A problem associated with the use of variable-length source codes is that loss of synchronization may lead to extended errors in the decoded text. In this correspondence it is shown that some binary Huffman codes contain a codeword that resynchronizes the decoder regardless of the synchronization slippage preceding that codeword. Such codes are self-synchronizing in a probabilistic sense, yet require no additional system overhead. Some sufficient conditions are found for the existence or nonexistence of self-synchronizing Huffman codes for many classes of source probabilities. One of our results shows that many common languages can be encoded with self-synchronizing Huffman codes.

Self-synchronizing Huffman codes (Corresp.)

1. RAM Model * 2. Lists * 3. Induction and Recursion * 4. Trees * 5. Algorithms Design Techniques * 6. Hashing * 7. Heaps * 8. Balanced Trees * 9. Sets Over a Small Universe * 10. Discrete Fourier Transform (DFT) * 11. Strings * 12. Graphs * 13. Parallel Models of Computation * Appendix of Common Sums * Bibliography * Notation * Index

An Introduction to Data Structures and Algorithms

New upper bounds on the redundancy of Huffman codes are provided. A bound that for 2/9 \leq P_{1} \leq 0.4 is sharper than the bound of Gallager, when the probability of the most likely source letter P_{1} is the only known probability is presented. The improved bound is the tightest possible for 1/3 \leq P_{1} \leq 0.4 . Upper bounds are presented on the redundancy of Huffman codes when the extreme probabilities P_{1} and P_{N} are known.

Bounds on the redundancy of Huffman codes (Corresp.)

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.

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Code and parse trees for lossless source encoding

A method for deriving optimal upper bounds on the redundancy of binary Huffman codes in terms of the probability p/sub 1/ of the most likely source letter is presented. This method will be used to compute bounds for all p/sub 1/>or=1/127, which were previously known only for a few special cases. Furthermore, the known optimal lower bound for binary Huffman codes is generalized to arbitrary code alphabets and some upper bounds for D-ary Huffman codes, 2 or=1/2. >

Tight bounds on the redundancy of Huffman codes

Some properties of Huffman codes are presented. It is shown that knowing the probability P_{1} of the most likely source letter, there exist new lower and upper bounds on the redundancy of the Huffman code which are tighter for P_{1} \geq 0.4 than those given by Shannon's first theorem or by the more recent results of Gallager. It is also shown that the new bounds are the tightest possible for P_{1} \geq 0.4 when it is supposed that PI is the only known probability.

O. Johnsen

Papers

On the redundancy of binary Huffman codes (Corresp.)