Empirical Coordination Subject to a Fidelity Criterion

Abstract

We study the problem of empirical coordination subject to a fidelity criterion for a general set-up. We prove a result which indicates a strong connection between our framework and the framework of empirical coordination developed in [1]. It turns out that when we design codes that achieve empirical coordination according to a given distribution and subject to the fidelity criterion, it is sufficient to consider codes that produce actions of the same joint type for a class of types which is close enough to our desired distribution is some sense.

Empirical Coordination with Multiple Descriptions

“…Here, in (23) we increase the number of terms in the second sum; and in (24) we use (4). Hence, by plugging (12),(21),(22),(24) in (11), and using (10), we get from (3) the following bound for Pr (Case 2):…”

“…In this paper, we apply ideas from a distributed source coding setup called the multiple description problem (MDP) [3] to the framework of empirical coordination using a fidelity criterion that was recently introduced in [4].…”

“…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]. Following [4], imperfect empirical coordination is established if the total variation between the joint type of the actions in a network comes close, on average, to a desired distribution within distance pre-specified by a threshold ∆.…”

“…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]. Following [4], imperfect empirical coordination is established if the total variation between the joint type of the actions in a network comes close, on average, to a desired distribution within distance pre-specified by a threshold ∆. Clearly, if ∆ = 0, then, we obtain the empirical coordination in the sense of [13].…”

Adaptive Interference Coordination over Channels with Unknown State at the Encoder and the Decoder

“…In contrast to the choice of the interference coordination criterion of [1], in our study we make use of the framework of imperfect empirical coordination. The framework of imperfect empirical coordination was introduced in [9] and compared to perfect empirical coordination of [3] which asks the joint type of the actions to be close to the desired empirical distribution in probability, it requires the average distance (as measured by total variation) between the joint type of the actions and the desired empirical distribution to be smaller than a certain level ∆ for long enough n-length sequences. Specifically, in parallel with the establishment of reliable communication between the encoder and the decoder, we ask for a different average level of precision ∆ s on the establishment of the interference coordination with the external observer, depending on the exact state s of the channel.…”