On the Redundancy Achieved by Huffman Codes

Abstract It has been recently proved that the redundancy r of any discrete memoryless source satisfies r ⩽ 1 − H (p N ) , where PN is the least likely source letter probability. This bound is achieved only by sources consisting of two letters. We prove a sharper bound if the number of source letters is greater than two. Also provided is a new upper bound on r, in terms of the two least likely source letter probabilities, which improves on a previous result.