47,438 research outputs found
Evaluation of the distance spectrum of variable-length finite-state codes
International audienceThe class of variable-length finite-state joint source-channel codes is defined and a polynomial complexity algorithm for the evaluation of their distance spectrum presented. Issues in truncating the spectrum to a finite number of (possibly approximate) terms are discussed and illustrated by experimental results
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
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
Fundamental Finite Key Limits for One-Way Information Reconciliation in Quantum Key Distribution
The security of quantum key distribution protocols is guaranteed by the laws
of quantum mechanics. However, a precise analysis of the security properties
requires tools from both classical cryptography and information theory. Here,
we employ recent results in non-asymptotic classical information theory to show
that one-way information reconciliation imposes fundamental limitations on the
amount of secret key that can be extracted in the finite key regime. In
particular, we find that an often used approximation for the information
leakage during information reconciliation is not generally valid. We propose an
improved approximation that takes into account finite key effects and
numerically test it against codes for two probability distributions, that we
call binary-binary and binary-Gaussian, that typically appear in quantum key
distribution protocols
New binary and ternary LCD codes
LCD codes are linear codes with important cryptographic applications.
Recently, a method has been presented to transform any linear code into an LCD
code with the same parameters when it is supported on a finite field with
cardinality larger than 3. Hence, the study of LCD codes is mainly open for
binary and ternary fields. Subfield-subcodes of -affine variety codes are a
generalization of BCH codes which have been successfully used for constructing
good quantum codes. We describe binary and ternary LCD codes constructed as
subfield-subcodes of -affine variety codes and provide some new and good LCD
codes coming from this construction
A Unified Framework for Linear-Programming Based Communication Receivers
It is shown that a large class of communication systems which admit a
sum-product algorithm (SPA) based receiver also admit a corresponding
linear-programming (LP) based receiver. The two receivers have a relationship
defined by the local structure of the underlying graphical model, and are
inhibited by the same phenomenon, which we call 'pseudoconfigurations'. This
concept is a generalization of the concept of 'pseudocodewords' for linear
codes. It is proved that the LP receiver has the 'maximum likelihood
certificate' property, and that the receiver output is the lowest cost
pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and
linear-programming pseudoconfigurations is also proved. A concept of 'system
pseudodistance' is defined which generalizes the existing concept of
pseudodistance for binary and nonbinary linear codes. It is demonstrated how
the LP design technique may be applied to the problem of joint equalization and
decoding of coded transmissions over a frequency selective channel, and a
simulation-based analysis of the error events of the resulting LP receiver is
also provided. For this particular application, the proposed LP receiver is
shown to be competitive with other receivers, and to be capable of
outperforming turbo equalization in bit and frame error rate performance.Comment: 13 pages, 6 figures. To appear in the IEEE Transactions on
Communication
A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels
This paper shows that the logarithm of the epsilon-error capacity (average
error probability) for n uses of a discrete memoryless channel is upper bounded
by the normal approximation plus a third-order term that does not exceed 1/2
log n + O(1) if the epsilon-dispersion of the channel is positive. This matches
a lower bound by Y. Polyanskiy (2010) for discrete memoryless channels with
positive reverse dispersion. If the epsilon-dispersion vanishes, the logarithm
of the epsilon-error capacity is upper bounded by the n times the capacity plus
a constant term except for a small class of DMCs and epsilon >= 1/2.Comment: published versio
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