Kolmogorov complexity and the asymptotic bound for error-correcting codes
نویسندگان
چکیده
منابع مشابه
Kolmogorov complexity and the asymptotic bound for error-correcting codes
The set of all error-correcting block codes over a fixed alphabet with q letters determines a recursively enumerable set of rational points in the unit square with coordinates (R, δ):= (relative transmission rate, relative minimal distance). Limit points of this set form a closed subset, defined by R ≤ αq(δ), where αq(δ) is a continuous decreasing function called the asymptotic bound. Its exist...
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Consider the set of all error–correcting block codes over a fixed alphabet with q letters. It determines a recursively enumerable set of points in the unit square with coordinates (R, δ):= (relative transmission rate, relative minimal distance). Limit points of this set form a closed subset, defined by R ≤ αq(δ), where αq(δ) is a continuous decreasing function called asymptotic bound. Its exist...
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We introduce the study of Kolmogorov complexity with error. For a metric d, we define Ca(x) to be the length of a shortest program p which prints a string y such that d(x, y) ≤ a. We also study a conditional version of this measure Ca,b(x|y) where the task is, given a string y′ such that d(y, y′) ≤ b, print a string x′ such that d(x, x′) ≤ a. This definition admits both a uniform measure, where...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2014
ISSN: 0022-040X
DOI: 10.4310/jdg/1404912104