Strong coordination over noisy channels: Is separation sufficient?

Abstract

Abstract-We study the problem of strong coordination of actions of two agents X and Y that communicate over a noisy communication channel such that the actions follow a given joint probability distribution. We propose two novel schemes for this noisy strong coordination problem, and derive inner bounds for the underlying strong coordination capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the communication channel to reduce the local randomness required in generating the action sequence at agent Y . The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. Finally, we present an example in which the joint scheme is able to outperform the separate scheme in terms of coordination rate. I. INTRODUCTIONThe problem of communication-based coordination of multi-agent systems arises in numerous applications including mobile robotic networks, smart traffic control, and distributed computing such as distributed games and grid computing [1]. Several theoretical and applied studies on multi-agent coordination have targeted questions on how agents exchange information and how their actions can be correlated to achieve a desired overall behavior. Two types of coordination have been addressed in the literature -empirical coordination where the histogram of induced actions is required to be close to a prescribed target distribution, and strong coordination, where the induced sequence of joint actions of all the agents is required to be statistically close (i.e., nearly indistinguishable) from a chosen target probability mass function (pmf).Recently, the capacity regions of several empirical and strong coordination network problems have been established [1]- [6]. Bounds for the capacity region for the point-to-point case were obtained in [7] under the assumption that the nodes communicate in a bidirectional fashion in order to achieve coordination. A similar framework was adopted and improved in [8]. In [4], [6], [9], the authors addressed inner and outer bounds for the capacity region of a three-terminal network in the presence of a relay. The work of [4] was later extended in [5], [10] to derive a precise characterization of the strong coordination region for multi-hop networks. Starkly, the majority of the recent works on coordination have considered noisefree communication channels with the exception of two works:

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

“…1 where only source and reproduction sequences are coordinated via a suitable polar coding scheme over DMCs. In particular, we design an explicit lowcomplexity nested polar coding scheme for strong coordination over noisy channels that achieves the inner bound of the two-node network capacity region of our earlier work [20]. In this work, we show that a joint coordination-channel coding scheme is able to strictly outperform a separationbased scheme in terms of achievable communication rate if the same amount of randomness is injected into the system.…”

“…Consider auxiliary random variables A ∈ A and C ∈ C with (A, C) ∼ P AC be jointly correlated with (X, Y ) as P XY ABC = P AC P X|AC P B|A P Y |BC . The joint strong coordination-channel random code with parameters (R c , R o , R a , N ) [20], where I 1, 2 N Rc , J 1, 2 N Ro , and K 1, 2 N Ra , consists of 1) Nested codebooks: A codebook C of size 2 N (Ro+Rc) is generated i.i.d. according to a pmf P C , i.e.,…”

“…The underlying proofs and details of the coding mechanism for this joint coordination-channel coding scheme for noisy strong coordination are based on a complex channel resolvability framework [20]. Channel resolvability has been successfully used to study different strong coordination problems due to its ability to approximate channel output statistics with random codebooks [22].…”

“…Theorem 1. (Strong coordination inner bound [20]) A tuple (R o , ρ 1 , ρ 2 ) is achievable for the strong noisy communication setup in Fig. 1 if for some R a , R c ≥ 0,…”

Strong Coordination over Noisy Channels

“…1: Point-to-point strong coordination over a DMC. separation-based scheme 1 in terms of achievable communication rate if the same amount of randomness is injected into the system in the high-capacity regime for the BSC, i.e., C → 1. This example reveals that separate coordination and channel coding is indeed sub-optimal in the context of strong coordination under the additional constraint of minimizing the communication rate.…”