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ASYMPTOTIC MINIMUM COVERING RADIUS OF BLOCK CODES.

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Title: ASYMPTOTIC MINIMUM COVERING RADIUS OF BLOCK CODES.
Authors: Chen, Po-Ning1 poning@cc.nctu.edu.tw, Han, Yunghsiang S.2 yshan@csie.ncnu.edu.tw
Source: SIAM Journal on Discrete Mathematics. 2001, Vol. 14 Issue 4, p549-564. 16p.
Subjects: Coding theory, RADIUS (Computer network protocol), Spectrum analysis, Mathematical notation
Abstract: In this paper, we restudy the covering radius of block codes from an information theoretic point of view by ignoring the combinatorial formulation of the problem. In the new setting, the formula of the statistically defined minimum covering radius, for which the probability mass of uncovered space by M spheres can be made arbitrarily small, is reduced to a minimization of a statistically defined spectrum formula among codeword-selecting distributions. The advantage of the new view is that no assumptions need to be made on the code alphabet (such as finite, countable, etc.) and the distance measure (such as additive, symmetric, bounded, etc.) in the problem transformation, and hence the spectrum formula can be applied in most general situations. We next address a sufficient condition under which uniform codeword-selecting distribution minimizes the spectrum formula. With the condition, the asymptotic minimum covering radius for block codes under J-ary quantized channels and constant weight codes under Hamming distance measure are determined to display the usage of the spectrum formula. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics 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: <searchLink fieldCode="AR" term="%22Chen%2C+Po-Ning%22">Chen, Po-Ning</searchLink><relatesTo>1</relatesTo><i> poning@cc.nctu.edu.tw</i><br /><searchLink fieldCode="AR" term="%22Han%2C+Yunghsiang+S%2E%22">Han, Yunghsiang S.</searchLink><relatesTo>2</relatesTo><i> yshan@csie.ncnu.edu.tw</i>
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  Data: <searchLink fieldCode="DE" term="%22Coding+theory%22">Coding theory</searchLink><br /><searchLink fieldCode="DE" term="%22RADIUS+%28Computer+network+protocol%29%22">RADIUS (Computer network protocol)</searchLink><br /><searchLink fieldCode="DE" term="%22Spectrum+analysis%22">Spectrum analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+notation%22">Mathematical notation</searchLink>
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  Data: In this paper, we restudy the covering radius of block codes from an information theoretic point of view by ignoring the combinatorial formulation of the problem. In the new setting, the formula of the statistically defined minimum covering radius, for which the probability mass of uncovered space by M spheres can be made arbitrarily small, is reduced to a minimization of a statistically defined spectrum formula among codeword-selecting distributions. The advantage of the new view is that no assumptions need to be made on the code alphabet (such as finite, countable, etc.) and the distance measure (such as additive, symmetric, bounded, etc.) in the problem transformation, and hence the spectrum formula can be applied in most general situations. We next address a sufficient condition under which uniform codeword-selecting distribution minimizes the spectrum formula. With the condition, the asymptotic minimum covering radius for block codes under J-ary quantized channels and constant weight codes under Hamming distance measure are determined to display the usage of the spectrum formula. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics 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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        Value: 10.1137/S0895480100379993
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        Type: general
      – SubjectFull: RADIUS (Computer network protocol)
        Type: general
      – SubjectFull: Spectrum analysis
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