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

Aria Nouri

TL;DR

This work tackles the problem of reconstructing a source sequence from multiple IDS-affected traces, a task whose optimal solution via joint MAP on a multi-trace BCJR trellis is computationally intractable as the number of traces grows. It introduces an iterative belief-propagation–based framework that exchanges soft symbol posteriors across traces on their own trellises, achieving a symbol-level consensus that matches the joint MAP statistic. Under a mild consensus condition, the method attains the same MAP estimates as applying BCJR to the full joint trellis while reducing the decoding complexity to $O(N \cdot \delta \Delta \cdot K^2)$, i.e., quadratic in the number of traces. Empirical results on real DNA reads and synthetic data demonstrate high reconstruction fidelity up to $K=16$ traces, validating the approach as a scalable alternative for multi-trace IDS channel reconstruction in DNA storage systems.

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.

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

TL;DR

This work tackles the problem of reconstructing a source sequence from multiple IDS-affected traces, a task whose optimal solution via joint MAP on a multi-trace BCJR trellis is computationally intractable as the number of traces grows. It introduces an iterative belief-propagation–based framework that exchanges soft symbol posteriors across traces on their own trellises, achieving a symbol-level consensus that matches the joint MAP statistic. Under a mild consensus condition, the method attains the same MAP estimates as applying BCJR to the full joint trellis while reducing the decoding complexity to , i.e., quadratic in the number of traces. Empirical results on real DNA reads and synthetic data demonstrate high reconstruction fidelity up to traces, validating the approach as a scalable alternative for multi-trace IDS channel reconstruction in DNA storage systems.

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.
Paper Structure (7 sections, 2 theorems, 20 equations, 5 figures, 1 algorithm)

This paper contains 7 sections, 2 theorems, 20 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Refined State Posteriors
  4. Sufficient Statistics for Joint MAP Estimation
  5. Calculation of Refined Per-Trace Posteriors
  6. Simulation Results
  7. Conclusion

Key Result

Lemma 1

Upon convergence of message passing in the factor graph representing the trace-wise inference problem (Fig. fig:BP), all per-trace input APPs equ:marginals, $\forall k,$ reach consensus on a common value $\Lambda_i^{(k)}(X_{q(i)})=\Lambda_i(X_{q(i)})$.

Figures (5)

  • Figure 1: Multi-trace insertion–deletion–substitution (IDS) channel.
  • Figure 2: Trellis section of the pointer-based IDS channel Markov model for a received trace of length $p_k(N)=3,$ and $\Sigma=\{\texttt{A,C,G,T}\}$.
  • Figure 3: Message-passing updates across the simplified factor graph.
  • Figure 4: Error rates for uncoded real DNA reads ($N=110$).
  • Figure 5: Error rates for uncoded random sequences ($N=100$).

Theorems & Definitions (3)

  • Example 1
  • Lemma 1: Symbol-Level Consensus
  • Theorem 1