PhD Thesis Defense

Real-time communication and control require information to be transmitted or acted upon as observations become available. Such zero-delay requirements arise both in communication over noisy channels and in control systems whose observations must be conveyed through rate-limited links. Information theory provides a way to identify the limits imposed by these constraints independently of particular coding or control implementations. The relevant quantities are channel capacity, which describes the largest rate of reliable communication, and the rate–cost function, which describes the minimum communication rate needed to attain a prescribed control performance.

This thesis studies communication with feedback and rate-limited control through the information-theoretic quantities governing their performance. For channels with structured memory, we develop a method based on local distributions and symmetry that yields single-letter feedback-capacity upper bounds and sufficient conditions for tightness. The method recovers the capacity of channels whose preceding output serves as the channel state and extends to more general graphical dependence. For general stochastic control systems, including nonlinear systems, we establish finite-horizon converse and achievability bounds that place the operational rate–cost function within an additive logarithmic gap of a directed-information minimum. For static time-invariant systems, in which the next state depends only on the latest action, we obtain a single-letter convex characterization of the asymptotic informational rate–cost function.

Together, these results connect operational communication guarantees with structural properties that reduce generally multi-letter information quantities to constant-size descriptions. They show how local dependence and symmetry can be used in both feedback-capacity maximization and cost-constrained information minimization. The resulting correspondence between the channel and control models gives a sequential counterpart of source–channel coding duality, while retaining the consistency between successive stages that is essential in systems with memory.