A Lower-Bound for Variable-Length Source Coding in Linear-Quadratic-Gaussian Control With Shared Randomness

@article{Cuvelier2022ALF,
  title={A Lower-Bound for Variable-Length Source Coding in Linear-Quadratic-Gaussian Control With Shared Randomness},
  author={Travis C. Cuvelier and Takashi Tanaka and Robert W. Heath},
  journal={IEEE Control Systems Letters},
  year={2022},
  volume={6},
  pages={2918-2923}
}
In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified via the channel bitrate) required to attain a given control performance. We assume that at every time step an encoder can convey a packet containing a variable number of bits over the channel to a decoder at the controller. Our system model provides for the possibility that the encoder and decoder… 

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