Summary Lecture

Comp760, Summary of Lecture 20

The material for today’s lecture is from [BGPW13]. Determining the 0-error internal information cost of the AND function is considerably more difficult that determining its external information cost. At the first glance it might seem surprising that one can do something different from the protocol that we discussed in the external case. First we state a protocol that is optimal for the case of ...

Comp760, Summary of Lecture 14

So far, in this course, we have been focused on the communication cost of protocols, and given various communication tasks, we studied the minimum communication cost required to perform those tasks. The information theoretic tools introduced in the past two lectures enable us to introduce another natural measure of complexity. Roughly speaking, given a protocol and a distribution on the inputs ...

Comp760, Summary of Lecture 12

In 1948, Shannon in his seminal paper [Sha48] introduced information theory as a tool for studying the communication cost of transmission tasks. In this setting, Alice receives a random input X ∼ (Ω, p) and wants to transmit it to Bob. Shannon’s source coding theorem (Theorem 2 below) concerns the case where Alice is sending many copies of X. More precisely, she receives (X1, . . . , Xn) where ...

Comp760, Summary of Lecture 15

We can think of these as communication tasks. Note that all the above definitions require something about the distribution of (X,Y, π(X,Y )). In the following definition we attempt to formally define a communication task. This is going to be useful when we discuss the direct sum theorems. However, the formalism of Definition 1 is not very essential for our purpose and the natural intuition that...

Comp760, Summary of Lecture 21