Variations on a theme by Huffman

Bibliography: leaf 29.Grant NSF-ENG76-24447.by Robert G. Gallager

Dynamic Shannon Coding

We present a new algorithm for dynamic prefix-free coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We show how our algorithm can be modified for efficient length-restricted coding, alphabetic coding and coding with unequal letter costs.Comment: 6 pages; conference version presented at ESA 2004; journal version submitted to IEEE Transactions on Information Theor

Maximal codeword lengths in Huffman codes

The following question about Huffman coding, which is an important technique for compressing data from a discrete source, is considered. If p is the smallest source probability, how long, in terms of p, can the longest Huffman codeword be? It is shown that if p is in the range 0 less than p less than or equal to 1/2, and if K is the unique index such that 1/F(sub K+3) less than p less than or equal to 1/F(sub K+2), where F(sub K) denotes the Kth Fibonacci number, then the longest Huffman codeword for a source whose least probability is p is at most K, and no better bound is possible. Asymptotically, this implies the surprising fact that for small values of p, a Huffman code's longest codeword can be as much as 44 percent larger than that of the corresponding Shannon code