A Lower-bound for Variable-length Source Coding in LQG Feedback Control [article]

Travis C. Cuvelier and Takashi Tanaka and Robert W. Heath Jr
2022 arXiv   pre-print
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
more » ... have shared randomness, as is the case in systems using dithered quantizers. We define two extremal prefix-free requirements that may be imposed on the message packets; such constraints are useful in that they allow the decoder, and potentially other agents to uniquely identify the end of a transmission in an online fashion. We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness. We also provide a generalization of the bound that applies if prefix-free requirements are relaxed. We conclude with a rate-distortion formulation.
arXiv:2203.12467v2 fatcat:5cteo7twgzcinfpgt3c23npime