Coded Kalman Filtering over MIMO Gaussian Channels with Feedback
<|reference_start|>Coded Kalman Filtering over MIMO Gaussian Channels with Feedback: We consider the problem of remotely stabilizing a linear dynamical system. In this setting, a sensor co-located with the system communicates the system's state to a controller over a noisy communication channel with feedback. The objective of the controller (decoder) is to use the channel outputs to estimate the vector state with finite zero-delay mean squared error (MSE) at the infinite horizon. It has been shown in [1] that for a vector Gauss-Markov source and either a single-input multiple-output (SIMO) or a multiple-input single-output (MISO) channel, linear codes require the minimum capacity to achieve finite MSE. This paper considers the more general problem of linear zero-delay joint-source channel coding (JSCC) of a vector-valued source over a multiple-input multiple-output (MIMO) Gaussian channel with feedback. We study sufficient and necessary conditions for linear codes to achieve finite MSE. For sufficiency, we introduce a coding scheme where each unstable source mode is allocated to a single channel for estimation. Our proof for the necessity of this scheme relies on a matrix-algebraic conjecture that we prove to be true if either the source or channel is scalar. We show that linear codes achieve finite MSE for a scalar source over a MIMO channel if and only if the best scalar sub-channel can achieve finite MSE. Finally, we provide a new counter-example demonstrating that linear codes are generally sub-optimal for coding over MIMO channels.<|reference_end|>
@article{han2024coded,
    title={Coded Kalman Filtering over MIMO Gaussian Channels with Feedback},
    author={Barron Han, Oron Sabag, Victoria Kostina, Babak Hassibi},
    journal={arXiv preprint arXiv:2406.17196},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.17196},
    primaryClass={cs.IT cs.SY eess.SY math.IT}
}