Code and parse trees for lossless source encoding

Abstract

This paper surveys the theoretical literature on fixed-to-variable-length lossless source code trees, called code trees, and on variable-length-to-fixed lossless source code trees, called parse trees. In particular, the following code tree topics are outlined in this survey: characteristics of the Huffman (1952) code tree; Huffman-type coding for infinite source alphabets and universal coding; the Huffman problem subject to a lexicographic constraint, or the Hu-Tucker (1982) problem; the Huffman problem subject to maximum codeword length constraints; code trees which minimize other functions besides average codeword length; coding for unequal cost code symbols, or the Karp problem, and finite state channels; and variants of Huffman coding in which the assignment of 0s and 1s within codewords is significant such as bidirectionality and synchronization. The literature on parse tree topics is less extensive. Treated here are: variants of Tunstall (1968) parsing; dualities between parsing and coding; dual tree coding in which parsing and coding are combined to yield variable-length-to-variable-length codes; and parsing and random number generation. Finally, questions related to counting and representing code and parse trees are also discussed.