和基于树的计算显著降低译码复杂度。此外，我们基于相同EP树表示发展了增强型ORBGRAND算法，在保持并行效率的同时提升朝向ML的译码性能。数值实验表明，所提并行SGRAND相比串行版本实现了3.96倍的译码延迟缩减，而增强型ORBGRAND实现了4.21倍的加速，验证了统一的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。