Information Complexity Density and Simulation of Protocols

Tyagi, Himanshu and Venkatakrishnan, Shaileshh Bojja and Viswanath, Pramod and Watanabe, Shun (2017) Information Complexity Density and Simulation of Protocols. In: IEEE TRANSACTIONS ON INFORMATION THEORY, 63 (11). pp. 6979-7002.

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Abstract

Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical distance of the joint distribution of the input and the transcript of the original protocol? We present an information spectrum approach for this problem whereby the information complexity of the protocol is replaced by its information complexity density. Our single-shot bounds relate the communication complexity of simulating a protocol to tail hounds for information complexity density. As a consequence, we obtain a strong converse and characterize the second-order asymptotic term in communication complexity for independent and identically distributed observation sequences. Furthermore, we obtain a general formula for the rate of communication complexity, which applies to any sequence of observations and protocols. Connections with results from theoretical computer science and implications for the function computation problem are discussed.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON INFORMATION THEORY
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering Division of Electrical Sciences > Electrical Communication Engineering > Electrical Communication Engineering - Technical Reports
Date Deposited:	17 Nov 2017 04:54
Last Modified:	17 Nov 2017 04:54
URI:	http://eprints.iisc.ac.in/id/eprint/58261

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