4 research outputs found
Relations between Information and Estimation in Discrete-Time L\'evy Channels
Fundamental relations between information and estimation have been
established in the literature for the discrete-time Gaussian and Poisson
channels. In this work, we demonstrate that such relations hold for a much
larger class of observation models. We introduce the natural family of
discrete-time L\'evy channels where the distribution of the output conditioned
on the input is infinitely divisible. For L\'evy channels, we establish new
representations relating the mutual information between the channel input and
output to an optimal expected estimation loss, thereby unifying and
considerably extending results from the Gaussian and Poisson settings. We
demonstrate the richness of our results by working out two examples of L\'evy
channels, namely the gamma channel and the negative binomial channel, with
corresponding relations between information and estimation. Extensions to the
setting of mismatched estimation are also presented
Extensions of the I-MMSE Relation
Unveiling a fundamental link between information theory and estimation
theory, the I-MMSE relation by Guo, Shamai and Verdu~\cite{gu05}, together with
its numerous extensions, has great theoretical significance and various
practical applications. On the other hand, its influences to date have been
restricted to channels without feedback or memory, due to the absence of its
extensions to such channels. In this paper, we propose extensions of the I-MMSE
relation to discrete-time and continuous-time Gaussian channels with feedback
and/or memory. Our approach is based on a very simple observation, which can be
applied to other scenarios, such as a simple and direct proof of the classical
de Bruijn's identity.Comment: 35 pages. arXiv admin note: text overlap with arXiv:1401.352
A Cram\'er-Rao Type Bound for Bayesian Risk with Bregman Loss
A general class of Bayesian lower bounds when the underlying loss function is
a Bregman divergence is demonstrated. This class can be considered as an
extension of the Weinstein--Weiss family of bounds for the mean squared error
and relies on finding a variational characterization of Bayesian risk. The
approach allows for the derivation of a version of the Cram\'er--Rao bound that
is specific to a given Bregman divergence. The new generalization of the
Cram\'er--Rao bound reduces to the classical one when the loss function is
taken to be the Euclidean norm. The effectiveness of the new bound is evaluated
in the Poisson noise setting and the Binomial noise setting.Comment: This version contains some new example
A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends
Multiple antennas have been exploited for spatial multiplexing and diversity
transmission in a wide range of communication applications. However, most of
the advances in the design of high speed wireless multiple-input multiple
output (MIMO) systems are based on information-theoretic principles that
demonstrate how to efficiently transmit signals conforming to Gaussian
distribution. Although the Gaussian signal is capacity-achieving, signals
conforming to discrete constellations are transmitted in practical
communication systems. As a result, this paper is motivated to provide a
comprehensive overview on MIMO transmission design with discrete input signals.
We first summarize the existing fundamental results for MIMO systems with
discrete input signals. Then, focusing on the basic point-to-point MIMO
systems, we examine transmission schemes based on three most important criteria
for communication systems: the mutual information driven designs, the mean
square error driven designs, and the diversity driven designs. Particularly, a
unified framework which designs low complexity transmission schemes applicable
to massive MIMO systems in upcoming 5G wireless networks is provided in the
first time. Moreover, adaptive transmission designs which switch among these
criteria based on the channel conditions to formulate the best transmission
strategy are discussed. Then, we provide a survey of the transmission designs
with discrete input signals for multiuser MIMO scenarios, including MIMO uplink
transmission, MIMO downlink transmission, MIMO interference channel, and MIMO
wiretap channel. Additionally, we discuss the transmission designs with
discrete input signals for other systems using MIMO technology. Finally,
technical challenges which remain unresolved at the time of writing are
summarized and the future trends of transmission designs with discrete input
signals are addressed.Comment: 110 pages, 512 references, submit to Proceedings of the IEE