Interactive Communication for Data Exchange

Abstract

Abstract-Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange which increases the communication size in steps until the task is done. We also derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bounds of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general source sequence such as a mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

Information Complexity Density and Simulation of Protocols

“…Note that a deterministic protocol corresponds to an interactive function. A specific instance of this situation appears in [49] where…”

“…(iv) Sum conditional entropy density of (XΠ, Y Π): The sum conditional entropy density is given by h (X Y ) = − log P X|Y (X|Y ) P Y |X (Y |X) has been shown recently to play a fundamental role in the communication complexity of the data exchange problem [49]. We shall use the sum conditional…”

“…Similar interactive Slepian-Wolf compression schemes have been considered earlier in different contexts (cf. [17], [38], [52], [25], [49]). …”

“…In a recent work [49], we derived tight lower and upper bounds for the length of a protocol that, for a given distribution P XY , will facilitate data exchange with probability of error less than ε. We review the proposed protocol and its performance here; first, we formally define the data exchange problem.…”

“…In fact, the specific protocol for data exchange proposed in [49] can be recovered as a special case of our simulation protocol in Section VI. The next result paraphrases [49, Theorem 2] and can also be recovered as a special case of Lemma 21.…”