319 research outputs found
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
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
High-Throughput Random Access via Codes on Graphs
Recently, contention resolution diversity slotted ALOHA (CRDSA) has been
introduced as a simple but effective improvement to slotted ALOHA. It relies on
MAC burst repetitions and on interference cancellation to increase the
normalized throughput of a classic slotted ALOHA access scheme. CRDSA allows
achieving a larger throughput than slotted ALOHA, at the price of an increased
average transmitted power. A way to trade-off the increment of the average
transmitted power and the improvement of the throughput is presented in this
paper. Specifically, it is proposed to divide each MAC burst in k sub-bursts,
and to encode them via a (n,k) erasure correcting code. The n encoded
sub-bursts are transmitted over the MAC channel, according to specific
time/frequency-hopping patterns. Whenever n-e>=k sub-bursts (of the same burst)
are received without collisions, erasure decoding allows recovering the
remaining e sub-bursts (which were lost due to collisions). An interference
cancellation process can then take place, removing in e slots the interference
caused by the e recovered sub-bursts, possibly allowing the correct decoding of
sub-bursts related to other bursts. The process is thus iterated as for the
CRDSA case.Comment: Presented at the Future Network and MobileSummit 2010 Conference,
Florence (Italy), June 201
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
Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access
In this paper, a random access scheme is introduced which relies on the
combination of packet erasure correcting codes and successive interference
cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph
representation of the SIC process, resembling iterative decoding of generalized
low-density parity-check codes over the erasure channel, is exploited to
optimize the selection probabilities of the component erasure correcting codes
via density evolution analysis. The capacity (in packets per slot) of the
scheme is then analyzed in the context of the collision channel without
feedback. Moreover, a capacity bound is developed and component code
distributions tightly approaching the bound are derived.Comment: The final version to appear in IEEE Trans. Inf. Theory. 18 pages, 10
figure
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