The construction of codes for infinite sets

Authors:
Michael G. G. Laidlaw
Affiliations:
School of Mathematics Statistics and Information Technology, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa
Venue:
SAICSIT '04 Proceedings of the 2004 annual research conference of the South African institute of computer scientists and information technologists on IT research in developing countries
Year:
2004

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Abstract

Run-length encoding is used in applications that process digitised analogue data. Lossless image compression is an example. Golomb encoding is optimal for infinite geometric probability distributions. A wider class of codes is presented here, all of which are suitable for encoding the elements from an infinite set. It is shown that each code can be described by a polynomial K(L), which determines the number of codewords of length L. An even wider class of codes is also considered in which the number of codewords grows geometrically with their length. Criteria are given for excluding such codes from further consideration.