Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes

This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope classes with exponent . The minimax redundancy of exponentially decreasing envelope classes is proved to be equivalent to 1 4 log e log2 n. Then, an adaptive algorithm is proposed, whose maximum redundancy is equivalent to the minimax redundancy.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Dominique Bontemps
• Keywords: CORR 2008, Countable Infinite Alphabet, Education, Envelope Classes, Minimax Redundancy