A Simple Encoding And Decoding Strategy For Stabilization Over Discrete Memoryless Channels

We study stabilization of a discrete-time scalar unstable plant over a noisy communication link, where the plant is perturbed at each time by an unknown, but bounded, additive disturbance. In order to have a simple encoding and decoding strategy, we restrict the observer/encoder to be nearly memoryless in that the channel inputs can only depend on the last sample taken of the plant state, while the controller/decoder is based on the ZJ or Stack Algorithm. Based on an argument due to Jelinek, we show that the suboptimal decoding algorithm achieves stabilization of the same moments as with ML decoding, without the unboundedly increasing computational cost of ML decoding. While in principle the decoder does require an unbounded amount of memory, the computational effort expended at every time instant is a random variable that does not grow with time on average.