Lecture Notes in Computer Science Volume 514, 1991, pp 309-317
Date: 01 Aug 2005

Minimum codeword length and redundancy of Huffman codes

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A tight upper bound on the redundancy r of Huffman codes, in terms of the minimum codeword length l, l≥1, is provided. The bound is a strictly decreasing function of l. For large l it yields rl−log(2 l+1−1)+1+β+O(2−2l ), where β≈0.0860.

By using this result we improve Gallager's bound on the redundancy when only the most likely source probability p 1 is known.

This work was partially supported by the National Council of Research (C.N.R.) under grant 90.01552.CT12.