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Information Complexity Density and Simulation of Protocols Extended Abstract]

Tyagi, Himanshu and Venkatakrishnan, Shaileshh and Viswanath, Pramod and Watanabe, Shun (2016) Information Complexity Density and Simulation of Protocols Extended Abstract]. In: 7th ACM Conference on Innovations in Theoretical Computer Science (ITCS), JAN 14-16, 2016, Massachusetts Inst Technol Cambridge, Cambridge, MA, pp. 381-391.

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Official URL: http://dx.doi.org/10.1145/2840728.2840754

Abstract

A simulation of an interactive protocol entails the use of interactive communication to produce the output of the protocol to within a fixed statistical distance epsilon. Recent works have proposed that the information complexity of the protocol plays a central role in characterizing the minimum number of bits that the parties must exchange for a successful simulation, namely the distributional communication complexity of simulating the protocol. Several simulation protocols have been proposed with communication complexity depending on the information complexity of the simulated protocol. However, in the absence of any general lower bounds for distributional communication complexity, the conjectured central role of information complexity is far from settled. We fill this gap and show that the distributional communication complexity of epsilon-simulating a protocol is bounded below by the epsilon-tail lambda(epsilon) of the information complexity density, a random variable with information complexity as its expected value. For protocols with bounded number of rounds, we give a simulation protocol that yields a matching upper bound. Thus, it is not information complexity but lambda(epsilon), that governs the distributional communication complexity. As applications of our bounds, in the amortized regime for product protocols, we identify the exact second order term, together with the precise dependence on epsilon. For general protocols such as a mixture of two product protocols or for the amortized case when the repetitions are not independent, we derive a general formula for the leading asymptotic term. These results sharpen and significantly extend known results in the amortized regime. In the single-shot regime, our lower bound sheds light on the dependence of communication complexity on epsilon. We illustrate this with an example that exhibits an arbitrary separation between distributional communication complexity and information complexity for all sufficiently small epsilon.

Item Type: Conference Proceedings
Additional Information: Copy right for this article belongs to the ASSOC COMPUTING MACHINERY, 1515 BROADWAY, NEW YORK, NY 10036-9998 USA
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 31 Jan 2017 05:25
Last Modified: 31 Jan 2017 05:25
URI: http://eprints.iisc.ac.in/id/eprint/55994

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