5,739 research outputs found
The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents
We consider the secret key generation problem when sources are randomly
excited by the sender and there is a noiseless public discussion channel. Our
setting is thus similar to recent works on channels with action-dependent
states where the channel state may be influenced by some of the parties
involved. We derive single-letter expressions for the secret key capacity
through a type of source emulation analysis. We also derive lower bounds on the
achievable reliability and secrecy exponents, i.e., the exponential rates of
decay of the probability of decoding error and of the information leakage.
These exponents allow us to determine a set of strongly-achievable secret key
rates. For degraded eavesdroppers the maximum strongly-achievable rate equals
the secret key capacity; our exponents can also be specialized to previously
known results.
In deriving our strong achievability results we introduce a coding scheme
that combines wiretap coding (to excite the channel) and key extraction (to
distill keys from residual randomness). The secret key capacity is naturally
seen to be a combination of both source- and channel-type randomness. Through
examples we illustrate a fundamental interplay between the portion of the
secret key rate due to each type of randomness. We also illustrate inherent
tradeoffs between the achievable reliability and secrecy exponents. Our new
scheme also naturally accommodates rate limits on the public discussion. We
show that under rate constraints we are able to achieve larger rates than those
that can be attained through a pure source emulation strategy.Comment: 18 pages, 8 figures; Submitted to the IEEE Transactions on
Information Theory; Revised in Oct 201
Rank Minimization over Finite Fields: Fundamental Limits and Coding-Theoretic Interpretations
This paper establishes information-theoretic limits in estimating a finite
field low-rank matrix given random linear measurements of it. These linear
measurements are obtained by taking inner products of the low-rank matrix with
random sensing matrices. Necessary and sufficient conditions on the number of
measurements required are provided. It is shown that these conditions are sharp
and the minimum-rank decoder is asymptotically optimal. The reliability
function of this decoder is also derived by appealing to de Caen's lower bound
on the probability of a union. The sufficient condition also holds when the
sensing matrices are sparse - a scenario that may be amenable to efficient
decoding. More precisely, it is shown that if the n\times n-sensing matrices
contain, on average, \Omega(nlog n) entries, the number of measurements
required is the same as that when the sensing matrices are dense and contain
entries drawn uniformly at random from the field. Analogies are drawn between
the above results and rank-metric codes in the coding theory literature. In
fact, we are also strongly motivated by understanding when minimum rank
distance decoding of random rank-metric codes succeeds. To this end, we derive
distance properties of equiprobable and sparse rank-metric codes. These
distance properties provide a precise geometric interpretation of the fact that
the sparse ensemble requires as few measurements as the dense one. Finally, we
provide a non-exhaustive procedure to search for the unknown low-rank matrix.Comment: Accepted to the IEEE Transactions on Information Theory; Presented at
IEEE International Symposium on Information Theory (ISIT) 201
Chiral Properties of Pseudoscalar Mesons on a Quenched Lattice with Overlap Fermions
The chiral properties of the pseudoscalar mesons are studied numerically on a
quenched lattice with the overlap fermion. We elucidate the role of the
zero modes in the meson propagators, particularly that of the pseudoscalar
meson. The non-perturbative renormalization constant is determined from
the axial Ward identity and is found to be almost independent of the quark mass
for the range of quark masses we study; this implies that the error is
small. The pion decay constant, , is calculated from which we
determine the lattice spacing to be 0.148 fm. We look for quenched chiral log
in the pseudoscalar decay constants and the pseudoscalar masses and we find
clear evidence for its presence. The chiral log parameter is
determined to be in the range 0.15 -- 0.4 which is consistent with that
predicted from quenched chiral perturbation theory.Comment: Version accepted for publication by PRD. A few minor typographical
errors have been corrected. 24 pages, 11 figure
Pion Decay Constant, and Chiral Log from Overlap Fermions
We report our calculation of the pion decay constant , the axial
renormalization constant , and the quenched chiral logarithms from the
overlap fermions. The calculation is done on a quenched lattice at
fm using tree level tadpole improved gauge action. The smallest pion
mass we reach is about 280 MeV. The lattice size is about 4 times the Compton
wavelength of the lowest mass pion.Comment: Lattice2001(Hadronic Matrix Elements), 3pages, 5figure
The First Fox Days, 1956-1969
The First Fox Days, 1956-1969 is a small book outlining the origins of Rollins College\u27s Fox Day, a day for the whole college family to spend time together. It includes a short history of Fox Days, a chronology of how it has changed over the years up to 1969, and copies of Rollins College President Hugh F. McKean\u27s proclamations to the student body for Fox Day.https://scholarship.rollins.edu/archv_books/1011/thumbnail.jp
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