Sequences with Low Correlation

TL;DR

This paper investigates the construction of binary sequence pairs with low autocorrelation and crosscorrelation, crucial for improving performance in communications and remote sensing applications.

Contribution

It reviews recent advances and historical context in constructing binary sequences with low aperiodic correlation, emphasizing pairs with desirable correlation properties.

Findings

Identified methods for constructing low-correlation sequence pairs

Reviewed recent research developments in the field

Highlighted importance of low correlation in practical applications

Abstract

Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in applications. We consider the problem of constructing pairs $(f,g)$ of sequences such that both $f$ and $g$ have low mean square autocorrelation and $f$ and $g$ have low mean square mutual crosscorrelation. We focus on aperiodic correlation of binary sequences, and review recent contributions along with some historical context.