1,201 research outputs found
Partial Strong Converse for the Non-Degraded Wiretap Channel
We prove the partial strong converse property for the discrete memoryless
\emph{non-degraded} wiretap channel, for which we require the leakage to the
eavesdropper to vanish but allow an asymptotic error probability to the legitimate receiver. We show that when the transmission rate is
above the secrecy capacity, the probability of correct decoding at the
legitimate receiver decays to zero exponentially. Therefore, the maximum
transmission rate is the same for , and the partial strong
converse property holds. Our work is inspired by a recently developed technique
based on information spectrum method and Chernoff-Cramer bound for evaluating
the exponent of the probability of correct decoding
The invalidity of a strong capacity for a quantum channel with memory
The strong capacity of a particular channel can be interpreted as a sharp
limit on the amount of information which can be transmitted reliably over that
channel. To evaluate the strong capacity of a particular channel one must prove
both the direct part of the channel coding theorem and the strong converse for
the channel. Here we consider the strong converse theorem for the periodic
quantum channel and show some rather surprising results. We first show that the
strong converse does not hold in general for this channel and therefore the
channel does not have a strong capacity. Instead, we find that there is a scale
of capacities corresponding to error probabilities between integer multiples of
the inverse of the periodicity of the channel. A similar scale also exists for
the random channel.Comment: 7 pages, double column. Comments welcome. Repeated equation removed
and one reference adde
Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities
This monograph presents a unified treatment of single- and multi-user
problems in Shannon's information theory where we depart from the requirement
that the error probability decays asymptotically in the blocklength. Instead,
the error probabilities for various problems are bounded above by a
non-vanishing constant and the spotlight is shone on achievable coding rates as
functions of the growing blocklengths. This represents the study of asymptotic
estimates with non-vanishing error probabilities.
In Part I, after reviewing the fundamentals of information theory, we discuss
Strassen's seminal result for binary hypothesis testing where the type-I error
probability is non-vanishing and the rate of decay of the type-II error
probability with growing number of independent observations is characterized.
In Part II, we use this basic hypothesis testing result to develop second- and
sometimes, even third-order asymptotic expansions for point-to-point
communication. Finally in Part III, we consider network information theory
problems for which the second-order asymptotics are known. These problems
include some classes of channels with random state, the multiple-encoder
distributed lossless source coding (Slepian-Wolf) problem and special cases of
the Gaussian interference and multiple-access channels. Finally, we discuss
avenues for further research.Comment: Further comments welcom
Second-Order Coding Rates for Channels with State
We study the performance limits of state-dependent discrete memoryless
channels with a discrete state available at both the encoder and the decoder.
We establish the epsilon-capacity as well as necessary and sufficient
conditions for the strong converse property for such channels when the sequence
of channel states is not necessarily stationary, memoryless or ergodic. We then
seek a finer characterization of these capacities in terms of second-order
coding rates. The general results are supplemented by several examples
including i.i.d. and Markov states and mixed channels
Strong Converse Theorems for Classes of Multimessage Multicast Networks: A R\'enyi Divergence Approach
This paper establishes that the strong converse holds for some classes of
discrete memoryless multimessage multicast networks (DM-MMNs) whose
corresponding cut-set bounds are tight, i.e., coincide with the set of
achievable rate tuples. The strong converse for these classes of DM-MMNs
implies that all sequences of codes with rate tuples belonging to the exterior
of the cut-set bound have average error probabilities that necessarily tend to
one (and are not simply bounded away from zero). Examples in the classes of
DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent
discrete memoryless channels (DMCs) as well as single-destination DM-MMNs
consisting of independent DMCs with destination feedback. Our elementary proof
technique leverages properties of the R\'enyi divergence.Comment: Submitted to IEEE Transactions on Information Theory, Jul 18, 2014.
Revised on Jul 31, 201
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