A D-ary Huffman code for a class of sources with countably infinite alphabets

The authors discuss Huffman coding with infinite alphabet. Our concern is how to construct an optimal D-ary prefix code given a probability distribution P on χ, where “optimal” means a code with the minimum expected codeword length over all the possible prefix codes for the P. Although the Huffman coding algorithm with finite source alphabet is known to achieve the optimal code, it is not applicable in general to the case with infinite source alphabet. However, some specific properties of the given distribution P are enough to ensure the applicability of Huffman-type coding algorithms to the infinite alphabet case as well