A Novelty in Blahut-Arimoto Type Algorithms: Optimal Control Over Noisy Communication Channels

A probability-theoretic problem under information constraints for the concept of optimal control over a noisy-memoryless channel is considered. For our ObserverController block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we propose a Blahut-Arimoto-type algorithm which is, to the best of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for min(P(i),i is an element of{Y,(s) over cap ,X,S,(X) over cap}) phi(1) I(Y; (S) over cap vertical bar X double left right arrow S) - phi I-2(Y; (X) over cap vertical bar X double left right arrow S). This problem is an NP-hard and nonconvex multi-objective optimisation (MOO) one, were the objective functions are respectively the distortion function dim(Null(I((S) over cap; S)) -> infinity and the memoryless-channel capacity dim(Null(I(X; (X) over cap)) -> 0. Our novel algorithm applies an Alternating optimisation method. Subsequently, a robust version of the algorithm is discussed with regard to the perturbed PMFs -parameter uncertainties in general. The aforementioned robustness is actualised by exploiting the simultaneous-perturbationstochastic-approximation (SPSA). The principles of detectabilityand-stabilisability as well as synchronisability are explored, in addition to providing the simulations-by which the efficiency of our work is shown. We also calculate the total complexity of our proposed algorithms respectively as O(TKM0(KlogK)) and O(TKM0(Klog K + 0.33K)). Our methodology is generic which can be applied to other fields of studies which are optimisation-driven.