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arXiv · 2311.14223

Information Velocity of Cascaded Gaussian Channels with Feedback

Elad Domanovitz·Anatoly Khina·Tal Philosof·Yuval Kochman
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Abstract

We consider a line network of nodes, connected by additive white Gaussian noise channels, equipped with local feedback. We study the velocity at which information spreads over this network. For transmission of a data packet, we give an explicit positive lower bound on the velocity, for any packet size. Furthermore, we consider streaming, that is, transmission of data packets generated at a given average arrival rate. We show that a positive velocity exists as long as the arrival rate is below the individual Gaussian channel capacity, and provide an explicit lower bound. Our analysis involves applying pulse-amplitude modulation to the data (successively in the streaming case), and using linear mean-squared error estimation at the network nodes. Due to the analog linear nature of the scheme, the results extend to any additive noise. For general noise, we derive exponential error-probability bounds. Moreover, for (sub-)Gaussian noise we show a doubly-exponential behavior, which reduces to the celebrated Schalkwijk-Kailath scheme when considering a single node. Viewing the constellation as an "analog source", we also provide bounds on the exponential decay of the mean-squared error of source transmission over the network.

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Elad Domanovitz, Anatoly Khina, Tal Philosof, Yuval Kochman. 2023-11-23. Information Velocity of Cascaded Gaussian Channels with Feedback. https://arxiv.org/abs/2311.14223

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