منابع مشابه
Codes Correcting Two Deletions
In this work, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log2 n+O(log2 log2 n) bits of redundancy, where n denotes the length of the code. To the best of the author’s knowledge, this represents the best known construction in that it requires the lowest number of redundant bits ...
متن کاملEfficient Low-Redundancy Codes for Correcting Multiple Deletions
We consider the problem of constructing binary codes to recover from k–bit deletions with efficient encoding/decoding, for a fixed k. The single deletion case is well understood, with the VarshamovTenengolts-Levenshtein code from 1965 giving an asymptotically optimal construction with ≈ 2n/n codewords of length n, i.e., at most logn bits of redundancy. However, even for the case of two deletion...
متن کاملAsymptotically Good Codes Correcting Insertions, Deletions, and Transpositions (Preliminary Version)
We present simple, polynomial-time encodable and decodable codes which are asymptotically good for channels allowing insertions, deletions and transpositions. As a corollary, they achieve exponential error probability in a stochastic model of insertion-deletion.
متن کاملCodes for Correcting a Burst of Deletions or Insertions
This paper studies codes which correct bursts of deletions. Namely, a binary code will be called a b-burst-correcting code if it can correct a deletion of any b consecutive bits. While the lower bound on the redundancy of such codes was shown by Levenshtein to be asymptotically log(n) + b− 1, the redundancy of the best code construction by Cheng et al. is b(log(n/b+1)). In this paper, we close ...
متن کاملCorrecting Bursty and Localized Deletions Using Guess & Check Codes
We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when δ ≤ w deletions occur in a window of size at most w bits. These δ deletions are not necessarily consecutive, but are restricted to the window of size w. The localized deletions model is a generalization o...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2019
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2018.2876281