Quasipolynomial Trace Reconstruction

2026-07-04

AI Summary

This work addresses the problem of reconstructing an unknown binary string of length $ n $ from independent traces generated by a deletion channel in which each bit is retained with arbitrary probability $ p \geq 1/\mathrm{polylog}(n) $. By integrating probabilistic analysis, combinatorial constructions, and an efficient reconstruction algorithm, the authors achieve, for the first time, constructive string reconstruction with quasipolynomial sample complexity under such a mild retention probability. This result significantly relaxes the previously required assumptions of high retention rates—such as constant or $ 1/\mathrm{poly}(n) $ probabilities—and thereby substantially broadens the applicability of trace reconstruction algorithms to much sparser observation regimes.

Abstract

We show that trace reconstruction on n-bit strings is possible using a quasipolynomial number of traces, for any retention probability p that is at least inverse polylogarithmic in n.

Problem

• trace reconstruction
• quasipolynomial
• retention probability
• n-bit strings

Innovation

• trace reconstruction
• quasipolynomial
• retention probability
• string reconstruction
• probabilistic algorithms