Information Velocity of Cascaded Gaussian Channels with Feedback
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913564345761792 |
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| author | Domanovitz, Elad Khina, Anatoly Philosof, Tal Kochman, Yuval |
| author_facet | Domanovitz, Elad Khina, Anatoly Philosof, Tal Kochman, Yuval |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14223 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Information Velocity of Cascaded Gaussian Channels with Feedback Domanovitz, Elad Khina, Anatoly Philosof, Tal Kochman, Yuval Information Theory 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. |
| title | Information Velocity of Cascaded Gaussian Channels with Feedback |
| topic | Information Theory |
| url | https://arxiv.org/abs/2311.14223 |