Let X be a discrete random variable drawn according to a probability mass function p(x), and suppose p(x), is dyadic, i.e., log(1 / p(x)) is an integer for each x. We show that the binary code length assignment f(x) = log(1/p(x)) dominates any other uniquely decodable assignment l'(x) in expected length in the sense that El(X)< El’(X) indicating optimality in long run performance (which is well known), and competitively dominates l'(x), in the sense that Pr{l(X)< l'(X)} > Pr{l(X) > l’(X)}, which indicates l is also optimal in the short run. In general, if p is not dyadic, then l = [log 1 /p] dominates l'+ 1 in expected length and competitively dominates l'+ 1, where l’ is any other uniquely decodable code. © 1991 IEEE
