1,026 research outputs found
M. Chiani, D. Dardari, and M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, no. 4, pp. 840 – 845, Jul. 2003.
M. Chiani, D. Dardari, and M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, no. 4, pp. 840 – 845, Jul. 2003.
On the probability that all eigenvalues of Gaussian, Wishart, and double Wishart random matrices lie within an interval
We derive the probability that all eigenvalues of a random matrix lie
within an arbitrary interval ,
, when is a real or complex finite dimensional Wishart,
double Wishart, or Gaussian symmetric/Hermitian matrix. We give efficient
recursive formulas allowing the exact evaluation of for Wishart
matrices, even with large number of variates and degrees of freedom. We also
prove that the probability that all eigenvalues are within the limiting
spectral support (given by the Mar{\v{c}}enko-Pastur or the semicircle laws)
tends for large dimensions to the universal values and for
the real and complex cases, respectively. Applications include improved bounds
for the probability that a Gaussian measurement matrix has a given restricted
isometry constant in compressed sensing.Comment: IEEE Transactions on Information Theory, 201
Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance
Let denote two independent real Gaussian and matrices with , each constituted by zero mean i.i.d. columns with
common covariance. The Roy's largest root criterion, used in multivariate
analysis of variance (MANOVA), is based on the statistic of the largest
eigenvalue, , of , where
and are independent central Wishart matrices. We derive a new
expression and efficient recursive formulas for the exact distribution of
. The expression can be easily calculated even for large parameters,
eliminating the need of pre-calculated tables for the application of the Roy's
test
M. Chiani “Introducing erasures in decision-feedback equalization to reduce error propagation,” IEEE Trans. Commun., vol. 45, no. 7, pp. 757–760, Jul. 1997.
Improving the Forward Link of the Future Airport Data Link by Space-Time Coding
In the context of the future communication system
for the airport surface operations (AeroMACS), we investigate
the 2×1 Alamouti scheme applied to the 802.16e standard for improving
the performance of the forward link. We propose a novel
space-time coding realization which preserves the original frame
structure of WiMAX, analyzing its performance in a realistic
airport environment. Simulation results show the performance
of the system over different scenarios
Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes
In this paper, a simple, general-purpose and effective tool for the design of
low-density parity-check (LDPC) codes for iterative correction of bursts of
erasures is presented. The design method consists in starting from the
parity-check matrix of an LDPC code and developing an optimized parity-check
matrix, with the same performance on the memory-less erasure channel, and
suitable also for the iterative correction of single bursts of erasures. The
parity-check matrix optimization is performed by an algorithm called pivot
searching and swapping (PSS) algorithm, which executes permutations of
carefully chosen columns of the parity-check matrix, after a local analysis of
particular variable nodes called stopping set pivots. This algorithm can be in
principle applied to any LDPC code. If the input parity-check matrix is
designed for achieving good performance on the memory-less erasure channel,
then the code obtained after the application of the PSS algorithm provides good
joint correction of independent erasures and single erasure bursts. Numerical
results are provided in order to show the effectiveness of the PSS algorithm
when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted
(submitted in Feb. 2007
Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices
One of the key issues in the acquisition of sparse data by means of
compressed sensing (CS) is the design of the measurement matrix. Gaussian
matrices have been proven to be information-theoretically optimal in terms of
minimizing the required number of measurements for sparse recovery. In this
paper we provide a new approach for the analysis of the restricted isometry
constant (RIC) of finite dimensional Gaussian measurement matrices. The
proposed method relies on the exact distributions of the extreme eigenvalues
for Wishart matrices. First, we derive the probability that the restricted
isometry property is satisfied for a given sufficient recovery condition on the
RIC, and propose a probabilistic framework to study both the symmetric and
asymmetric RICs. Then, we analyze the recovery of compressible signals in noise
through the statistical characterization of stability and robustness. The
presented framework determines limits on various sparse recovery algorithms for
finite size problems. In particular, it provides a tight lower bound on the
maximum sparsity order of the acquired data allowing signal recovery with a
given target probability. Also, we derive simple approximations for the RICs
based on the Tracy-Widom distribution.Comment: 11 pages, 6 figures, accepted for publication in IEEE transactions on
information theor
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