Every Bit Counts: A New Version of Non-binary VT Codes with More Efficient Encoder

TL;DR

This paper introduces a new version of non-binary VT codes with more efficient linear-time encoding algorithms that significantly reduce redundancy while correcting single insertions or deletions over q-ary alphabets.

Contribution

It presents the first linear-time encoding algorithms for non-binary VT codes with near-optimal redundancy, improving upon previous methods by reducing redundant symbols.

Findings

Linear-time encoding algorithms for non-binary VT codes

Reduces redundancy compared to previous encoders

Achieves near-optimal redundancy bounds

Abstract

In this work, we present a new version of non-binary VT codes that are capable of correcting a single deletion or single insertion. Moreover, we provide the first known linear time algorithms that encode user messages into these codes of length n over the $q$-ary alphabet for $q\ge 2$ with at most $\ceil{\log_q n} + 1$ redundant symbols, while the optimal redundancy required is at least $\log_q n + \log_q (q - 1)$ symbols. Our designed encoder reduces the redundancy of the best-known encoder of Tenengolts (1984) by at least $2+\log_q(3)$ redundant symbols, or equivalently $2\log_2 q+3$ redundant bits.