Efficient Systematic Encoding of Non-binary VT Codes

TL;DR

This paper introduces a linear-time encoding method for non-binary VT codes, enabling efficient systematic encoding and establishing a new lower bound on their size.

Contribution

It presents the first simple linear-time systematic encoding technique for non-binary VT codes and derives a new lower bound on their size.

Findings

Linear-time encoding method for non-binary VT codes

Systematic mapping of binary messages to VT codewords

New lower bound on the size of q-ary VT codes

Abstract

Varshamov-Tenengolts (VT) codes are a class of codes which can correct a single deletion or insertion with a linear-time decoder. This paper addresses the problem of efficient encoding of non-binary VT codes, defined over an alphabet of size $q >2$. We propose a simple linear-time encoding method to systematically map binary message sequences onto VT codewords. The method provides a new lower bound on the size of $q$-ary VT codes of length $n$.