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arXiv · 2212.10721

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

Tuan Thanh Nguyen·Kui Cai·Paul H. Siegel
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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.

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Tuan Thanh Nguyen, Kui Cai, Paul H. Siegel. 2022-12-21. Every Bit Counts: A New Version of Non-binary VT Codes with More Efficient Encoder. https://arxiv.org/abs/2212.10721

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