1,054 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
Expurgated Bounds for the Asymmetric Broadcast Channel
This work contains two main contributions concerning the expurgation of
hierarchical ensembles for the asymmetric broadcast channel. The first is an
analysis of the optimal maximum likelihood (ML) decoders for the weak and
strong user. Two different methods of code expurgation will be used, that will
provide two competing error exponents. The second is the derivation of
expurgated exponents under the generalized stochastic likelihood decoder (GLD).
We prove that the GLD exponents are at least as tight as the maximum between
the random coding error exponents derived in an earlier work by Averbuch and
Merhav (2017) and one of our ML-based expurgated exponents. By that, we
actually prove the existence of hierarchical codebooks that achieve the best of
the random coding exponent and the expurgated exponent simultaneously for both
users
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
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