Comp760, Summary of Lecture 14
نویسنده
چکیده
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 of Alice and Bob, the information cost of this protocol is the amount of information that the communication between Alice and Bob reveals about their inputs. Note that a protocol with a very high communication cost might still have a small information cost if the communication between Alice and Bob does not reveal much about their inputs. Naturally, we will be interested in finding the smallest information cost required to perform a given communication task. The concept of information complexity is deeply connected to communication complexity. Recall how entropy captured the amount of information in a random variable, and how this quantity gave us the exact asymptotic of the transmission cost of many independent copies of X. That is the simplest setting of communication where there is a one-way channel and Alice wants to transmit her data to Bob. The general setting of communication complexity is more complicated as Alice and Bob are allowed to interact. However as the recent results in this area have demonstrated, similar to the way that the information content of a random variable gives the asymptotics of the transmission cost, information complexity provides valuable information about the communication complexity, and specially in the asymptotic case where Alice and Bob are performing many instances of a given communication task.
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تاریخ انتشار 2015