400 research outputs found
Optimization-Based Linear Network Coding for General Connections of Continuous Flows
For general connections, the problem of finding network codes and optimizing
resources for those codes is intrinsically difficult and little is known about
its complexity. Most of the existing solutions rely on very restricted classes
of network codes in terms of the number of flows allowed to be coded together,
and are not entirely distributed. In this paper, we consider a new method for
constructing linear network codes for general connections of continuous flows
to minimize the total cost of edge use based on mixing. We first formulate the
minimumcost network coding design problem. To solve the optimization problem,
we propose two equivalent alternative formulations with discrete mixing and
continuous mixing, respectively, and develop distributed algorithms to solve
them. Our approach allows fairly general coding across flows and guarantees no
greater cost than any solution without network coding.Comment: 1 fig, technical report of ICC 201
The large deviation principle for the On/Off Weibull Sojourn Process
This article proves that the on-off renewal process with Weibull sojourn times satisfies the large deviation principle on a non-linear scale. Unusually, its rate function is not convex. Apart from on a compact set, the rate function is infinite, which enables us to construct natural processes that satisfy the LDP with non-trivial rate functions on more than one time scale
Confident decoding with GRAND
We establish that during the execution of any Guessing Random Additive Noise
Decoding (GRAND) algorithm, an interpretable, useful measure of decoding
confidence can be evaluated. This measure takes the form of a log-likelihood
ratio (LLR) of the hypotheses that, should a decoding be found by a given
query, the decoding is correct versus its being incorrect. That LLR can be used
as soft output for a range of applications and we demonstrate its utility by
showing that it can be used to confidently discard likely erroneous decodings
in favor of returning more readily managed erasures. As an application, we show
that feature can be used to compromise the physical layer security of short
length wiretap codes by accurately and confidently revealing a proportion of a
communication when code-rate is above capacity
Guessing a password over a wireless channel (on the effect of noise non-uniformity)
A string is sent over a noisy channel that erases some of its characters.
Knowing the statistical properties of the string's source and which characters
were erased, a listener that is equipped with an ability to test the veracity
of a string, one string at a time, wishes to fill in the missing pieces. Here
we characterize the influence of the stochastic properties of both the string's
source and the noise on the channel on the distribution of the number of
attempts required to identify the string, its guesswork. In particular, we
establish that the average noise on the channel is not a determining factor for
the average guesswork and illustrate simple settings where one recipient with,
on average, a better channel than another recipient, has higher average
guesswork. These results stand in contrast to those for the capacity of wiretap
channels and suggest the use of techniques such as friendly jamming with
pseudo-random sequences to exploit this guesswork behavior.Comment: Asilomar Conference on Signals, Systems & Computers, 201
Logarithmic asymptotics for unserved messages at a FIFO
We consider an infinite{buffered single server First In, First Out (FIFO) queue. Messages
arrives at stochastic intervals and take random amounts of time to process. Logarithmic
asymptotics are proved for the tail of the distribution of the number of messages
awaiting service, under general large deviation and stability assumptions, and formulae
presented for the asymptotic decay rate
Tail asymptotics for busy periods
The busy period for a queue is cast as the area swept under the random walk
until it first returns to zero, . Encompassing non-i.i.d. increments, the
large-deviations asymptotics of is addressed, under the assumption that the
increments satisfy standard conditions, including a negative drift. The main
conclusions provide insight on the probability of a large busy period, and the
manner in which this occurs:
I) The scaled probability of a large busy period has the asymptote, for any
, \lim_{n\to\infty} \frac{1}{\sqrt{n}} \log P(B\geq bn) = -K\sqrt{b},
\hbox{where} \quad K = 2 \sqrt{-\int_0^{\lambda^*} \Lambda(\theta) d\theta},
\quad \hbox{with ,} and with
denoting the scaled cumulant generating function of the increments
process.
II) The most likely path to a large swept area is found to be a simple
rescaling of the path on given by, [\psi^*(t) =
-\Lambda(\lambda^*(1-t))/\lambda^*.] In contrast to the piecewise linear most
likely path leading the random walk to hit a high level, this is strictly
concave in general. While these two most likely paths have very different
forms, their derivatives coincide at the start of their trajectories, and at
their first return to zero.
These results partially answer an open problem of Kulick and Palmowski
regarding the tail of the work done during a busy period at a single server
queue. The paper concludes with applications of these results to the estimation
of the busy period statistics based on observations of the
increments, offering the possibility of estimating the likelihood of a large
busy period in advance of observing one.Comment: 15 pages, 5 figure
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