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Huffman Redundancy for Large Alphabet Sources

The performance of optimal prefix-free encoding for memoryless sources with a large alphabet size is studied. It is shown that the redundancy of the Huffman code for almost all sources with a large alphabet size n is very close to that of the average distribution of the monotone sources with n symbols. This value lies between 0.02873 and 0.02877 bit for sufficiently large n.