5 research outputs found
On the reliability exponent of the exponential timing channel
Cataloged from PDF version of article.We determine the reliability exponent E(R) of the Anantharam-Verdu exponential server timing channel with service rate p for all rates R between a critical rate R-c = (mu/4) log 2 and the channel capacity C = e(-1)mu. For rates between 0 and R-c, we provide a random-coding lower bound E,(R) and a sphere-packing upper bound E-r(R) on E(R). We also determine that the cutoff rate R-0 for this channel equals mu/4, thus answering a question posed by Sundaresan and Verdu. An interesting aspect of our results is that the lower bound E, (R) for the reliability exponent of the timing channel coincides with Wyner's reliability exponent for the photon-counting channel with no dark current and with peak power constraint mu. Whether the reliability exponents of the two channels are actually equal everywhere remains open. This shows that the exponential server timing channel is at least as reliable as this type of a photon-counting channel for all rates
Bits through queues with feedback
In their paper Anantharam and Verd\'u showed that feedback does not
increase the capacity of a queue when the service time is exponentially
distributed. Whether this conclusion holds for general service times has
remained an open question which this paper addresses.
Two main results are established for both the discrete-time and the
continuous-time models. First, a sufficient condition on the service
distribution for feedback to increase capacity under FIFO service policy.
Underlying this condition is a notion of weak feedback wherein instead of the
queue departure times the transmitter is informed about the instants when
packets start to be served. Second, a condition in terms of output entropy rate
under which feedback does not increase capacity. This condition is general in
that it depends on the output entropy rate of the queue but explicitly depends
neither on the queue policy nor on the service time distribution. This
condition is satisfied, for instance, by queues with LCFS service policies and
bounded service times
A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses
A judicious application of the Berry-Esseen theorem via suitable Augustin
information measures is demonstrated to be sufficient for deriving the sphere
packing bound with a prefactor that is
for all codes on certain
families of channels -- including the Gaussian channels and the non-stationary
Renyi symmetric channels -- and for the constant composition codes on
stationary memoryless channels. The resulting non-asymptotic bounds have
definite approximation error terms. As a preliminary result that might be of
interest on its own, the trade-off between type I and type II error
probabilities in the hypothesis testing problem with (possibly non-stationary)
independent samples is determined up to some multiplicative constants, assuming
that the probabilities of both types of error are decaying exponentially with
the number of samples, using the Berry-Esseen theorem.Comment: 20 page
Divergence Measures
Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures