On Unique Decoding from Insertions and Deletions

TL;DR

This paper investigates the likelihood of unique decoding in error-correcting codes affected by insertions and deletions, providing tight bounds and analyzing specific code types relevant to synchronization and DNA storage.

Contribution

It derives tight upper bounds on the probability of unique decoding from insertions and deletions, including improved bounds for linear codes and VT-codes.

Findings

Derived tight upper bounds on unique decoding probability

Analyzed probabilistic channels for insertions and deletions

Provided improved bounds for specific code classes

Abstract

In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used for long term data storage. We define natural probabilistic channels that make $t$ insertions or $t$ deletions, and study the probability of unique decoding. Our most substantial contribution is the derivation of tight upper bounds on the probability of unique decoding for messages passed though these channels. We also consider other aspects of the problem, and derive improved upper bounds for linear codes and VT-codes.