This dissertation investigates communication and estimation over channels whose transmission characteristics change with previous channel utilization and transmissions. We define three classes of channels: 1) Use-dependent discrete switching channels, 2) Use-dependent packet-drop channels, and 3) Shared-resource multiple packet-drop channels. In each of these classes of channels, there is a channel state that determines the channel's transmission characteristics.

For use-dependent discrete switching and packet-drop channels, there is a channel transmission policy that calculates the input to the channel state system. There is also an encoding policy that calculates the data to transmit over the channel. For these channels, we explore the properties, structure, and calculation of optimal channel transmission and encoding policies.

A discrete channel and a finite state machine, the channel state, form a use-dependent discrete switching channel. For each channel state, the discrete channel has different symbol transmission statistics. The transmission policy has access to the output of the discrete channel. For a remote estimation problem with a conditional entropy cost over these channels, we show a partial separation between the design of transmission policies and encoding policies. Also, the optimal transmission and encoding policy are calculated for a specific use-dependent discrete switching channel.

A Bernoulli packet-drop link and a finite state machine, the channel state, form a use-dependent packet-drop channel. The channel state influences transmission performance by adjusting the probability of a packet-drop on the Bernoulli link. Each channel state corresponds to a specific drop probability. For a remote estimation problem with an expected mean-squared error cost over these channels, the structure of optimal transmission policies is explored.

For shared-resource multiple packet-drop channels, the channel has various modes of operation for transmitting multiple sensor measurements to an estimator over Bernoulli packet-drop links. Each mode of operation, or channel state, prioritizes the transmission of some sensor measurements over others. The channel state sets transmission priorities by adjusting the probability of packet-drop for each Bernoulli packet-drop link. In a given channel state, one sensor's drop probability is low, while another sensor's drop probability is high. For a remote estimation problem of transmitting the state of multiple systems over these channels, algorithms are presented to design the transition between transmission prioritization, channel states, to simultaneously stabilize the expected mean-squared estimation error of all the systems.

A detailed application of these results to operator support system design and a literature review of systematic design methods for decision support tools are presented.