On the minimum redundancy of homophonic coding

"This paper establishes the condition for the Rocha-Massey homophonic coding scheme to have lower redundancy than the Jendal-Kuhn-Massey scheme, for sources whose symbol probabilities are rational numbers. The condition is that each probability, in the probability distribution of the symbols of a discrete memoryless source, must contain only countably infinite binary expansions. Both schemes are briefly reviewed and the condition for achieving the minimum redundancy h(2^{-m}) in a perfect homophonic substitution scheme is determined, where h(.) denotes the binary entropy function and m is the least positive integer for which all probability entries in the expanded alphabet of the Rocha-Massey scheme have denominators which are powers of 2."