Filtering Results for A Joint Control-Decoding Problem in Optical Communications.

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Gubner, John A.
We consider a doubly-stochastic time-space Poisson-process model for a direct-detection receiver in an optical communication system. Using a Bayesian decision approach to specify the design of the receiver, we encounter a likelihood ratio which, in general, is a function of a certain conditional expectation. We show how the design of the receiver leads to what we call the Joint Control-Decoding Probiem. In a degenerate case, we completely solve the Joint Control-Decoding Problem and compute the conditional expectation mentioned. In the general case, we cannot compute the conditional expectation mentioned above, and hence, cannot proceed to solve the Joint Control-Decoding problem; however, in order to gain insight into the general filtering problem given time-space point-process observations, we attempt to apply known filtering methods to the computation of a related conditional expectation. Finally, we consider linear estimates to substitute for the needed conditional expectation. In the case of a deterministic control, we reduce the linear estimation problem to the solution of a Fredholm integral equation. In the final chapter, we present a discrete-time version of our model which we hope will render the corresponding Discrete-Time Joint Control-Decoding Problem more tractable.