A simple upper bound on the redundancy of Huffman codes

Upper bounds on the redundancy of Huffman codes have been extensively studied in the literature. Almost all of these bounds are in terms of the probability of either the most likely or the least likely source symbol. We prove a simple upper bound in terms of the probability of any source symbol.

[1]  Alfredo De Santis,et al.  A note on D-ary Huffman codes , 1991, IEEE Trans. Inf. Theory.

[2]  B. V. K. Vijaya Kumar,et al.  On the average codeword length of optimal binary codes for extended sources , 1987, IEEE Trans. Inf. Theory.

[3]  Robert G. Gallager,et al.  Variations on a theme by Huffman , 1978, IEEE Trans. Inf. Theory.

[4]  Raymond W. Yeung,et al.  Some basic properties of fix-free codes , 2001, IEEE Trans. Inf. Theory.

[5]  Alfredo De Santis,et al.  On the Redundancy Achieved by Huffman Codes , 1996, Inf. Sci..

[6]  Ottar Johnsen,et al.  On the redundancy of binary Huffman codes (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[7]  Inder Jeet Taneja,et al.  Bounds on the redundancy of Huffman codes , 1986, IEEE Trans. Inf. Theory.

[8]  Alfredo De Santis,et al.  New bounds on the redundancy of Huffman codes , 1991, IEEE Trans. Inf. Theory.

[9]  Julia Abrahams,et al.  On the redundancy of optimal binary prefix-condition codes for finite and infinite sources , 1987, IEEE Trans. Inf. Theory.

[10]  Alfredo De Santis,et al.  Binary prefix codes ending in a "1" , 1994, IEEE Trans. Inf. Theory.

[11]  Raymond W. Yeung.  Local redundancy and progressive bounds on the redundancy of a Huffman code , 1991, IEEE Trans. Inf. Theory.

[12]  Alfredo De Santis,et al.  Tight upper bounds on the redundancy of Huffman codes , 1989, IEEE Trans. Inf. Theory.