6,735 research outputs found
Channel Capacity under General Nonuniform Sampling
This paper develops the fundamental capacity limits of a sampled analog
channel under a sub-Nyquist sampling rate constraint. In particular, we derive
the capacity of sampled analog channels over a general class of time-preserving
sampling methods including irregular nonuniform sampling. Our results indicate
that the optimal sampling structures extract out the set of frequencies that
exhibits the highest SNR among all spectral sets of support size equal to the
sampling rate. The capacity under sub-Nyquist sampling can be attained through
filter-bank sampling, or through a single branch of modulation and filtering
followed by uniform sampling. The capacity under sub-Nyquist sampling is a
monotone function of the sampling rate. These results indicate that the optimal
sampling schemes suppress aliasing, and that employing irregular nonuniform
sampling does not provide capacity gain over uniform sampling sets with
appropriate preprocessing for a large class of channels.Comment: 5 pages, to appear in IEEE International Symposium on Information
Theory (ISIT), 201
Channel Capacity under Sub-Nyquist Nonuniform Sampling
This paper investigates the effect of sub-Nyquist sampling upon the capacity
of an analog channel. The channel is assumed to be a linear time-invariant
Gaussian channel, where perfect channel knowledge is available at both the
transmitter and the receiver. We consider a general class of right-invertible
time-preserving sampling methods which include irregular nonuniform sampling,
and characterize in closed form the channel capacity achievable by this class
of sampling methods, under a sampling rate and power constraint. Our results
indicate that the optimal sampling structures extract out the set of
frequencies that exhibits the highest signal-to-noise ratio among all spectral
sets of measure equal to the sampling rate. This can be attained through
filterbank sampling with uniform sampling at each branch with possibly
different rates, or through a single branch of modulation and filtering
followed by uniform sampling. These results reveal that for a large class of
channels, employing irregular nonuniform sampling sets, while typically
complicated to realize, does not provide capacity gain over uniform sampling
sets with appropriate preprocessing. Our findings demonstrate that aliasing or
scrambling of spectral components does not provide capacity gain, which is in
contrast to the benefits obtained from random mixing in spectrum-blind
compressive sampling schemes.Comment: accepted to IEEE Transactions on Information Theory, 201
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and
geometric-based approaches to sampling are investigated. Some aspects of coding
and communication through a Gaussian channel are considered. In particular, a
constructive method to determine the quantizing dimension in Zador's theorem is
provided. A geometric version of Shannon's Second Theorem is introduced.
Applications to Pulse Code Modulation and Vector Quantization of Images are
addressed.Comment: 19 pages, submitted for publicatio
On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling
This paper investigates the information rate loss in analog channels when the
sampler is designed to operate independent of the instantaneous channel
occupancy. Specifically, a multiband linear time-invariant Gaussian channel
under universal sub-Nyquist sampling is considered. The entire channel
bandwidth is divided into subbands of equal bandwidth. At each time only
constant-gain subbands are active, where the instantaneous subband
occupancy is not known at the receiver and the sampler. We study the
information loss through a capacity loss metric, that is, the capacity gap
caused by the lack of instantaneous subband occupancy information. We
characterize the minimax capacity loss for the entire sub-Nyquist rate regime,
provided that the number of subbands and the SNR are both large. The
minimax limits depend almost solely on the band sparsity factor and the
undersampling factor, modulo some residual terms that vanish as and SNR
grow. Our results highlight the power of randomized sampling methods (i.e. the
samplers that consist of random periodic modulation and low-pass filters),
which are able to approach the minimax capacity loss with exponentially high
probability.Comment: accepted to IEEE Transactions on Information Theory. It has been
presented in part at the IEEE International Symposium on Information Theory
(ISIT) 201
High-resolution distributed sampling of bandlimited fields with low-precision sensors
The problem of sampling a discrete-time sequence of spatially bandlimited
fields with a bounded dynamic range, in a distributed,
communication-constrained, processing environment is addressed. A central unit,
having access to the data gathered by a dense network of fixed-precision
sensors, operating under stringent inter-node communication constraints, is
required to reconstruct the field snapshots to maximum accuracy. Both
deterministic and stochastic field models are considered. For stochastic
fields, results are established in the almost-sure sense. The feasibility of
having a flexible tradeoff between the oversampling rate (sensor density) and
the analog-to-digital converter (ADC) precision, while achieving an exponential
accuracy in the number of bits per Nyquist-interval per snapshot is
demonstrated. This exposes an underlying ``conservation of bits'' principle:
the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed
along the amplitude axis (sensor-precision) and space (sensor density) in an
almost arbitrary discrete-valued manner, while retaining the same (exponential)
distortion-rate characteristics. Achievable information scaling laws for field
reconstruction over a bounded region are also derived: With N one-bit sensors
per Nyquist-interval, Nyquist-intervals, and total network
bitrate (per-sensor bitrate ), the maximum pointwise distortion goes to zero as
or . This is shown to be possible
with only nearest-neighbor communication, distributed coding, and appropriate
interpolation algorithms. For a fixed, nonzero target distortion, the number of
fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal
Processing and re-submitted to the IEEE Transactions on Information Theor
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