28,602 research outputs found
Secure Compute-and-Forward in a Bidirectional Relay
We consider the basic bidirectional relaying problem, in which two users in a
wireless network wish to exchange messages through an intermediate relay node.
In the compute-and-forward strategy, the relay computes a function of the two
messages using the naturally-occurring sum of symbols simultaneously
transmitted by user nodes in a Gaussian multiple access (MAC) channel, and the
computed function value is forwarded to the user nodes in an ensuing broadcast
phase. In this paper, we study the problem under an additional security
constraint, which requires that each user's message be kept secure from the
relay. We consider two types of security constraints: perfect secrecy, in which
the MAC channel output seen by the relay is independent of each user's message;
and strong secrecy, which is a form of asymptotic independence. We propose a
coding scheme based on nested lattices, the main feature of which is that given
a pair of nested lattices that satisfy certain "goodness" properties, we can
explicitly specify probability distributions for randomization at the encoders
to achieve the desired security criteria. In particular, our coding scheme
guarantees perfect or strong secrecy even in the absence of channel noise. The
noise in the channel only affects reliability of computation at the relay, and
for Gaussian noise, we derive achievable rates for reliable and secure
computation. We also present an application of our methods to the multi-hop
line network in which a source needs to transmit messages to a destination
through a series of intermediate relays.Comment: v1 is a much expanded and updated version of arXiv:1204.6350; v2 is a
minor revision to fix some notational issues; v3 is a much expanded and
updated version of v2, and contains results on both perfect secrecy and
strong secrecy; v3 is a revised manuscript submitted to the IEEE Transactions
on Information Theory in April 201
Convolutional compressed sensing using deterministic sequences
This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain
Insertion and deletion tolerance of point processes
We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the original process. This condition and the related notion of deletion-tolerance are extensions of the so-called finite energy condition for discrete random processes. We prove several equivalent formulations of each condition, including versions involving Palm processes. Certain other seemingly natural variants of the conditions turn out not to be equivalent. We illustrate the concepts in the context of a number of examples, including Gaussian zero processes and randomly perturbed lattices, and we provide applications to continuum percolation and stable matching
A CLT for a band matrix model
A law of large numbers and a central limit theorem are derived for linear
statistics of random symmetric matrices whose on-or-above diagonal entries are
independent, but neither necessarily identically distributed, nor necessarily
all of the same variance. The derivation is based on systematic combinatorial
enumeration, study of generating functions, and concentration inequalities of
the Poincare type. Special cases treated, with an explicit evaluation of
limiting variances, are generalized Wigner and Wishart matrices.Comment: To appear, Prob. Theory Rel. Field
Spectral statistics of large dimensional Spearman's rank correlation matrix and its application
Let be a random vector drawn from the uniform
distribution on the set of all permutations of . Let
, where is the mean zero variance one random
variable obtained by centralizing and normalizing , . Assume
that are i.i.d. copies of
and is the random matrix
with as its th row. Then is called the
Spearman's rank correlation matrix which can be regarded as a high dimensional
extension of the classical nonparametric statistic Spearman's rank correlation
coefficient between two independent random variables. In this paper, we
establish a CLT for the linear spectral statistics of this nonparametric random
matrix model in the scenario of high dimension, namely, and as . We propose a novel evaluation scheme to
estimate the core quantity in Anderson and Zeitouni's cumulant method in [Ann.
Statist. 36 (2008) 2553-2576] to bypass the so-called joint cumulant
summability. In addition, we raise a two-step comparison approach to obtain the
explicit formulae for the mean and covariance functions in the CLT. Relying on
this CLT, we then construct a distribution-free statistic to test complete
independence for components of random vectors. Owing to the nonparametric
property, we can use this test on generally distributed random variables
including the heavy-tailed ones.Comment: Published at http://dx.doi.org/10.1214/15-AOS1353 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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