6,430 research outputs found
On the Usefulness of Predicates
Motivated by the pervasiveness of strong inapproximability results for
Max-CSPs, we introduce a relaxed notion of an approximate solution of a
Max-CSP. In this relaxed version, loosely speaking, the algorithm is allowed to
replace the constraints of an instance by some other (possibly real-valued)
constraints, and then only needs to satisfy as many of the new constraints as
possible.
To be more precise, we introduce the following notion of a predicate
being \emph{useful} for a (real-valued) objective : given an almost
satisfiable Max- instance, there is an algorithm that beats a random
assignment on the corresponding Max- instance applied to the same sets of
literals. The standard notion of a nontrivial approximation algorithm for a
Max-CSP with predicate is exactly the same as saying that is useful for
itself.
We say that is useless if it is not useful for any . This turns out to
be equivalent to the following pseudo-randomness property: given an almost
satisfiable instance of Max- it is hard to find an assignment such that the
induced distribution on -bit strings defined by the instance is not
essentially uniform.
Under the Unique Games Conjecture, we give a complete and simple
characterization of useful Max-CSPs defined by a predicate: such a Max-CSP is
useless if and only if there is a pairwise independent distribution supported
on the satisfying assignments of the predicate. It is natural to also consider
the case when no negations are allowed in the CSP instance, and we derive a
similar complete characterization (under the UGC) there as well.
Finally, we also include some results and examples shedding additional light
on the approximability of certain Max-CSPs
Feedforward data-aided phase noise estimation from a DCT basis expansion
This contribution deals with phase noise estimation from pilot symbols. The phase noise process is approximated by an expansion of discrete cosine transform (DCT) basis functions containing only a few terms. We propose a feedforward algorithm that estimates the DCT coefficients without requiring detailed knowledge about the phase noise statistics. We demonstrate that the resulting (linearized) mean-square phase estimation error consists of two contributions: a contribution from the additive noise, that equals the Cramer-Rao lower bound, and a noise independent contribution, that results front the phase noise modeling error. We investigate the effect of the symbol sequence length, the pilot symbol positions, the number of pilot symbols, and the number of estimated DCT coefficients it the estimation accuracy and on the corresponding bit error rate (PER). We propose a pilot symbol configuration allowing to estimate any number of DCT coefficients not exceeding the number of pilot Symbols, providing a considerable Performance improvement as compared to other pilot symbol configurations. For large block sizes, the DCT-based estimation algorithm substantially outperforms algorithms that estimate only the time-average or the linear trend of the carrier phase. Copyright (C) 2009 J. Bhatti and M. Moeneclaey
Fusing Censored Dependent Data for Distributed Detection
In this paper, we consider a distributed detection problem for a censoring
sensor network where each sensor's communication rate is significantly reduced
by transmitting only "informative" observations to the Fusion Center (FC), and
censoring those deemed "uninformative". While the independence of data from
censoring sensors is often assumed in previous research, we explore spatial
dependence among observations. Our focus is on designing the fusion rule under
the Neyman-Pearson (NP) framework that takes into account the spatial
dependence among observations. Two transmission scenarios are considered, one
where uncensored observations are transmitted directly to the FC and second
where they are first quantized and then transmitted to further improve
transmission efficiency. Copula-based Generalized Likelihood Ratio Test (GLRT)
for censored data is proposed with both continuous and discrete messages
received at the FC corresponding to different transmission strategies. We
address the computational issues of the copula-based GLRTs involving
multidimensional integrals by presenting more efficient fusion rules, based on
the key idea of injecting controlled noise at the FC before fusion. Although,
the signal-to-noise ratio (SNR) is reduced by introducing controlled noise at
the receiver, simulation results demonstrate that the resulting noise-aided
fusion approach based on adding artificial noise performs very closely to the
exact copula-based GLRTs. Copula-based GLRTs and their noise-aided counterparts
by exploiting the spatial dependence greatly improve detection performance
compared with the fusion rule under independence assumption
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