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The universality of grammar-based codes for sources with countably infinite alphabets

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2 Author(s)
Da-ke He ; Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Ont., Canada ; En-hui Yang

In this paper, we investigate the performance of grammar-based codes for sources with countably infinite alphabets. Let Λ denote an arbitrary class of stationary, ergodic sources with a countably infinite alphabet. It is shown that grammar-based codes can be modified so that they are universal with respect to any Λ if and only if there exists a universal code for Λ. Moreover, upper bounds on the worst case redundancies of grammar-based codes among large sets of length-n individual sequences from a countably infinite alphabet are established. Depending upon the conditions satisfied by length-n individual sequences, these bounds range from O(loglogn/logn) to O(1/log1-αn) for some 0<α<1. These results complement the previous universality and redundancy results in the literature on the performance of grammar-based codes for sources with finite alphabets.

Published in:

Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 11 )

Date of Publication:

Nov. 2005

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