Codes for Correcting Localized Deletions

TL;DR

This paper introduces explicit systematic codes capable of correcting localized deletions within a window, generalizing burst deletion correction, with efficient algorithms and low redundancy.

Contribution

The authors develop new explicit codes based on Guess & Check codes for correcting localized deletions, extending to multiple windows with efficient encoding and decoding.

Findings

Codes correct localized deletions with high probability

Codes are systematic with low redundancy

Efficient deterministic encoding and decoding algorithms

Abstract

We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $\delta \leq w$ deletions are localized in a window of size $w$ bits. These $\delta$ deletions do not necessarily occur in consecutive positions, but are restricted to the window of size $w$. The localized deletions model is a generalization of the bursty model, in which all the deleted bits are consecutive. In this paper, we construct new explicit codes for the localized model, based on the family of Guess & Check codes which was previously introduced by the authors. The codes that we construct can correct, with high probability, $\delta \leq w$ deletions that are localized in a single window of size $w$, where $w$ grows with the block length. Moreover, these codes are systematic; have low redundancy; and have efficient deterministic encoding and decoding algorithms. We also generalize these codes to deletions that are localized within multiple windows in the codeword.