The Communication Complexity of Correlation

We examine the communication required for generating random variables remotely. One party Alice will be given a distribution D, and she has to send a message to Bob, who is then required to generate a value with distribution exactly D. Alice and Bob are allowed to share random bits generated without the knowledge of D. There are two settings based on how the distribution D provided to Alice is chosen. Average case: D is itself chosen randomly from some set (the set and distribution are known in advance) and we wish to minimize the expected communication in order for Alice to generate a value y, with distribution D. We characterize the communication required in this case based on the mutual information between the input to Alice and the output Bob is required to generate. Worst case: D is chosen from a set of distributions D, and we wish to devise a protocol so that the expected communication (the randomness comes from the shared random string and Alice’s coin tosses) is small for ea...

• Type: Conference
• Year: 2007
• Where: COCO
• Authors: Prahladh Harsha, Rahul Jain, David A. McAllester, Jaikumar Radhakrishnan
• Keywords: COCO 2007, Communication, Distribution D, Party Alice