Capacity of discrete time Gaussian channel with and without feedback, II

1989 ◽  
Vol 6 (2) ◽  
pp. 245-258 ◽  
Author(s):  
Shunsuke Ihara ◽  
Kenjiro Yanagi
Keyword(s):  
Discrete Time ◽  
Gaussian Channel

scholarly journals On Continuous-Time Gaussian Channels

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 67 ◽  
Author(s):  
Xianming Liu ◽  
Guangyue Han
Keyword(s):  
Discrete Time ◽  
Gaussian Noise ◽  
Continuous Time ◽  
Multiple Access ◽  
Stochastic Calculus ◽  
Broadcast Channels ◽  
Gaussian Channel ◽  
Approximation Approach ◽  
Multiple Access Channels ◽  
Gaussian Channels

A continuous-time white Gaussian channel can be formulated using a white Gaussian noise, and a conventional way for examining such a channel is the sampling approach based on the Shannon–Nyquist sampling theorem, where the original continuous-time channel is converted to an equivalent discrete-time channel, to which a great variety of established tools and methodology can be applied. However, one of the key issues of this scheme is that continuous-time feedback and memory cannot be incorporated into the channel model. It turns out that this issue can be circumvented by considering the Brownian motion formulation of a continuous-time white Gaussian channel. Nevertheless, as opposed to the white Gaussian noise formulation, a link that establishes the information-theoretic connection between a continuous-time channel under the Brownian motion formulation and its discrete-time counterparts has long been missing. This paper is to fill this gap by establishing causality-preserving connections between continuous-time Gaussian feedback/memory channels and their associated discrete-time versions in the forms of sampling and approximation theorems, which we believe will play important roles in the long run for further developing continuous-time information theory. As an immediate application of the approximation theorem, we propose the so-called approximation approach to examine continuous-time white Gaussian channels in the point-to-point or multi-user setting. It turns out that the approximation approach, complemented by relevant tools from stochastic calculus, can enhance our understanding of continuous-time Gaussian channels in terms of giving alternative and strengthened interpretation to some long-held folklore, recovering “long-known” results from new perspectives, and rigorously establishing new results predicted by the intuition that the approximation approach carries. More specifically, using the approximation approach complemented by relevant tools from stochastic calculus, we first derive the capacity regions of continuous-time white Gaussian multiple access channels and broadcast channels, and we then analyze how feedback affects their capacity regions: feedback will increase the capacity regions of some continuous-time white Gaussian broadcast channels and interference channels, while it will not increase capacity regions of continuous-time white Gaussian multiple access channels.

scholarly journals On Gaussian covert communication in continuous time

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ligong Wang
Keyword(s):  
Discrete Time ◽  
Gaussian Noise ◽  
Continuous Time ◽  
Covert Communication ◽  
Gaussian Channel ◽  
Channel Output

AbstractThe paper studies covert communication over a continuous-time Gaussian channel. The covertness condition requires that the channel output must statistically resemble pure noise. When the additive Gaussian noise is “white” over the bandwidth of interest, a formal coding theorem is proven, extending earlier results on covert Gaussian communication in discrete time. This coding theorem is applied to study scenarios where the input bandwidth can be infinite and where positive or even infinite per-second rates may be achievable.

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