  A networked controlled system (NCS) in which the plant communicates to the
controller over a channel with random delay loss is considered. The channel
model is motivated by recent development of tree codes for NCS, which
effectively translates an erasure channel to one with random delay. A causal
transform coding scheme is presented which exploits the plant state memory for
efficient communications (compression) and provides robustness to channel delay
loss. In this setting, we analyze the performance of linear quadratic Gaussian
(LQG) closed-loop systems and the design of the optimal controller. The design
of the transform code for LQG systems is posed as a channel optimized source
coding problem of minimizing a weighted mean squared error over the channel.
The solution is characterized in two steps of obtaining the optimized causal
encoding and decoding transforms and rate allocation across a set of transform
coding quantizers. Numerical and simulation results for Gauss-Markov sources
and an LQG system demonstrate the effectiveness of the proposed schemes.
