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SUMMARY:Cheuk Ting LI (The Chinese University of Hong Kong)
DTSTART:20260225T160000Z
DTEND:20260225T171500Z
DTSTAMP:20260423T021311Z
UID:AAIT/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AAIT/49/">Di
 screte Layered Entropy\, Conditional Compression and a Tighter Strong Func
 tional Representation Lemma.</a>\nby Cheuk Ting LI (The Chinese University
  of Hong Kong) as part of Seminar on Algorithmic Aspects of Information Th
 eory\n\n\nAbstract\nGiven two pieces of information\, we can take the "uni
 on" of them (the joint random variable)\, but the natural definition of th
 e difference between them (the information in X but not in Y) is less clea
 r. The conditional entropy H(X|Y) is often interpreted as the amount of in
 formation in X but not in Y\, but H(X|Y) cannot be regarded as the entropy
  of the "conditional random variable X|Y"\, i.e.\, conditional entropy is 
 not a special case of entropy. In this talk\, we discuss a notion of diffe
 rence motivated by a conditional compression problem\, and a quantity Lamb
 da(X)\, called discrete layered entropy. Lambda(X) has properties similar 
 to the Shannon entropy H(X)\, and is close to H(X) within a logarithmic ga
 p. Moreover\, Lambda(X|Y) is indeed the discrete layered entropy of the "c
 onditional random variable X|Y"\, so conditional discrete layered entropy 
 is a special case of discrete layered entropy (unlike Shannon entropy). Th
 ese properties make Lambda(X) useful for analyzing conditional compression
  problems such as channel simulation with common randomness. In particular
 \, it can give a tighter bound for the strong functional representation le
 mma.\n
LOCATION:https://researchseminars.org/talk/AAIT/49/
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