Dynamic source–channel coding for estimation and control over binary symmetric channels

The authors study causal dynamic source-channel codes for mean-square stabilisation of a linear plant with random initial state, over binary symmetric channels (BSCs). A binary expansion source coding scheme and two types of channel coding schemes are investigated: (i) dynamic repetition encoding under sequential majority logic decoding, and (ii) dynamic Fountain encoding under sequential BP decoding. The coding schemes are first analysed for an open-loop system, where the goal is to transmit a real-valued source over BSCs with the objective of minimising end-to-end mean-square error distortion. They derive upper- and lower bounds on the achievable distortion which is a function of time. Based on these distortion bounds, they show that the dynamic Fountain codes are able to stabilise (in mean-square sense) an unstable linear plant over BSCs.