1,242 research outputs found
On Continuous-Time 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
The Wiretap Channel with Feedback: Encryption over the Channel
In this work, the critical role of noisy feedback in enhancing the secrecy
capacity of the wiretap channel is established. Unlike previous works, where a
noiseless public discussion channel is used for feedback, the feed-forward and
feedback signals share the same noisy channel in the present model. Quite
interestingly, this noisy feedback model is shown to be more advantageous in
the current setting. More specifically, the discrete memoryless modulo-additive
channel with a full-duplex destination node is considered first, and it is
shown that the judicious use of feedback increases the perfect secrecy capacity
to the capacity of the source-destination channel in the absence of the
wiretapper. In the achievability scheme, the feedback signal corresponds to a
private key, known only to the destination. In the half-duplex scheme, a novel
feedback technique that always achieves a positive perfect secrecy rate (even
when the source-wiretapper channel is less noisy than the source-destination
channel) is proposed. These results hinge on the modulo-additive property of
the channel, which is exploited by the destination to perform encryption over
the channel without revealing its key to the source. Finally, this scheme is
extended to the continuous real valued modulo- channel where it is
shown that the perfect secrecy capacity with feedback is also equal to the
capacity in the absence of the wiretapper.Comment: Submitted to IEEE Transactions on Information Theor
Random Access Channel Coding in the Finite Blocklength Regime
Consider a random access communication scenario over a channel whose
operation is defined for any number of possible transmitters. Inspired by the
model recently introduced by Polyanskiy for the Multiple Access Channel (MAC)
with a fixed, known number of transmitters, we assume that the channel is
invariant to permutations on its inputs, and that all active transmitters
employ identical encoders. Unlike Polyanskiy, we consider a scenario where
neither the transmitters nor the receiver know which transmitters are active.
We refer to this agnostic communication setup as the Random Access Channel, or
RAC. Scheduled feedback of a finite number of bits is used to synchronize the
transmitters. The decoder is tasked with determining from the channel output
the number of active transmitters () and their messages but not which
transmitter sent which message. The decoding procedure occurs at a time
depending on the decoder's estimate of the number of active transmitters,
, thereby achieving a rate that varies with the number of active
transmitters. Single-bit feedback at each time , enables all
transmitters to determine the end of one coding epoch and the start of the
next. The central result of this work demonstrates the achievability on a RAC
of performance that is first-order optimal for the MAC in operation during each
coding epoch. While prior multiple access schemes for a fixed number of
transmitters require simultaneous threshold rules, the proposed
scheme uses a single threshold rule and achieves the same dispersion.Comment: Presented at ISIT18', submitted to IEEE Transactions on Information
Theor
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