Empirical coordination in a triangular multiterminal network

Abstract

In this paper, we investigate the problem of the empirical coordination in a triangular multiterminal network. A triangular multiterminal network consists of three terminals where two terminals observe two external i.i.d correlated sequences. The third terminal wishes to generate a sequence with desired empirical joint distribution. For this problem, we derive inner and outer bounds on the empirical coordination capacity region. It is shown that the capacity region of the degraded source network and the inner and outer bounds on the capacity region of the cascade multiterminal network can be directly obtained from our inner and outer bounds. For a cipher system, we establish key distribution over a network with a reliable terminal, using the results of the empirical coordination. As another example, the problem of rate distortion in the triangular multiterminal network is investigated in which a distributed doubly symmetric binary source is available.

Joint coordination-channel coding for strong coordination over noisy channels based on polar codes

“…where (a) holds by invertibility of G n ; (b) -(d) follows from the chain rule of the KL divergence [28]; (e) results from the definitions of the conditional distributions in (8), and (9); (f) follows from the definitions of the index sets as shown in Figures 4 and 5; (g) results from the encoding of U N 1i and U N 2i bit-by-bit at E 1 and E 2 , respectively, with uniformly distributed randomness bits and message bits. These bits are generated by applying successive cancellation encoding using previous bits and side information with conditional distributions defined in (8) and (9); (h) holds by the one-to-one relation between U N 2 and C N ; (i) follows from the sets defined in (5) and (6).…”

“…A significant amount of work has been devoted to finding the capacity regions of various coordination problems based on both empirical and strong coordination [1]- [10], where [4], [6]- [8], [10] focus on small to moderate network settings. This work is supported by NSF grants CCF-1440014, CCF-1439465.…”

Empirical Coordination Subject to a Fidelity Criterion

“…According to [1], empirical coordination is established if the joint type of the actions in the network is close to the desired distribution. This kind of coordination has been studied in various set-ups (see e.g., [2]- [4]) and it has been combined with ideas from other fields like game theory (see e.g., [5]). Strong coordination instead deals with the joint probability distribution of the actions.…”

Empirical Coordination with Multiple Descriptions

“…The notion of empirical coordination was introduced in [13] and it is achieved if the joint type, measured by total variation distance, of the actions (or nodes) in a network is close to the desired distribution, in probability. This kind of coordination has been studied in various settings, see e.g., [14] and merged with ideas from other research fields, such as game theory [15] and networked control systems [16]. The framework of empirical coordination of [13] was recently extended to the more general framework of empirical coordination subject to fidelity also termed "imperfect empirical coordination" by [4] who was inspired by the work of [17].…”