Fixed-prefix encoding of the integers can be Huffman-optimal

Various source coding schemes encode the set of integers using a binary representation of the integers to be encoded, prefixed by some information about the length of that representation. In the context of recency rank encoding, these can be regarded as attempts to assign codewords with lengths close to the logarithm of the integer to be encoded, or as attempts to construct a code for a distribution function Q(*) on the integers, where Q(k)=(1/k)/Σ_i(1/i), i∈I, and I is a finite set of positive integers to be encoded. It is shown that fixed-prefix encoding is equivalent to Huffman coding for the distribution Q(*)