801 research outputs found
Density Evolution for Asymmetric Memoryless Channels
Density evolution is one of the most powerful analytical tools for
low-density parity-check (LDPC) codes and graph codes with message passing
decoding algorithms. With channel symmetry as one of its fundamental
assumptions, density evolution (DE) has been widely and successfully applied to
different channels, including binary erasure channels, binary symmetric
channels, binary additive white Gaussian noise channels, etc. This paper
generalizes density evolution for non-symmetric memoryless channels, which in
turn broadens the applications to general memoryless channels, e.g. z-channels,
composite white Gaussian noise channels, etc. The central theorem underpinning
this generalization is the convergence to perfect projection for any fixed size
supporting tree. A new iterative formula of the same complexity is then
presented and the necessary theorems for the performance concentration theorems
are developed. Several properties of the new density evolution method are
explored, including stability results for general asymmetric memoryless
channels. Simulations, code optimizations, and possible new applications
suggested by this new density evolution method are also provided. This result
is also used to prove the typicality of linear LDPC codes among the coset code
ensemble when the minimum check node degree is sufficiently large. It is shown
that the convergence to perfect projection is essential to the belief
propagation algorithm even when only symmetric channels are considered. Hence
the proof of the convergence to perfect projection serves also as a completion
of the theory of classical density evolution for symmetric memoryless channels.Comment: To appear in the IEEE Transactions on Information Theor
A Bit of Secrecy for Gaussian Source Compression
In this paper, the compression of an independent and identically distributed
Gaussian source sequence is studied in an unsecure network. Within a game
theoretic setting for a three-party noiseless communication network (sender
Alice, legitimate receiver Bob, and eavesdropper Eve), the problem of how to
efficiently compress a Gaussian source with limited secret key in order to
guarantee that Bob can reconstruct with high fidelity while preventing Eve from
estimating an accurate reconstruction is investigated. It is assumed that Alice
and Bob share a secret key with limited rate. Three scenarios are studied, in
which the eavesdropper ranges from weak to strong in terms of the causal side
information she has. It is shown that one bit of secret key per source symbol
is enough to achieve perfect secrecy performance in the Gaussian squared error
setting, and the information theoretic region is not optimized by joint
Gaussian random variables
A Rate-Distortion Based Secrecy System with Side Information at the Decoders
A secrecy system with side information at the decoders is studied in the
context of lossy source compression over a noiseless broadcast channel. The
decoders have access to different side information sequences that are
correlated with the source. The fidelity of the communication to the legitimate
receiver is measured by a distortion metric, as is traditionally done in the
Wyner-Ziv problem. The secrecy performance of the system is also evaluated
under a distortion metric. An achievable rate-distortion region is derived for
the general case of arbitrarily correlated side information. Exact bounds are
obtained for several special cases in which the side information satisfies
certain constraints. An example is considered in which the side information
sequences come from a binary erasure channel and a binary symmetric channel.Comment: 8 pages. Allerton 201
A Non-Cooperative Power Control Game in Delay-Constrained Multiple-Access Networks
A game-theoretic approach for studying power control in multiple-access
networks with transmission delay constraints is proposed. A non-cooperative
power control game is considered in which each user seeks to choose a transmit
power that maximizes its own utility while satisfying the user's delay
requirements. The utility function measures the number of reliable bits
transmitted per joule of energy and the user's delay constraint is modeled as
an upper bound on the delay outage probability. The Nash equilibrium for the
proposed game is derived, and its existence and uniqueness are proved. Using a
large-system analysis, explicit expressions for the utilities achieved at
equilibrium are obtained for the matched filter, decorrelating and minimum mean
square error multiuser detectors. The effects of delay constraints on the
users' utilities (in bits/Joule) and network capacity (i.e., the maximum number
of users that can be supported) are quantified.Comment: To apprear in the proceedings of the 2005 IEEE International
Symposium on Information Theory, Adelaide, Australia, September 4-9, 200
The Likelihood Encoder for Lossy Source Compression
In this work, a likelihood encoder is studied in the context of lossy source
compression. The analysis of the likelihood encoder is based on a soft-covering
lemma. It is demonstrated that the use of a likelihood encoder together with
the soft-covering lemma gives alternative achievability proofs for classical
source coding problems. The case of the rate-distortion function with side
information at the decoder (i.e. the Wyner-Ziv problem) is carefully examined
and an application of the likelihood encoder to the multi-terminal source
coding inner bound (i.e. the Berger-Tung region) is outlined.Comment: 5 pages, 2 figures, ISIT 201
The Likelihood Encoder for Lossy Compression
A likelihood encoder is studied in the context of lossy source compression.
The analysis of the likelihood encoder is based on the soft-covering lemma. It
is demonstrated that the use of a likelihood encoder together with the
soft-covering lemma yields simple achievability proofs for classical source
coding problems. The cases of the point-to-point rate-distortion function, the
rate-distortion function with side information at the decoder (i.e. the
Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the
Berger-Tung problem) are examined in this paper. Furthermore, a non-asymptotic
analysis is used for the point-to-point case to examine the upper bound on the
excess distortion provided by this method. The likelihood encoder is also
related to a recent alternative technique using properties of random binning
Energy-Efficient Resource Allocation in Wireless Networks: An Overview of Game-Theoretic Approaches
An overview of game-theoretic approaches to energy-efficient resource
allocation in wireless networks is presented. Focusing on multiple-access
networks, it is demonstrated that game theory can be used as an effective tool
to study resource allocation in wireless networks with quality-of-service (QoS)
constraints. A family of non-cooperative (distributed) games is presented in
which each user seeks to choose a strategy that maximizes its own utility while
satisfying its QoS requirements. The utility function considered here measures
the number of reliable bits that are transmitted per joule of energy consumed
and, hence, is particulary suitable for energy-constrained networks. The
actions available to each user in trying to maximize its own utility are at
least the choice of the transmit power and, depending on the situation, the
user may also be able to choose its transmission rate, modulation, packet size,
multiuser receiver, multi-antenna processing algorithm, or carrier allocation
strategy. The best-response strategy and Nash equilibrium for each game is
presented. Using this game-theoretic framework, the effects of power control,
rate control, modulation, temporal and spatial signal processing, carrier
allocation strategy and delay QoS constraints on energy efficiency and network
capacity are quantified.Comment: To appear in the IEEE Signal Processing Magazine: Special Issue on
Resource-Constrained Signal Processing, Communications and Networking, May
200
Joint Source-Channel Secrecy Using Hybrid Coding
The secrecy performance of a source-channel model is studied in the context
of lossy source compression over a noisy broadcast channel. The source is
causally revealed to the eavesdropper during decoding. The fidelity of the
transmission to the legitimate receiver and the secrecy performance at the
eavesdropper are both measured by a distortion metric. Two achievability
schemes using the technique of hybrid coding are analyzed and compared with an
operationally separate source-channel coding scheme. A numerical example is
provided and the comparison results show that the hybrid coding schemes
outperform the operationally separate scheme.Comment: 5 pages, 1 figure, ISIT 201
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