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Generalized Source Coding Theorems and Hypothesis Testing: Part II --Operational Limits

Summary: Generalized Source Coding Theorems and Hypothesis
Testing: Part II -- Operational Limits
Po­Ning Chen Fady Alajaji
Dept. of Communications Engineering Dept. of Mathematics and Statistics
National Chiao Tung University Queen's University
1001, Ta­Hsueh Road, Hsin Chu Kingston, Ontario K7L 3N6
Taiwan 30050, R.O.C. Canada
Key Words: Shannon theory, AEP, source coding theorems,
hypothesis testing, Neyman­Pearson error exponent
In light of the information measures introduced in Part I, a generalized version of the Asymp­
totic Equipartition Property (AEP) is proved. General fixed­length data compaction and data
compression (source coding) theorems for arbitrary finite­alphabet sources are also established.
Finally, the general expression of the Neyman­Pearson type­II error exponent subject to upper
bounds on the type­I error probability is examined.

I. Introduction
In Part I of this paper [5], generalized versions of the inf/sup­entropy/information/divergence
rates of Han and Verd'u were proposed and analyzed. Equipped with these information measures,
we herein demonstrate a generalized Asymptotic Equipartition Property (AEP) Theorem and


Source: Alajaji, Fady - Department of Mathematics and Statistics, Queen's University (Kingston)


Collections: Engineering