8,523 research outputs found
An efficient CDMA decoder for correlated information sources
We consider the detection of correlated information sources in the ubiquitous
Code-Division Multiple-Access (CDMA) scheme. We propose a message-passing based
scheme for detecting correlated sources directly, with no need for source
coding. The detection is done simultaneously over a block of transmitted binary
symbols (word). Simulation results are provided demonstrating a substantial
improvement in bit-error-rate in comparison with the unmodified detector and
the alternative of source compression. The robustness of the error-performance
improvement is shown under practical model settings, including wrong estimation
of the generating Markov transition matrix and finite-length spreading codes.Comment: 11 page
Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes
The focus of this work is on local stability of a class of nonlinear ordinary
differential equations (ODE) that describe limits of empirical measures
associated with finite-state weakly interacting N-particle systems. Local
Lyapunov functions are identified for several classes of such ODE, including
those associated with systems with slow adaptation and Gibbs systems. Using
results from [5] and large deviations heuristics, a partial differential
equation (PDE) associated with the nonlinear ODE is introduced and it is shown
that positive definite subsolutions of this PDE serve as local Lyapunov
functions for the ODE. This PDE characterization is used to construct explicit
Lyapunov functions for a broad class of models called locally Gibbs systems.
This class of models is significantly larger than the family of Gibbs systems
and several examples of such systems are presented, including models with
nearest neighbor jumps and models with simultaneous jumps that arise in
applications.Comment: Updated to include Acknowledgement
Limits of relative entropies associated with weakly interacting particle systems
The limits of scaled relative entropies between probability distributions
associated with N-particle weakly interacting Markov processes are considered.
The convergence of such scaled relative entropies is established in various
settings. The analysis is motivated by the role relative entropy plays as a
Lyapunov function for the (linear) Kolmogorov forward equation associated with
an ergodic Markov process, and Lyapunov function properties of these scaling
limits with respect to nonlinear finite-state Markov processes are studied in
the companion paper [6]
Reduction of Markov Chains using a Value-of-Information-Based Approach
In this paper, we propose an approach to obtain reduced-order models of
Markov chains. Our approach is composed of two information-theoretic processes.
The first is a means of comparing pairs of stationary chains on different state
spaces, which is done via the negative Kullback-Leibler divergence defined on a
model joint space. Model reduction is achieved by solving a
value-of-information criterion with respect to this divergence. Optimizing the
criterion leads to a probabilistic partitioning of the states in the high-order
Markov chain. A single free parameter that emerges through the optimization
process dictates both the partition uncertainty and the number of state groups.
We provide a data-driven means of choosing the `optimal' value of this free
parameter, which sidesteps needing to a priori know the number of state groups
in an arbitrary chain.Comment: Submitted to Entrop
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