# Sample Complexity of the Boolean Multireference Alignment Problem

## TL;DR

This paper derives an explicit expression for the error exponent in the Boolean multireference alignment problem, linking measurement requirements to signal autocorrelations, especially in low SNR conditions.

## Contribution

It provides a novel explicit characterization of measurement complexity based on higher order autocorrelations for various signal dimensions.

## Key findings

- Error exponent expression for the MAP decoder
- Measurement bounds in low SNR regime
- Explicit results for prime and even dimensions

## Abstract

The Boolean multireference alignment problem consists in recovering a Boolean signal from multiple shifted and noisy observations. In this paper we obtain an expression for the error exponent of the maximum A posteriori decoder. This expression is used to characterize the number of measurements needed for signal recovery in the low SNR regime, in terms of higher order autocorrelations of the signal. The characterization is explicit for various signal dimensions, such as prime and even dimensions.