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Register a new userOptimal Merging Algorithms for Lossless Codes with Generalized Criteria
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Themistoklis Charalambous
Publication date
2011
fields
Informatics Engineering
and research's language is
English
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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.
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In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code, where the minimizers are the codeword lengths -- real numbers for arithmetic or Shannon codes -- while the maximizers are the source distributions from the total variational distance ball. Firstly, we examine the maximization of the average codeword length by converting it into an equivalent optimization problem, and we give the optimal codeword lenghts via a waterfilling solution. Secondly, we show that the equivalent optimization problem can be solved via an optimal partition of the source alphabet, and re-normalization and merging of the fixed nominal probabilities. For the computation of the optimal codeword lengths we also develop a fast algorithm with a computational complexity of order ${cal O}(n)$.
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