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

Abstract

We construct a joint coordination-channel polar coding scheme for strong coordination of actions between two agents X and Y, which communicate over a discrete memoryless channel (DMC) such that the joint distribution of actions follows a prescribed probability distribution. We show that polar codes are able to achieve our previously established inner bound to the strong noisy coordination capacity region and thus provide a constructive alternative to a random coding proof. Our polar coding scheme also offers a constructive solution to a channel simulation problem where a DMC and shared randomness are together employed to simulate another DMC. In particular, our proposed solution is able to utilize the randomness of the DMC to reduce the amount of local randomness required to generate the sequence of actions at agent Y. By leveraging our earlier random coding results for this problem, we conclude that the proposed joint coordinationchannel coding scheme strictly outperforms a separate scheme in terms of achievable communication rate for the same amount of injected randomness into both systems.

Strong Coordination of Signals and Actions Over Noisy Channels With Two-Sided State Information

“…3) Remove the extra randomness F: Even though the extra common randomness F is required to coordinate (U n , S n , Z n , X n , Y n , V n , W n ) we will show that we do not need it in order to coordinate only (U n , S n , Z n , X n , Y n , V n ). Observe that by Lemma 2, equation (22) implies that…”

“…Polar coding for strong point-to-point coordination has been presented in [20,37]. In [22] the authors construct a joint coordination-channel polar coding scheme for strong coordination of actions. We present a joint source-channel polar coding scheme for strong coordination and we require joint coordination of signals and actions over a noisy channel.…”

“…We conclude the paper by considering the design of an explicit coordination scheme in this setting. Coding schemes for coordination based on polar codes have already been designed in [19][20][21][22]. Inspired by the binning technique using polar codes in [23], we propose an explicit polar coding scheme that achieves the inner bound for the coordination capacity region in [1] by extending our coding scheme in [2] to strong coordination.…”

Strong Coordination over Noisy Channels

“…The only existing design of polar codes for the noisy empirical coordination case [21] is based on the joint source-channel coordination approach in [13]. A construction based on polar codes for the noisy strong coordination problem has been first presented in our previous conference work [2], which is part of this paper.…”

“…This work was supported by NSF grants CCF-1440014, CCF-1439465. This work was presented in part at the IEEE International Symposium on Information Theory (ISIT 2017), Aachen, Germany [1] and at the 55th Annual Allerton Conference, Monticello, IL, USA [2].…”