Optimal Prefix Codes for Infinite Alphabets With Nonlinear Costs
Baer, M.B.
Ocarina Networks Inc., San Jose, CA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: March 2008
Volume: 54,
Issue: 3
On page(s): 1273-1286
ISSN: 0018-9448
INSPEC Accession Number: 10145102
Digital Object Identifier: 10.1109/TIT.2007.915696
Current Version Published: 2008-02-22
Abstract
Let P={p(i)} 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 P 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, beta-exponential means, those of the form loga Sigmaip(i)an(i), where n(i) is the length of the ith codeword and a is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in single-shot communications (a<1) and a previously known problem of minimizing the chance of buffer overflow in a queueing system (a>1). 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.
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