Optimal source codes for geometrically distributed integer alphabets (Corresp.)

Let be a probability assignment on the set of nonnegative integers where is an arbitrary real number, . We show that an optimal binary source code for this probability assignment is constructed as follows. Let be the integer satisfying and represent each nonnegative integer as when , the integer part of , and . Encode by a unary code (i.e., zeros followed by a single one), and encode by a Huffman code, using codewords of length , for , and length otherwise. An optimal code for the nonnegative integers is the concatenation of those two codes.