Tight Bounds on the Redundancy of Huffman Codes
<|reference_start|>Tight Bounds on the Redundancy of Huffman Codes: In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of such Huffman codes, which yields in a tight upper bound. We also derive a tight lower bound for the redundancy under the same assumption.   We further apply the method introduced in this paper to other related problems. It is shown that several other previously known bounds with different constraints follow immediately from our results.<|reference_end|>
@article{mohajer2005tight,
    title={Tight Bounds on the Redundancy of Huffman Codes},
    author={Soheil Mohajer, Payam Pakzad and Ali Kakhbod},
    journal={arXiv preprint arXiv:cs/0508039},
    year={2005},
    doi={10.1109/ITW.2006.1633796},
    archivePrefix={arXiv},
    eprint={cs/0508039},
    primaryClass={cs.IT math.IT}
}