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Kraft’s inequality [9] is essential for the classical theory of noiseless coding [1, 8]. In algorithmic information theory [5, 7, 2] one needs an extension of Kraft’s condition from finite sets to (infinite) recursively enumerable sets. This extension, known as Kraft-Chaitin Theorem, was obtained by Chaitin in his seminal paper [4] (see also, [3, 2], [10]). The aim of this note is to offer a si...
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Kraft's inequality [9] is essential for the classical theory of noiseless coding [1, 8]. In algorithmic information theory [5, 7, 2] one needs an extension of Kraft's condition from nite sets to (in nite) recursively enumerable sets. This extension, known as Kraft-Chaitin Theorem, was obtained by Chaitin in his seminal paper [4] (see also, [3, 2]). The aim of this note is to o er a simpler proo...
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In the previous lecture, we showed that Shannon constructed a code, which was a one-to-one mapping, that took a stream of data X = (X1, ..., Xn) generated iid from a distribution P (X) over a finite alphabet A = (a1, ..., aA) of size A, and compressed it using ≈ nH(X) bits in total or ≈ H(X) bits per symbol, on average (for sufficiently large n). The code was based considering a special subset ...
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ژورنال
عنوان ژورنال: itw : im dialog
سال: 2017
ISSN: 2297-6523
DOI: 10.16905/itwid.2016.20.