133 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
Distillation protocols for Fourier states in quantum computing
Fourier states are multi-qubit registers that facilitate phase rotations in
fault-tolerant quantum computing. We propose distillation protocols for
constructing the fundamental, -qubit Fourier state with error at
a cost of Toffoli gates and Clifford gates, or any arbitrary
Fourier state using gates. We analyze these protocols with methods
from digital signal processing. These results suggest that phase kickback,
which uses Fourier states, could be the current lowest-overhead method for
generating arbitrary phase rotations.Comment: 18 pages, 4 figure
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