Coding schemes for locally balanced constraints

TL;DR

This paper develops explicit encoding and decoding schemes for binary strings under locally balanced constraints, motivated by DNA storage applications, and explores their capacity and combinatorial properties.

Contribution

It introduces coding schemes for strongly and locally balanced constraints and analyzes the recurrence relations for specific locally balanced strings.

Findings

Coding schemes for strongly locally balanced constraints.

Analysis of the number of (6,1)-locally balanced strings.

Insights into capacity and coding strategies for locally balanced constraints.

Abstract

Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any consecutive substring of length $\ell$ is between $\frac{\ell}{2}-\delta$ and $\frac{\ell}{2}+\delta$. In this paper we present coding schemes for the strongly locally balanced constraints and the locally balanced constraints, respectively. Moreover, we introduce an additional result on the linear recurrence formula of the number of binary strings which are $(6,1)$-locally balanced, as a further attempt to both capacity characterization and new coding strategies for locally balanced constraints.