34,064 research outputs found
Capacity Approximation of Continuous Channels by Discrete Inputs
International audienceIn this paper, discrete approximations of the capacity are introduced where the input distribution is constrained to be discrete in addition to any other constraints on the input. For point-to-point memoryless additive noise channels, rates of convergence to the capacity of the original channel are established for a wide range of channels for which the capacity is finite. These results are obtained by viewing discrete approximations as a capacity sensitivity problem, where capacity losses are studied when there are perturbations in any of the parameters describing the channel. In particular, it is shown that the discrete approximation converges arbitrarily close to the channel capacity at rate O(∆), where ∆ is the discretization level of the approximation. Examples of channels where this rate of convergence holds are also given, including additive Cauchy and inverse Gaussian noise channels
Information capacity in the weak-signal approximation
We derive an approximate expression for mutual information in a broad class
of discrete-time stationary channels with continuous input, under the
constraint of vanishing input amplitude or power. The approximation describes
the input by its covariance matrix, while the channel properties are described
by the Fisher information matrix. This separation of input and channel
properties allows us to analyze the optimality conditions in a convenient way.
We show that input correlations in memoryless channels do not affect channel
capacity since their effect decreases fast with vanishing input amplitude or
power. On the other hand, for channels with memory, properly matching the input
covariances to the dependence structure of the noise may lead to almost
noiseless information transfer, even for intermediate values of the noise
correlations. Since many model systems described in mathematical neuroscience
and biophysics operate in the high noise regime and weak-signal conditions, we
believe, that the described results are of potential interest also to
researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review
Power Allocation and Time-Domain Artificial Noise Design for Wiretap OFDM with Discrete Inputs
Optimal power allocation for orthogonal frequency division multiplexing
(OFDM) wiretap channels with Gaussian channel inputs has already been studied
in some previous works from an information theoretical viewpoint. However,
these results are not sufficient for practical system design. One reason is
that discrete channel inputs, such as quadrature amplitude modulation (QAM)
signals, instead of Gaussian channel inputs, are deployed in current practical
wireless systems to maintain moderate peak transmission power and receiver
complexity. In this paper, we investigate the power allocation and artificial
noise design for OFDM wiretap channels with discrete channel inputs. We first
prove that the secrecy rate function for discrete channel inputs is nonconcave
with respect to the transmission power. To resolve the corresponding nonconvex
secrecy rate maximization problem, we develop a low-complexity power allocation
algorithm, which yields a duality gap diminishing in the order of
O(1/\sqrt{N}), where N is the number of subcarriers of OFDM. We then show that
independent frequency-domain artificial noise cannot improve the secrecy rate
of single-antenna wiretap channels. Towards this end, we propose a novel
time-domain artificial noise design which exploits temporal degrees of freedom
provided by the cyclic prefix of OFDM systems {to jam the eavesdropper and
boost the secrecy rate even with a single antenna at the transmitter}.
Numerical results are provided to illustrate the performance of the proposed
design schemes.Comment: 12 pages, 7 figures, accepted by IEEE Transactions on Wireless
Communications, Jan. 201
Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
We study non-asymptotic fundamental limits for transmitting classical
information over memoryless quantum channels, i.e. we investigate the amount of
classical information that can be transmitted when a quantum channel is used a
finite number of times and a fixed, non-vanishing average error is permissible.
We consider the classical capacity of quantum channels that are image-additive,
including all classical to quantum channels, as well as the product state
capacity of arbitrary quantum channels. In both cases we show that the
non-asymptotic fundamental limit admits a second-order approximation that
illustrates the speed at which the rate of optimal codes converges to the
Holevo capacity as the blocklength tends to infinity. The behavior is governed
by a new channel parameter, called channel dispersion, for which we provide a
geometrical interpretation.Comment: v2: main results significantly generalized and improved; v3: extended
to image-additive channels, change of title, journal versio
Unified Capacity Limit of Non-coherent Wideband Fading Channels
In non-coherent wideband fading channels where energy rather than spectrum is
the limiting resource, peaky and non-peaky signaling schemes have long been
considered species apart, as the first approaches asymptotically the capacity
of a wideband AWGN channel with the same average SNR, whereas the second
reaches a peak rate at some finite critical bandwidth and then falls to zero as
bandwidth grows to infinity. In this paper it is shown that this distinction is
in fact an artifact of the limited attention paid in the past to the product
between the bandwidth and the fraction of time it is in use. This fundamental
quantity, called bandwidth occupancy, measures average bandwidth usage over
time. For all signaling schemes with the same bandwidth occupancy, achievable
rates approach to the wideband AWGN capacity within the same gap as the
bandwidth occupancy approaches its critical value, and decrease to zero as the
occupancy goes to infinity. This unified analysis produces quantitative
closed-form expressions for the ideal bandwidth occupancy, recovers the
existing capacity results for (non-)peaky signaling schemes, and unveils a
trade-off between the accuracy of approximating capacity with a generalized
Taylor polynomial and the accuracy with which the optimal bandwidth occupancy
can be bounded.Comment: Accepted for publication in IEEE Transactions on Wireless
Communications. Copyright may be transferred without notic
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
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