TY - JOUR

T1 - Information Velocity of Cascaded Gaussian Channels With Feedback

AU - Domanovitz, Elad

AU - Khina, Anatoly

AU - Philosof, Tal

AU - Kochman, Yuval

N1 - Publisher Copyright:
IEEE

PY - 2024

Y1 - 2024

N2 - We consider a line network of nodes, connected by additive white 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. For general white noise, we derive exponential error-probability bounds. For single-packet transmission over channels with (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.

AB - We consider a line network of nodes, connected by additive white 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. For general white noise, we derive exponential error-probability bounds. For single-packet transmission over channels with (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.

KW - Channel capacity

KW - Channel estimation

KW - Electronic mail

KW - Error probability

KW - Noise

KW - Relays

KW - Transmitters

UR - http://www.scopus.com/inward/record.url?scp=85196484307&partnerID=8YFLogxK

U2 - 10.1109/JSAIT.2024.3416310

DO - 10.1109/JSAIT.2024.3416310

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AN - SCOPUS:85196484307

SN - 2641-8770

SP - 1

JO - IEEE Journal on Selected Areas in Information Theory

JF - IEEE Journal on Selected Areas in Information Theory

ER -