In this paper, we propose an efficient two-stage decoding algorithm for non-adaptive Group Testing (GT) with general correlated prior statistics. The proposed solution can be applied to any correlated statistical prior represented in trellis, e.g., finite state machines and Markov processes. We introduce a variation of List Viterbi Algorithm (LVA) to enable accurate recovery using much fewer tests than objectives, which efficiently gains from the correlated prior statistics structure. We also provide a sufficiency bound to the number of pooled tests required by any Maximum A Posteriori (MAP) decoder with an arbitrary correlation, i.e., dependence between infected items. Our numerical results demonstrate that the proposed two-stage decoding GT (2SDGT) algorithm can obtain the optimal MAP performance with feasible complexity in practical regimes, such as with COVID-19 and sparse signal recovery applications, and reduce in the scenarios tested the number of pooled tests by at least $25\%$ compared to existing classical low complexity GT algorithms. Moreover, we analytically characterize the complexity of the proposed 2SDGT algorithm that guarantees its efficiency.

翻译：本文针对具有一般相关先验统计信息的非自适应群组检测问题，提出一种高效的两阶段解码算法。所提方案适用于任何采用网格图表示的相关统计先验模型，例如有限状态机和马尔可夫过程。我们引入列表维特比算法的改进形式，利用远少于目标数量的检测实现精确恢复，从而高效利用相关先验统计结构。我们还为任意相关感染项依赖关系下的最大后验概率解码器，推导了所需混合检测数量的充分性界。数值结果表明，所提出的两阶段解码群组检测算法能够在实际应用场景（如COVID-19检测与稀疏信号恢复）中以可行复杂度达到最优MAP性能，在测试场景中较现有经典低复杂度GT算法至少减少$25\%$的混合检测次数。此外，我们通过解析方法刻画了所提2SDGT算法的复杂度特征，从理论上保证了其高效性。