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Almost disjunctive list-decoding codes.

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Název: Almost disjunctive list-decoding codes.
Autoři: D'yachkov, A., Vorob'ev, I., Polyansky, N., Shchukin, V.
Zdroj: Problems of Information Transmission; Apr2015, Vol. 51 Issue 2, p110-131, 22p
Témata: CODING theory, MATHEMATICAL bounds, SET theory, EXISTENCE theorems, COMBINATORIAL probabilities
Abstrakt: We say that an s-subset of codewords of a binary code X is s-bad in X if there exists an L-subset of other codewords in X whose disjunctive sum is covered by the disjunctive sum of the given s codewords. Otherwise, this s-subset of codewords is said to be s-good in X. A binary code X is said to be a list-decoding disjunctive code of strength s and list size L (an s-LD code) if it does not contain s-bad subsets of codewords. We consider a probabilistic generalization of s-LD codes; namely, we say that a code X is an almost disjunctive s- LD code if the fraction of s-good subsets of codewords in X is close to 1. Using the random coding method on the ensemble of binary constant-weight codes, we establish lower bounds on the capacity and error exponent of almost disjunctive s-LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s-LD codes is greater than the zero-error capacity of disjunctive s-LD codes. [ABSTRACT FROM AUTHOR]
Copyright of Problems of Information Transmission is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Almost disjunctive list-decoding codes.
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  Data: Problems of Information Transmission; Apr2015, Vol. 51 Issue 2, p110-131, 22p
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  Data: We say that an s-subset of codewords of a binary code X is s-bad in X if there exists an L-subset of other codewords in X whose disjunctive sum is covered by the disjunctive sum of the given s codewords. Otherwise, this s-subset of codewords is said to be s-good in X. A binary code X is said to be a list-decoding disjunctive code of strength s and list size L (an s-LD code) if it does not contain s-bad subsets of codewords. We consider a probabilistic generalization of s-LD codes; namely, we say that a code X is an almost disjunctive s- LD code if the fraction of s-good subsets of codewords in X is close to 1. Using the random coding method on the ensemble of binary constant-weight codes, we establish lower bounds on the capacity and error exponent of almost disjunctive s-LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s-LD codes is greater than the zero-error capacity of disjunctive s-LD codes. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Problems of Information Transmission is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: SET theory
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              Text: Apr2015
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