Optimal Merging Algorithms for Lossless Codes with Generalized Criteria

• Published in: arXiv.org
• Main Authors: Charalambous, Themistoklis, Charalambous, Charalambos D, Rezaei, Farzad
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 06.08.2012
• Subjects: Algorithms; Codes; Coding; Criteria; Exponential functions; Huffman codes; Multiuser systems
• ISSN: 2331-8422

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.