2,491 research outputs found
Energy and Sampling Constrained Asynchronous Communication
The minimum energy, and, more generally, the minimum cost, to transmit one
bit of information has been recently derived for bursty communication when
information is available infrequently at random times at the transmitter. This
result assumes that the receiver is always in the listening mode and samples
all channel outputs until it makes a decision. If the receiver is constrained
to sample only a fraction f>0 of the channel outputs, what is the cost penalty
due to sparse output sampling?
Remarkably, there is no penalty: regardless of f>0 the asynchronous capacity
per unit cost is the same as under full sampling, ie, when f=1. There is not
even a penalty in terms of decoding delay---the elapsed time between when
information is available until when it is decoded. This latter result relies on
the possibility to sample adaptively; the next sample can be chosen as a
function of past samples. Under non-adaptive sampling, it is possible to
achieve the full sampling asynchronous capacity per unit cost, but the decoding
delay gets multiplied by 1/f. Therefore adaptive sampling strategies are of
particular interest in the very sparse sampling regime.Comment: Submitted to the IEEE Transactions on Information Theor
Quantum Entanglement Capacity with Classical Feedback
For any quantum discrete memoryless channel, we define a quantity called
quantum entanglement capacity with classical feedback (), and we show that
this quantity lies between two other well-studied quantities. These two
quantities - namely the quantum capacity assisted by two-way classical
communication () and the quantum capacity with classical feedback ()
- are widely conjectured to be different: there exists quantum discrete
memoryless channel for which . We then present a general scheme to
convert any quantum error-correcting codes into adaptive protocols for this
newly-defined quantity of the quantum depolarizing channel, and illustrate with
Cat (repetition) code and Shor code. We contrast the present notion with
entanglement purification protocols by showing that whilst the Leung-Shor
protocol can be applied directly, recurrence methods need to be supplemented
with other techniques but at the same time offer a way to improve the
aforementioned Cat code. For the quantum depolarizing channel, we prove a
formula that gives lower bounds on the quantum capacity with classical feedback
from any protocols. We then apply this formula to the protocols
that we discuss to obtain new lower bounds on the quantum capacity with
classical feedback of the quantum depolarizing channel
Constellation Optimization in the Presence of Strong Phase Noise
In this paper, we address the problem of optimizing signal constellations for
strong phase noise. The problem is investigated by considering three
optimization formulations, which provide an analytical framework for
constellation design. In the first formulation, we seek to design
constellations that minimize the symbol error probability (SEP) for an
approximate ML detector in the presence of phase noise. In the second
formulation, we optimize constellations in terms of mutual information (MI) for
the effective discrete channel consisting of phase noise, additive white
Gaussian noise, and the approximate ML detector. To this end, we derive the MI
of this discrete channel. Finally, we optimize constellations in terms of the
MI for the phase noise channel. We give two analytical characterizations of the
MI of this channel, which are shown to be accurate for a wide range of
signal-to-noise ratios and phase noise variances. For each formulation, we
present a detailed analysis of the optimal constellations and their performance
in the presence of strong phase noise. We show that the optimal constellations
significantly outperform conventional constellations and those proposed in the
literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor
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