Bounds on the expected cost of one-to-one codes

This paper generalizes one-to-one encodings of a discrete random variable to finite code alphabets with memoryless letter costs and establish some upper and lower bounds on the expected cost per source symbol of the best one-to-one codes. We show that the average cost per symbol of the optimal one-to-one code sometimes is a tighter lower bound to the average cost per symbol of the optimal uniquely decodable code than Shannon´s original bound.