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SUMMARY:Refinement of Two Fundamental Tools in Information Theory - Profes
 sor Raymond Yeung\, Co-Director\, Institute of Network Coding The Chinese 
 University of Hong Kong
DTSTART:20130722T130000Z
DTEND:20130722T144500Z
UID:TALK46232@talks.cam.ac.uk
CONTACT:Nicholas Teh
DESCRIPTION:In Shannon's original paper and many references in information
  theory\, the entropy of a discrete random variable is assumed or shown to
  be a continuous function. However\, we found that all Shannon's informati
 on measures including entropy and mutual information are discontinuous in 
 the general case that the random variables take values in possibly countab
 ly infinite alphabets. This fundamental property explains why strong typic
 ality and Fano's inequality can only be applied on finite alphabets. Note 
 that strong typicality and Fano's inequality have wide applications in inf
 ormation theory so that it is important to extend them in full generality.
 \n\nIn this talk\, details about the discontinuity of Shannon's informatio
 n measures will be given. We will show how these results lead to a new def
 inition of typicality and an inequality tighter than Fano's inequality. Ap
 plications in network coding and information theoretic security will be di
 scussed.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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