2,313 research outputs found
Fixed-length lossy compression in the finite blocklength regime
This paper studies the minimum achievable source coding rate as a function of
blocklength and probability that the distortion exceeds a given
level . Tight general achievability and converse bounds are derived that
hold at arbitrary fixed blocklength. For stationary memoryless sources with
separable distortion, the minimum rate achievable is shown to be closely
approximated by , where
is the rate-distortion function, is the rate dispersion, a
characteristic of the source which measures its stochastic variability, and
is the inverse of the standard Gaussian complementary cdf
Secure Multiterminal Source Coding with Side Information at the Eavesdropper
The problem of secure multiterminal source coding with side information at
the eavesdropper is investigated. This scenario consists of a main encoder
(referred to as Alice) that wishes to compress a single source but
simultaneously satisfying the desired requirements on the distortion level at a
legitimate receiver (referred to as Bob) and the equivocation rate --average
uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed
the presence of a (public) rate-limited link between Alice and Bob. In this
setting, Eve perfectly observes the information bits sent by Alice to Bob and
has also access to a correlated source which can be used as side information. A
second encoder (referred to as Charlie) helps Bob in estimating Alice's source
by sending a compressed version of its own correlated observation via a
(private) rate-limited link, which is only observed by Bob. For instance, the
problem at hands can be seen as the unification between the Berger-Tung and the
secure source coding setups. Inner and outer bounds on the so called
rates-distortion-equivocation region are derived. The inner region turns to be
tight for two cases: (i) uncoded side information at Bob and (ii) lossless
reconstruction of both sources at Bob --secure distributed lossless
compression. Application examples to secure lossy source coding of Gaussian and
binary sources in the presence of Gaussian and binary/ternary (resp.) side
informations are also considered. Optimal coding schemes are characterized for
some cases of interest where the statistical differences between the side
information at the decoders and the presence of a non-zero distortion at Bob
can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table
Lossy joint source-channel coding in the finite blocklength regime
This paper finds new tight finite-blocklength bounds for the best achievable
lossy joint source-channel code rate, and demonstrates that joint
source-channel code design brings considerable performance advantage over a
separate one in the non-asymptotic regime. A joint source-channel code maps a
block of source symbols onto a length channel codeword, and the
fidelity of reproduction at the receiver end is measured by the probability
that the distortion exceeds a given threshold . For memoryless
sources and channels, it is demonstrated that the parameters of the best joint
source-channel code must satisfy , where and are the channel capacity and channel
dispersion, respectively; and are the source
rate-distortion and rate-dispersion functions; and is the standard Gaussian
complementary cdf. Symbol-by-symbol (uncoded) transmission is known to achieve
the Shannon limit when the source and channel satisfy a certain probabilistic
matching condition. In this paper we show that even when this condition is not
satisfied, symbol-by-symbol transmission is, in some cases, the best known
strategy in the non-asymptotic regime
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 Conditional Rate-Distortion
This paper characterizes the second-order coding rates for lossy source
coding with side information available at both the encoder and the decoder. We
first provide non-asymptotic bounds for this problem and then specialize the
non-asymptotic bounds for three different scenarios: discrete memoryless
sources, Gaussian sources, and Markov sources. We obtain the second-order
coding rates for these settings. It is interesting to observe that the
second-order coding rate for Gaussian source coding with Gaussian side
information available at both the encoder and the decoder is the same as that
for Gaussian source coding without side information. Furthermore, regardless of
the variance of the side information, the dispersion is nats squared per
source symbol.Comment: 20 pages, 2 figures, second-order coding rates, finite blocklength,
network information theor
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