Optimal Merging Algorithms for Lossless Codes with Generalized Criteria
Abstract
This paper presents lossless prefix codes optimized with respect to a pay-off criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new coding algorithm which transforms the initial source probability vector into a new probability vector according to a merging rule. The coding algorithm is equivalent to a partition of the source alphabet into disjoint sets on which a new transformed probability vector is defined as a function of the initial source probability vector and a scalar parameter. The pay-off criterion considered encompasses a trade-off between maximum and average codeword length; it is related to a pay-off criterion consisting of a convex combination of average codeword length and average of an exponential function of the codeword length, and to an average codeword length pay-off criterion subject to a limited length constraint. A special case of the first related pay-off is connected to coding problems involving source probability uncertainty and codeword overflow probability, while the second related pay-off compliments limited length Huffman coding algorithms.
Cite
@article{arxiv.1112.1715,
title = {Optimal Merging Algorithms for Lossless Codes with Generalized Criteria},
author = {Themistoklis Charalambous and Charalambos D. Charalambous and Farzad Rezaei},
journal= {arXiv preprint arXiv:1112.1715},
year = {2012}
}
Comments
40 pages long, arXiv admin note: text overlap with arXiv:1102.2207, arXiv:1202.0136