On-off dual channel coding as a team decision problem

We consider the 'single-letter' ('one-shot' or 'zero-delay') source-channel coding of a sensor's measurements in the presence of two channels as a constrained team decision theory problem. Under a global power constraint and quadratic distortion measure, the action space of coding strategies is restricted to on-off (transmission or silence) decisions. The latter are communicated to the decoder through a binary side channel, whereas in case of transmission the uncoded analog measurement is sent over the main communication channel between the transmitter and the receiver. By further restrictions on the behavior of the encoder, suboptimal team control strategies are derived in closed form, along with their parameters that stem from a numerical optimization problem. The distortion of the resulting strategy is compared with other schemes under non-Gaussian source and noise.