10 research outputs found
Strong Converse and Second-Order Asymptotics of Channel Resolvability
We study the problem of channel resolvability for fixed i.i.d. input
distributions and discrete memoryless channels (DMCs), and derive the strong
converse theorem for any DMCs that are not necessarily full rank. We also
derive the optimal second-order rate under a condition. Furthermore, under the
condition that a DMC has the unique capacity achieving input distribution, we
derive the optimal second-order rate of channel resolvability for the worst
input distribution.Comment: 7 pages, a shorter version will appear in ISIT 2014, this version
includes the proofs of technical lemmas in appendice
MAC Resolvability: First And Second Order Results
Building upon previous work on the relation between secrecy and channel
resolvability, we revisit a secrecy proof for the multiple-access channel from
the perspective of resolvability. We then refine the approach in order to
obtain some novel results on the second-order achievable rates.Comment: Slightly extended version of the paper accepted at the 4th Workshop
on Physical-Layer Methods for Wireless Security during IEEE CNS 2017. v2:
Fixed typos and extended literature section in accordance with reviewers'
recommendation
Resolvability on Continuous Alphabets
We characterize the resolvability region for a large class of point-to-point
channels with continuous alphabets. In our direct result, we prove not only the
existence of good resolvability codebooks, but adapt an approach based on the
Chernoff-Hoeffding bound to the continuous case showing that the probability of
drawing an unsuitable codebook is doubly exponentially small. For the converse
part, we show that our previous elementary result carries over to the
continuous case easily under some mild continuity assumption.Comment: v2: Corrected inaccuracies in proof of direct part. Statement of
Theorem 3 slightly adapted; other results unchanged v3: Extended version of
camera ready version submitted to ISIT 201
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects
Smoothing of binary codes, uniform distributions, and applications
The action of a noise operator on a code transforms it into a distribution on
the respective space. Some common examples from information theory include
Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting
on a lattice in the Euclidean space. We aim to characterize the cases when the
output distribution is close to the uniform distribution on the space, as
measured by R{\'e}nyi divergence of order . A version of
this question is known as the channel resolvability problem in information
theory, and it has implications for security guarantees in wiretap channels,
error correction, discrepancy, worst-to-average case complexity reductions, and
many other problems.
Our work quantifies the requirements for asymptotic uniformity (perfect
smoothing) and identifies explicit code families that achieve it under the
action of the Bernoulli and ball noise operators on the code. We derive
expressions for the minimum rate of codes required to attain asymptotically
perfect smoothing. In proving our results, we leverage recent results from
harmonic analysis of functions on the Hamming space. Another result pertains to
the use of code families in Wyner's transmission scheme on the binary wiretap
channel. We identify explicit families that guarantee strong secrecy when
applied in this scheme, showing that nested Reed-Muller codes can transmit
messages reliably and securely over a binary symmetric wiretap channel with a
positive rate. Finally, we establish a connection between smoothing and error
correction in the binary symmetric channel
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