Belief-Combining Framework for Multi-Trace Reconstruction over Channels with Insertions, Deletions, and Substitutions

TL;DR

This paper introduces an iterative belief-combining method for reconstructing source sequences from multiple noisy traces with insertions, deletions, and substitutions, achieving optimal accuracy with reduced computational complexity.

Contribution

The paper presents a novel belief-combining framework that matches joint maximum a posteriori performance while significantly lowering computational complexity.

Findings

Method achieves performance equivalent to joint MAP estimation.

Complexity is reduced to quadratic in the number of traces.

Validated on real-world DNA sequencing data.

Abstract

Optimal reconstruction of a source sequence from multiple noisy traces corrupted by random insertions, deletions, and substitutions typically requires joint processing of all traces, leading to computational complexity that grows exponentially with the number of traces. In this work, we propose an iterative belief-combining procedure that computes symbol-wise a posteriori probabilities by propagating trace-wise inferences via message passing. We prove that, upon convergence, our method achieves the same reconstruction performance as joint maximum a posteriori estimation, while reducing the complexity to quadratic in the number of traces. This performance equivalence is validated using a real-world dataset of clustered short-strand DNA reads.