Minimum codeword length and redundancy of Huffman codes
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 r≤l−log(2l+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 p1 is known.
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