GPU-Parallelization of Markov Chain Pool Decoding with Unbiased MCMC

Abstract

Markov chain pool decoding (MCPD) devised by Knill et al. (1996) identifies likely positive clones from noisy pooled-test results. The standard MCPD estimates clone-wise posterior probabilities using Gibbs sampling, but it may allocate excessive computational effort to low-scoring clones. This paper focuses on parallelizing MCPD on GPU architectures. Whereas the standard MCPD employs systematic-scan updates, we propose a score-weighted update scheme that updates high-scoring clones more frequently. We prove that the stationary distribution of the proposed Markov chain coincides with the target posterior distribution. To enable efficient GPU parallelization, we further incorporate the unbiased MCMC framework of Jacob et al. (2020) and employ a slot-refilling technique based on the arguments by Glynn and Heidelberger (1991) about the coupling of Markov chains. Experiments involving 1,298 clones, 97 pools, and three true positives demonstrate improved recovery compared with uniform decoders, while maintaining high overlap under high-noise conditions.