196 research outputs found
Time Localization and Capacity of Faster-Than-Nyquist Signaling
In this paper, we consider communication over the bandwidth limited analog
white Gaussian noise channel using non-orthogonal pulses. In particular, we
consider non-orthogonal transmission by signaling samples at a rate higher than
the Nyquist rate. Using the faster-than-Nyquist (FTN) framework, Mazo showed
that one may transmit symbols carried by sinc pulses at a higher rate than that
dictated by Nyquist without loosing bit error rate. However, as we will show in
this paper, such pulses are not necessarily well localized in time. In fact,
assuming that signals in the FTN framework are well localized in time, one can
construct a signaling scheme that violates the Shannon capacity bound. We also
show directly that FTN signals are in general not well localized in time.
Therefore, the results of Mazo do not imply that one can transmit more data per
time unit without degrading performance in terms of error probability.
We also consider FTN signaling in the case of pulses that are different from
the sinc pulses. We show that one can use a precoding scheme of low complexity
to remove the inter-symbol interference. This leads to the possibility of
increasing the number of transmitted samples per time unit and compensate for
spectral inefficiency due to signaling at the Nyquist rate of the non sinc
pulses. We demonstrate the power of the precoding scheme by simulations
Estimating ensemble flows on a hidden Markov chain
We propose a new framework to estimate the evolution of an ensemble of
indistinguishable agents on a hidden Markov chain using only aggregate output
data. This work can be viewed as an extension of the recent developments in
optimal mass transport and Schr\"odinger bridges to the finite state space
hidden Markov chain setting. The flow of the ensemble is estimated by solving a
maximum likelihood problem, which has a convex formulation at the
infinite-particle limit, and we develop a fast numerical algorithm for it. We
illustrate in two numerical examples how this framework can be used to track
the flow of identical and indistinguishable dynamical systems.Comment: 8 pages, 4 figure
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