Information Velocity of Cascaded Gaussian Channels with Feedback.
CoRR(2023)
摘要
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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