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- W3100467227 abstract "<para xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> Let <emphasis><formula formulatype=inline><tex>$P= { p(i)}$</tex> </formula></emphasis> be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial <emphasis><formula formulatype=inline> <tex>$P$</tex></formula></emphasis> for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective functions, <emphasis><formula formulatype=inline> <tex>$beta$</tex></formula></emphasis>-exponential means, those of the form <emphasis><formula formulatype=inline><tex>$log _{a} sum _{i} p(i)a^{ n(i)}$</tex></formula></emphasis>, where <emphasis><formula formulatype=inline><tex>$n(i)$</tex></formula></emphasis> is the length of the <emphasis><formula formulatype=inline><tex>$i$</tex></formula></emphasis>th codeword and <emphasis><formula formulatype=inline><tex>$a$</tex></formula></emphasis> is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in single-shot communications <emphasis><formula formulatype=inline><tex>$(a≪ 1)$</tex></formula></emphasis> and a previously known problem of minimizing the chance of buffer overflow in a queueing system <emphasis><formula formulatype=inline><tex>$(a>1)$</tex></formula></emphasis>. This paper introduces methods for finding codes optimal for such exponential means. One method applies to geometric distributions, while another applies to distributions with lighter tails. The latter algorithm is applied to Poisson distributions and both are extended to alphabetic codes, as well as to minimizing maximum pointwise redundancy. The aforementioned application of minimizing the chance of buffer overflow is also considered. </para>" @default.
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- W3100467227 date "2008-03-01" @default.
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- W3100467227 title "Optimal Prefix Codes for Infinite Alphabets With Nonlinear Costs" @default.
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