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

Information Theory 2022-12-22 v1 Combinatorics math.IT

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 qq-ary alphabet for q2q\ge 2 with at most \ceillogqn+1\ceil{\log_q n} + 1 redundant symbols, while the optimal redundancy required is at least logqn+logq(q1)\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+logq(3)2+\log_q(3) redundant symbols, or equivalently 2log2q+32\log_2 q+3 redundant bits.

Keywords

Cite

@article{arxiv.2212.10721,
  title  = {Every Bit Counts: A New Version of Non-binary VT Codes with More Efficient Encoder},
  author = {Tuan Thanh Nguyen and Kui Cai and Paul H. Siegel},
  journal= {arXiv preprint arXiv:2212.10721},
  year   = {2022}
}
R2 v1 2026-06-28T07:45:57.810Z