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

https://www.intlpress.com/site/pub/files/_fulltext/journals/cis/2001/0001/0002/CIS-2001-0001-0002-a001.pdf

Code and parse tree for lossless source encoding

Reserving space fur a symbol that is not in the source alphabet has been shown to provide excellent error detection. In this paper, we show how to exploit this capability using two sequential decoder structures to provide powerful error correction capability. This joint source/channel coder design provides significant packet loss recovery with minimal rate overhead, and compares favorably with conventional schemes.

Joint source/channel coding using arithmetic codes

Reserving space for a symbol that is not in the source alphabet has been shown to provide excellent error detection. In this paper we show how to use this capability using a sequential decoder structure to provide powerful error correction capability. This joint source/channel coder design provides significant packet loss recovery with minimal overhead.

Joint Source Channel Coding Using Arithmetic Codes

The synchronization recovery property of variable-length (VL) codes has been extensively studied. In the paper, the mean error propagation length (MEPL) and the variance of error propagation length (VEPL), which are the secondary performance criteria of a VL code, are introduced to measure the synchronization recovery capability of a VL code. For the same probability distribution, there exist many different VL codes which have the same redundancy as the Huffman code but quite different MEPLs and VEPLs. To find one of the VL codes which has the minimum MEPL is a very difficult problem. We present two design algorithms for finding minimum-redundancy VL codes with short MEPL and VEPL. These two algorithms are simple and have the property that the codewords are assigned one by one. The efficiency of the algorithms are tested extensively by comparing the algorithms with known construction methods available in literature. Actually, VL codes obtained by the two algorithms outperform almost all codes available.

Synchronization recovery of variable-length codes

Variable-length codes (e.g. Huffman codes) are commonly employed to minimize the average codeword length for noiseless encoding of discrete sources. Upon transmission over noisy channels, conflicting views note that such codes "tend to be self-synchronizing" and suffer from the "catastrophic effect of the error's propagation". Maxted and Robinson (1985) used a state model to describe the error recovery of the decoder. The present paper extends their results in several ways.

P. DiCicco

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