The complexity of bit retrieval

TL;DR

This paper investigates the problem of reconstructing binary sequences from autocorrelation data, compares various algorithms, and identifies the relaxed-reflect-reflect method as the most effective for noisy scenarios.

Contribution

It introduces the bit retrieval problem, compares multiple algorithms, and highlights the relaxed-reflect-reflect algorithm as the best for noisy data.

Findings

Relaxed-reflect-reflect algorithm outperforms others in noisy conditions.

Comparison of algorithms provides insights into their effectiveness.

The problem has applications in cryptography and crystallography.

Abstract

Bit retrieval is the problem of reconstructing a binary sequence from its periodic autocorrelation, with applications in cryptography and x-ray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxed-reflect-reflect, is currently the best algorithm for noisy bit retrieval.