Information Complexity Density and Simulation of Protocols

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 singleshot bounds relate the communication complexity of simulating a protocol to tail bounds 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.

Interactive Secure Function Computation

“…Interactive computation of deterministic functions was addressed by Orlitsky and Roche [4] and also by Ma and Ishwar [5]. Interactive schemes for computing randomized functions were studied by Yassaee et al [6] and Tyagi et al [7].…”

“…To evaluate the expression in (44), it is sufficient to take minimization over encoder-decoder pairs (p U |X , p Z|U,Y =y2 ) 7 When we restrict Bob's input to y2, then Alice's input X takes values in {x1, x3}. For securely computing (q X|Y =y 2 , q Z|X,Y =y 2 ) with p ∈ (0, 1), we have k = 3 and α…”

The Role of Interaction and Common Randomness in Two-User Secure Computation

“…W (common randomness) Two-user interactive computation (with no privacy) has been extensively studied in computer science literature [1] as well as in information theory literature [2]- [6]. In [2], Kaspi considered two-user interactive source coding.…”

“…Interactive function computation of deterministic functions was addressed in [3], [4]. The problem of computing randomized functions was studied in [5], [6].…”

Interactive Communication for Data Exchange

“…As a by-product, we obtain a precise characterization of gain due to interaction, one of the few such instances available in the literature. Drawing on the techniques introduced in this paper, the much more involved problem of simulation of interactive protocols was addressed in [33], [34].…”