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Generalizing the Kraft-McMillan inequality to restricted languages

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2 Author(s)
Golin, M.J. ; Dept. of Comput. Sci., Hong Kong Univ. of Sci. & Technol., Kowloon, China ; Hyeon-Suk Na

Let ℓ 1,ℓ 2,...,ℓ n be a (possibly infinite) sequence of nonnegative integers and Σ some D-ary alphabet. The Kraft-inequality states that ℓ 1,ℓ 2,...,ℓ n are the lengths of the words in some prefix (free) code over Σ if and only if Σi=1nD-ℓ i≤1. Furthermore, the code is exhaustive if and only if equality holds. The McMillan inequality states that if ℓ n are the lengths of the words in some uniquely decipherable code, then the same condition holds. In this paper we examine how the Kraft-McMillan inequality conditions for the existence of a prefix or uniquely decipherable code change when the code is not only required to be prefix but all of the codewords are restricted to belong to a given specific language L. For example, L might be all words that end in a particular pattern or, if Σ is binary, might be all words in which the number of zeros equals the number of ones.

Published in:

Data Compression Conference, 2005. Proceedings. DCC 2005

Date of Conference:

29-31 March 2005