310 research outputs found
On Communication through a Gaussian Channel with an MMSE Disturbance Constraint
This paper considers a Gaussian channel with one transmitter and two
receivers. The goal is to maximize the communication rate at the
intended/primary receiver subject to a disturbance constraint at the
unintended/secondary receiver. The disturbance is measured in terms of minimum
mean square error (MMSE) of the interference that the transmission to the
primary receiver inflicts on the secondary receiver.
The paper presents a new upper bound for the problem of maximizing the mutual
information subject to an MMSE constraint. The new bound holds for vector
inputs of any length and recovers a previously known limiting (when the length
of vector input tends to infinity) expression from the work of Bustin
The key technical novelty is a new upper bound on the MMSE.
This bound allows one to bound the MMSE for all signal-to-noise ratio (SNR)
values a certain SNR at which the MMSE is known (which
corresponds to the disturbance constraint). This bound complements the
`single-crossing point property' of the MMSE that upper bounds the MMSE for all
SNR values a certain value at which the MMSE value is known.
The MMSE upper bound provides a refined characterization of the
phase-transition phenomenon which manifests, in the limit as the length of the
vector input goes to infinity, as a discontinuity of the MMSE for the problem
at hand.
For vector inputs of size , a matching lower bound, to within an
additive gap of order (where
is the disturbance constraint), is shown by means of the mixed
inputs technique recently introduced by Dytso Comment: Submitted to IEEE Transactions on Information Theor
On the Minimum Mean -th Error in Gaussian Noise Channels and its Applications
The problem of estimating an arbitrary random vector from its observation
corrupted by additive white Gaussian noise, where the cost function is taken to
be the Minimum Mean -th Error (MMPE), is considered. The classical Minimum
Mean Square Error (MMSE) is a special case of the MMPE. Several bounds,
properties and applications of the MMPE are derived and discussed. The optimal
MMPE estimator is found for Gaussian and binary input distributions. Properties
of the MMPE as a function of the input distribution, SNR and order are
derived. In particular, it is shown that the MMPE is a continuous function of
and SNR. These results are possible in view of interpolation and change of
measure bounds on the MMPE. The `Single-Crossing-Point Property' (SCPP) that
bounds the MMSE for all SNR values {\it above} a certain value, at which the
MMSE is known, together with the I-MMSE relationship is a powerful tool in
deriving converse proofs in information theory. By studying the notion of
conditional MMPE, a unifying proof (i.e., for any ) of the SCPP is shown. A
complementary bound to the SCPP is then shown, which bounds the MMPE for all
SNR values {\it below} a certain value, at which the MMPE is known. As a first
application of the MMPE, a bound on the conditional differential entropy in
terms of the MMPE is provided, which then yields a generalization of the
Ozarow-Wyner lower bound on the mutual information achieved by a discrete input
on a Gaussian noise channel. As a second application, the MMPE is shown to
improve on previous characterizations of the phase transition phenomenon that
manifests, in the limit as the length of the capacity achieving code goes to
infinity, as a discontinuity of the MMSE as a function of SNR. As a final
application, the MMPE is used to show bounds on the second derivative of mutual
information, that tighten previously known bounds
Asynchronous CDMA Systems with Random Spreading-Part II: Design Criteria
Totally asynchronous code-division multiple-access (CDMA) systems are
addressed. In Part I, the fundamental limits of asynchronous CDMA systems are
analyzed in terms of spectral efficiency and SINR at the output of the optimum
linear detector. The focus of Part II is the design of low-complexity
implementations of linear multiuser detectors in systems with many users that
admit a multistage representation, e.g. reduced rank multistage Wiener filters,
polynomial expansion detectors, weighted linear parallel interference
cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay
distribution on CDMA with suboptimum linear receiver structures are
investigated. Recursive expressions for universal weight design are given. The
performance in terms of SINR is derived in the large-system limit and the
performance improvement over synchronous systems is quantified. The
considerations distinguish between two ways of forming discrete-time
statistics: chip-matched filtering and oversampling
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted
clusters. It is widely employed as a canonical model to study clustering and
community detection, and provides generally a fertile ground to study the
statistical and computational tradeoffs that arise in network and data
sciences.
This note surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational thresholds, and for various recovery
requirements such as exact, partial and weak recovery (a.k.a., detection). The
main results discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial
recovery, the learning of the SBM parameters and the gap between
information-theoretic and computational thresholds.
The note also covers some of the algorithms developed in the quest of
achieving the limits, in particular two-round algorithms via graph-splitting,
semi-definite programming, linearized belief propagation, classical and
nonbacktracking spectral methods. A few open problems are also discussed
Wireless multiuser communication systems: diversity receiver performance analysis, GSMuD design, and fading channel simulator
Multipath fading phenomenon is central to the design and analysis of wireless communication systems including multiuser systems. If untreated, the fading will corrupt the transmitted signal and often cause performance degradations such as increased communication error and decreased data rate, as compared to wireline channels with little or no multipath fading. On the other hand, this multipath fading phenomenon, if fully utilized, can actually lead to system designs that provide additional gains in system performance as compared to systems that experience non-fading channels.;The central question this thesis tries to answer is how to design and analyze a wireless multiuser system that takes advantage of the benefits the diversity multipath fading channel provides. Two particular techniques are discussed and analyzed in the first part of the thesis: quadrature amplitude modulation (QAM) and diversity receivers, including maximal ratio combining (MRC) and generalized selection combining (GSC). We consider the practical case of imperfect channel estimation (ICE) and develop a new decision variable (DV) of MRC receiver output for M-QAM. By deriving its moment generating function (MGF), we obtain the exact bit error rate (BER) performance under arbitrary correlated Rayleigh and Rician channels, with ICE. GSC provides a tradeoff between receiver complexity and performance. We study the effect of ICE on the GSC output effective SNR under generalized fading channels and obtain the exact BER results for M-QAM systems. The significance of this part lies in that these results provide system designers means to evaluate how different practical channel estimators and their parameters can affect the system\u27s performance and help them distribute system resources that can most effectively improve performance.;In the second part of the thesis, we look at a new diversity technique unique to multiuser systems under multipath fading channels: the multiuser diversity. We devise a generalized selection multiuser diversity (GSMuD) scheme for the practical CDMA downlink systems, where users are selected for transmission based on their respective channel qualities. We include the effect of ICE in the design and analysis of GSMuD. Based on the marginal distribution of the ranked user signal-noise ratios (SNRs), we develop a practical adaptive modulation and coding (AMC) scheme and equal power allocation scheme and statistical optimal 1-D and 2-D power allocation schemes, to fully exploit the available multiuser diversity. We use the convex optimization procedures to obtain the 1-D and 2-D power allocation algorithms, which distribute the total system power in the waterfilling fashion alone the user (1-D) or both user and time (2-D) for the power-limited and energy-limited system respectively. We also propose a normalized SNR based GSMuD scheme where user access fairness issues are explicitly addressed. We address various fairness-related performance metrics such as the user\u27s average access probability (AAP), average access time (AAT), and average wait time (AWT) in the absolute- and normalized-SNR based GSMuD. These metrics are useful for system designers to determine parameters such as optimal packet size and delay constraints.;We observe that Nakakagami-m fading channel model is widely applied to model the real world multipath fading channels of different severity. In the last part of the thesis, we propose a Nakagami-m channel simulator that can generate accurate channel coefficients that follow the Nakagami-m model, with independent quadrature parts, accurate phase distribution and arbitrary auto-correlation property. We demonstrate that the proposed simulator can be extremely useful in simulations involving Nakagami-m fading channel models, evident from the numerous simulation results obtained in earlier parts of the thesis where the fading channel coefficients are generated using this proposed simulator
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