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47
MIMO Broadcast Channels With FiniteRate Feedback
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has per ..."
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Cited by 183 (1 self)
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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The wellknown zeroforcing transmission technique is considered, and simple expressions for the throughput degradation due to finiterate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signaltonoise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to pointtopoint multipleinput multipleoutput (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR.
MIMO broadcast channels with finite rate feedback
 IEEE Trans. on Inform. Theory
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channe ..."
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Cited by 148 (10 self)
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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well known zero forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the SNR (in dB) in order to achieve the full multiplexing gain, which is in sharp contrast to pointtopoint MIMO systems in which it is not necessary to increase the feedback rate as a function of the SNR. I.
On some inequalities for the gamma and psi functions
 MATH. COMP
, 1997
"... We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) = ..."
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Cited by 78 (3 self)
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We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) =
OrderPreserving Encryption Revisited: Improved Security Analysis and Alternative Solutions
, 2011
"... We further the study of orderpreserving symmetric encryption (OPE), a primitive for allowing efficient range queries on encrypted data, recently initiated (from a cryptographic perspective) by Boldyreva et al. (Eurocrypt ’09). First, we address the open problem of characterizing what encryption via ..."
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Cited by 46 (1 self)
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We further the study of orderpreserving symmetric encryption (OPE), a primitive for allowing efficient range queries on encrypted data, recently initiated (from a cryptographic perspective) by Boldyreva et al. (Eurocrypt ’09). First, we address the open problem of characterizing what encryption via a random orderpreserving function (ROPF) leaks about underlying data (ROPF being the “ideal object ” in the security definition, POPF, satisfied by their scheme.) In particular, we show that, for a database of randomly distributed plaintexts and appropriate choice of parameters, ROPF encryption leaks neither the precise value of any plaintext nor the precise distance between any two of them. The analysis here introduces useful new techniques. On the other hand, we show that ROPF encryption leaks approximate value of any plaintext as well as approximate distance between any two plaintexts, each to an accuracy of about square root of the domain size. We then study schemes that are not orderpreserving, but which nevertheless allow efficient range queries and achieve security notions stronger than POPF. In a setting where the entire database is known in advance of keygeneration (considered in several prior works), we show that recent constructions of “monotone minimal perfect hash functions” allow to efficiently achieve (an adaptation of) the notion
A completely monotonic function involving divided differences of psi and polygamma functions and an application
 RGMIA Res. Rep. Coll
"... Abstract. A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of t ..."
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Cited by 37 (25 self)
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Abstract. A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in R n−1 and R n respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized. 1.
The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
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Cited by 27 (1 self)
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The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
ROBUST COMPUTATION OF LINEAR MODELS, OR HOW TO FIND A NEEDLE IN A HAYSTACK
"... Abstract. Consider a dataset of vectorvalued observations that consists of a modest number of noisy inliers, which are explained well by a lowdimensional subspace, along with a large number of outliers, which have no linear structure. This work describes a convex optimization problem, called reape ..."
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Cited by 18 (5 self)
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Abstract. Consider a dataset of vectorvalued observations that consists of a modest number of noisy inliers, which are explained well by a lowdimensional subspace, along with a large number of outliers, which have no linear structure. This work describes a convex optimization problem, called reaper, that can reliably fit a lowdimensional model to this type of data. The paper provides an efficient algorithm for solving the reaper problem, and it documents numerical experiments which confirm that reaper can dependably find linear structure in synthetic and natural data. In addition, when the inliers are contained in a lowdimensional subspace, there is a rigorous theory that describes when reaper can recover the subspace exactly. 1.
Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels
, 2009
"... We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Ra ..."
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Cited by 17 (0 self)
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We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2B i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (ratemaximizing) training and feedback overhead (T and B) as L and the number of transmit antennas Nt both become large. The optimal Nt is limited by the coherence time, and increases as L / logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1 / logNt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1 / log² Nt).
SOME PROPERTIES OF THE GAMMA AND PSI FUNCTIONS, WITH APPLICATIONS
"... Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some wellknown results for the volume Ωn of the unit ball B n ⊂ R n,thesu ..."
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Cited by 15 (0 self)
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Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some wellknown results for the volume Ωn of the unit ball B n ⊂ R n,thesurface area ωn−1 of the unit sphere S n−1, and some related constants. 1.
The extended mean values: definition, properties, monotonicities, comparison, convexities, generalizations, and applications
 No.1, Art.5. Available online at http://rgmia.vu.edu.au/v5n1.html
"... Abstract. The extended mean values E(r, s;x, y) play an important role in theory of mean values and theory of inequalities, and even in the whole mathematics, since many norms in mathematics are always means. Its study is not only interesting but important, both because most of the twovariable mea ..."
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Cited by 15 (14 self)
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Abstract. The extended mean values E(r, s;x, y) play an important role in theory of mean values and theory of inequalities, and even in the whole mathematics, since many norms in mathematics are always means. Its study is not only interesting but important, both because most of the twovariable mean values are special cases of E(r, s;x, y), and because it is challenging to study a function whose formulation is so indeterminate. In this expositive article, we summarize the recent main results about study of E(r, s;x, y), including definition, basic properties, monotonicities, comparison, logarithmic convexities, Schurconvexities, generalizations of concepts of mean values, applications to quantum, to theory of special functions, to establishment of Steffensen pairs, and to generalization of HermiteHadamard’s inequality. 1. Definition and expressions of the extended mean values The histories of mean values and inequalities are long [9]. The mean values are related to the Mean Value Theorems for derivative or for integral, which are the bridge between the local and global properties of functions. The arithmeticmeangeometricmean inequality is probably the most important inequality, and certainly a keystone of the theory of inequalities [2]. Inequalities of mean values are one of the main parts of theory of inequalities, they have explicit geometric meanings [14]. The theory of mean values plays an important role in the whole mathematics, since many norms in mathematics are always means. 1.1. Definition of the extended mean values. In 1975, the extended mean values E(r, s;x, y) were defined in [51] by K. B. Stolarsky as follows E(r, s;x, y) = r