Skip to Main Content
The concept of local redundancy is introduced, and it is shown that it is a simple but powerful tool for understanding the redundancy of a prefix code. Based on this concept, the redundancy of a prefix code when the structure of the code is partially known is proven. It is shown how this theorem can be used to obtain well-known lower bounds on RHuff, the redundancy of a Huffman code. The theorem is used to obtain a sequence of new lower bounds on RHuff based on the Huffman procedure. A similar sequence of upper bounds on RHuff is obtained. New lower and upper bounds on RHuff when the two smallest probabilities of the source distribution are known are given as corollaries of these results.