Reed Solomon Codes Against Adversarial Insertions and Deletions

نویسندگان

چکیده

In this work, we study the performance of Reed–Solomon codes against adversarial insertion-deletion (insdel) errors. We prove that over fields size $n^{O(k)}$ there are notation="LaTeX">$[n,k]$ Reed-Solomon can decode from notation="LaTeX">$n-2k+1$ insdel errors and hence attain half-Singleton bound. also give a deterministic construction such much larger (of notation="LaTeX">$n^{k^{O(k)}}$ ). Nevertheless, for notation="LaTeX">$k=O(\log n /\log \log n)$ our runs in polynomial time. For special case notation="LaTeX">$k=2$ , which received lot attention literature, construct an notation="LaTeX">$[n], [2]$ code field notation="LaTeX">$O(n^{4})$ notation="LaTeX">$n-3$ Earlier constructions required exponential size. Lastly, any requires notation="LaTeX">$\Omega (n^{3})$ .

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ژورنال

عنوان ژورنال: IEEE Transactions on Information Theory

سال: 2023

ISSN: ['0018-9448', '1557-9654']

DOI: https://doi.org/10.1109/tit.2023.3237711