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Universal compression for I.I.D. sources with large alphabets

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1 Author(s)
Shamir, G.I. ; Dept. of Electr. & Comput. Eng., Utah Univ., Salt Lake City, UT, USA

The minimum description length (MDL) principle is derived for universal compression of i.i.d. sources with large alphabets of size k that may be up to sub-linear with the data sequence length n. Each unknown source probability parameter is shown to cost 0.5log(n/k) bits. This result is shown to be a lower bound in the average minimax sense, and also for most sources in the class. The bound is shown to be achievable even sequentially with the well-known Krichevsky-Trofimov low-complexity scheme.

Published in:

Information Theory, 2003. Proceedings. IEEE International Symposium on

Date of Conference:

29 June-4 July 2003