4 research outputs found
A Lower-bound for Variable-length Source Coding in LQG Feedback Control
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 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.Comment: Under dual submission to the IEEE Control Systems Letters and the
61st IEEE Conference on Decision and Control. This version fixed typo in the
references for the original versio
A Noncoherent Space-Time Code from Quantum Error Correction
In this work, we develop a space-time block code for noncoherent
communication using techniques from the field of quantum error correction. We
decompose the multiple-input multiple-output (MIMO) channel into operators from
quantum mechanics, and design a non-coherent space time code using the quantum
stabilizer formalism. We derive an optimal decoder, and analyze the former
through a quantum mechanical lens. We compare our approach to a comparable
coherent approach and a noncoherent differential approach, achieving comparable
or better performance.Comment: 6 pages, one figure, accepted at the 53rd annual Conference on
Information Sciences and System