Today, blocklength, rate, SNR, frequency, quantizer resolution, and
network size are well-studied and recognized resources for
communication in information theory. A relatively less well recognized
and less understood resource for communication and computation is
interaction. Interaction as a resource becomes particularly valuable
in the context of distributed function computation where it may be
necessary for nodes to exchange information bidirectionally, perform
computations, and harness the structure of the functions,
statistical-dependencies, and the network topology to maximize the
overall computation-efficiency as opposed to only generating,
receiving, and forwarding data.

This talk will focus on a distributed block source coding problem
involving potentially an infinite number of messages with
infinitesimal-rate for two-terminal interactive function computation.
Viewing the sum-rate-distortion function as a functional of the joint
source pmf and distortion levels, I will describe a new type of
single-letter characterization of the infinite-message limit. I will
show how this leads to an iterative algorithm for numerical evaluation
and the first example demonstrating that two messages can strictly
improve the one-message Wyner-Ziv rate-distortion function resolving a
question raised by Kaspi in 1985.  In closing, I will briefly mention
extensions to star networks where interaction changes the scaling law
of the sum-rate in terms of the network size and collocated networks
where for computing symmetric functions of binary sources, a new lower
bound for the minimum sum-rate is order-wise tight whereas the cut-set
bound is order-wise loose.