Correcting an ordered deletion-erasure

TL;DR

This paper demonstrates that a modified Varshamov-Tenengolts code can correct a combined ordered deletion and erasure pattern with minimal redundancy, improving error correction capabilities for certain communication scenarios.

Contribution

It introduces a simple modification to the Varshamov-Tenengolts code to correct ordered deletion-erasure patterns, achieving near-optimal redundancy for large code lengths.

Findings

The modified code corrects ordered deletion-erasure patterns.

Redundancy remains logarithmic and near optimal for large codes.

The approach extends the applicability of VT codes to new error patterns.

Abstract

In this paper, we show that the single deletion correcting Varshamov-Tenengolts code, with minor modifications, can also correct an ordered deletion-erasure pattern where one deletion and at most one erasure occur and the deletion always occurs before the erasure. For large code lengths, the constructed code has the same logarithmic redundancy as optimal codes.