39,485 research outputs found
Information Spectrum Approach to the Source Channel Separation Theorem
A source-channel separation theorem for a general channel has recently been
shown by Aggrawal et. al. This theorem states that if there exist a coding
scheme that achieves a maximum distortion level d_{max} over a general channel
W, then reliable communication can be accomplished over this channel at rates
less then R(d_{max}), where R(.) is the rate distortion function of the source.
The source, however, is essentially constrained to be discrete and memoryless
(DMS). In this work we prove a stronger claim where the source is general,
satisfying only a "sphere packing optimality" feature, and the channel is
completely general. Furthermore, we show that if the channel satisfies the
strong converse property as define by Han & verdu, then the same statement can
be made with d_{avg}, the average distortion level, replacing d_{max}. Unlike
the proofs there, we use information spectrum methods to prove the statements
and the results can be quite easily extended to other situations
Source Broadcasting to the Masses: Separation has a Bounded Loss
This work discusses the source broadcasting problem, i.e. transmitting a
source to many receivers via a broadcast channel. The optimal rate-distortion
region for this problem is unknown. The separation approach divides the problem
into two complementary problems: source successive refinement and broadcast
channel transmission. We provide bounds on the loss incorporated by applying
time-sharing and separation in source broadcasting. If the broadcast channel is
degraded, it turns out that separation-based time-sharing achieves at least a
factor of the joint source-channel optimal rate, and this factor has a positive
limit even if the number of receivers increases to infinity. For the AWGN
broadcast channel a better bound is introduced, implying that all achievable
joint source-channel schemes have a rate within one bit of the separation-based
achievable rate region for two receivers, or within bits for
receivers
Linear-Codes-Based Lossless Joint Source-Channel Coding for Multiple-Access Channels
A general lossless joint source-channel coding (JSCC) scheme based on linear
codes and random interleavers for multiple-access channels (MACs) is presented
and then analyzed in this paper. By the information-spectrum approach and the
code-spectrum approach, it is shown that a linear code with a good joint
spectrum can be used to establish limit-approaching lossless JSCC schemes for
correlated general sources and general MACs, where the joint spectrum is a
generalization of the input-output weight distribution. Some properties of
linear codes with good joint spectra are investigated. A formula on the
"distance" property of linear codes with good joint spectra is derived, based
on which, it is further proved that, the rate of any systematic codes with good
joint spectra cannot be larger than the reciprocal of the corresponding
alphabet cardinality, and any sparse generator matrices cannot yield linear
codes with good joint spectra. The problem of designing arbitrary rate coding
schemes is also discussed. A novel idea called "generalized puncturing" is
proposed, which makes it possible that one good low-rate linear code is enough
for the design of coding schemes with multiple rates. Finally, various coding
problems of MACs are reviewed in a unified framework established by the
code-spectrum approach, under which, criteria and candidates of good linear
codes in terms of spectrum requirements for such problems are clearly
presented.Comment: 18 pages, 3 figure
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
The effect of point sources on satellite observations of the cosmic microwave background
We study the effect of extragalactic point sources on satellite observations
of the cosmic microwave background (CMB). In order to separate the
contributions due to different foreground components, a maximum-entropy method
is applied to simulated observations by the Planck Surveyor satellite. In
addition to point sources, the simulations include emission from the CMB and
the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy clusters,
as well as Galactic dust, free-free and synchrotron emission. We find that the
main input components are faithfully recovered and, in particular, that the
quality of the CMB reconstruction is only slightly reduced by the presence of
point sources. In addition, we find that it is possible to recover accurate
point source catalogues at each of the Planck Surveyor observing frequencies.Comment: 12 pages, 9 figures, submitted to MNRA
Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability
In this paper the conditions for identifiability, separability and uniqueness
of linear complex valued independent component analysis (ICA) models are
established. These results extend the well-known conditions for solving
real-valued ICA problems to complex-valued models. Relevant properties of
complex random vectors are described in order to extend the Darmois-Skitovich
theorem for complex-valued models. This theorem is used to construct a proof of
a theorem for each of the above ICA model concepts. Both circular and
noncircular complex random vectors are covered. Examples clarifying the above
concepts are presented.Comment: To appear in IEEE TR-IT March 200
Eigen-Inference for Energy Estimation of Multiple Sources
In this paper, a new method is introduced to blindly estimate the transmit
power of multiple signal sources in multi-antenna fading channels, when the
number of sensing devices and the number of available samples are sufficiently
large compared to the number of sources. Recent advances in the field of large
dimensional random matrix theory are used that result in a simple and
computationally efficient consistent estimator of the power of each source. A
criterion to determine the minimum number of sensors and the minimum number of
samples required to achieve source separation is then introduced. Simulations
are performed that corroborate the theoretical claims and show that the
proposed power estimator largely outperforms alternative power inference
techniques.Comment: to appear in IEEE Trans. on Information Theory, 17 pages, 13 figure
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