3:30 pm, Seminar Hall CMI Silver Jubilee Lecture Mutual Information in One-Shot Jaikumar Radhakrishnan TIFR, Mumbai. 12-11-14 Abstract Using two examples, we will describe information theoretic quantities such as Shannon Entropy, Relative Entropy and Mutual Information. Example 1: We have a pair of random variables (X,Y) taking values in S x T. One party (the Sender) is given a value x in S chosen according to the distribution of X and needs to ensure that the other party (he Receiver) gets a value y in T so that (x,y) have the same distribution as (X,Y). How many bits on average must the Sender send the Receiver? Example 2: There is one Sender and there two Receivers talking over a noisy channel: the sender feeds a letter into the channel and the two receivers receive something in response. How efficiently can the Sender communicate with the receivers? In Example 1, we will obtain an operational one-shot meaning for Shannon's Mutual Information. In Example 2, we will obtain a one-shot version of Marton's bound. We will assume no prior background in information theory. (Based on joint work with David McAllester, Prahladh Harsha, Rahul Jain, Pranab Sen and Naqueeb Warsi.)
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