83 research outputs found
Limit Theorems in Hidden Markov Models
In this paper, under mild assumptions, we derive a law of large numbers, a
central limit theorem with an error estimate, an almost sure invariance
principle and a variant of Chernoff bound in finite-state hidden Markov models.
These limit theorems are of interest in certain ares in statistics and
information theory. Particularly, we apply the limit theorems to derive the
rate of convergence of the maximum likelihood estimator in finite-state hidden
Markov models.Comment: 35 page
Generalized PSK in Space Time Coding
A wireless communication system using multiple antennas promises reliable
transmission under Rayleigh flat fading assumptions. Design criteria and
practical schemes have been presented for both coherent and non-coherent
communication channels. In this paper we generalize one dimensional phase shift
keying (PSK) signals and introduce space time constellations from generalized
phase shift keying (GPSK) signals based on the complex and real orthogonal
designs. The resulting space time constellations reallocate the energy for each
transmitting antenna and feature good diversity products, consequently their
performances are better than some of the existing comparable codes. Moreover
since the maximum likelihood (ML) decoding of our proposed codes can be
decomposed to one dimensional PSK signal demodulation, the ML decoding of our
codes can be implemented in a very efficient way.Comment: 22 pages, 3 figures, submitted to IEEE transactions on communicaton
On Continuous-Time Gaussian Channels
A continuous-time white Gaussian channel can be formulated using a white
Gaussian noise, and a conventional way for examining such a channel is the
sampling approach based on the Shannon-Nyquist sampling theorem, where the
original continuous-time channel is converted to an equivalent discrete-time
channel, to which a great variety of established tools and methodology can be
applied. However, one of the key issues of this scheme is that continuous-time
feedback and memory cannot be incorporated into the channel model. It turns out
that this issue can be circumvented by considering the Brownian motion
formulation of a continuous-time white Gaussian channel. Nevertheless, as
opposed to the white Gaussian noise formulation, a link that establishes the
information-theoretic connection between a continuous-time channel under the
Brownian motion formulation and its discrete-time counterparts has long been
missing. This paper is to fill this gap by establishing causality-preserving
connections between continuous-time Gaussian feedback/memory channels and their
associated discrete-time versions in the forms of sampling and approximation
theorems, which we believe will play important roles in the long run for
further developing continuous-time information theory.
As an immediate application of the approximation theorem, we propose the
so-called approximation approach to examine continuous-time white Gaussian
channels in the point-to-point or multi-user setting. It turns out that the
approximation approach, complemented by relevant tools from stochastic
calculus, can enhance our understanding of continuous-time Gaussian channels in
terms of giving alternative and strengthened interpretation to some long-held
folklore, recovering "long known" results from new perspectives, and rigorously
establishing new results predicted by the intuition that the approximation
approach carries
Concavity of Mutual Information Rate for Input-Restricted Finite-State Memoryless Channels at High SNR
We consider a finite-state memoryless channel with i.i.d. channel state and
the input Markov process supported on a mixing finite-type constraint. We
discuss the asymptotic behavior of entropy rate of the output hidden Markov
chain and deduce that the mutual information rate of such a channel is concave
with respect to the parameters of the input Markov processes at high
signal-to-noise ratio. In principle, the concavity result enables good
numerical approximation of the maximum mutual information rate and capacity of
such a channel.Comment: 26 page
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