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

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
$q$
> 2 with at most [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.