7 research outputs found
Optimal Prefix Codes for Infinite Alphabets with Nonlinear Costs
Let 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 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, -exponential means,
those of the form , where is the length of
the th codeword and is a positive constant. Applications of such
minimizations include a novel problem of maximizing the chance of message
receipt in single-shot communications () and a previously known problem of
minimizing the chance of buffer overflow in a queueing system (). 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.Comment: 14 pages, 6 figures, accepted to IEEE Trans. Inform. Theor
A general framework for codes involving redundancy minimization
Abstract — A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework involves a two-parameter class encompassing problems previously proposed by Huffman [1], Campbell [2], Nath [3], and Drmota and Szpankowski [4]. It sheds light on the relationships among these problems. In particular, Nath’s problem can be seen as bridging that of Huffman with that of Drmota and Szpankowski. This leads to a linear-time algorithm for the last of these with a solution that solves a range of Nath subproblems. We find simple bounds and linear-time Huffmanlike optimization algorithms for all nontrivial problems within the class