  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.
