358 research outputs found
Generalization Bounds via Information Density and Conditional Information Density
We present a general approach, based on an exponential inequality, to derive
bounds on the generalization error of randomized learning algorithms. Using
this approach, we provide bounds on the average generalization error as well as
bounds on its tail probability, for both the PAC-Bayesian and single-draw
scenarios. Specifically, for the case of subgaussian loss functions, we obtain
novel bounds that depend on the information density between the training data
and the output hypothesis. When suitably weakened, these bounds recover many of
the information-theoretic available bounds in the literature. We also extend
the proposed exponential-inequality approach to the setting recently introduced
by Steinke and Zakynthinou (2020), where the learning algorithm depends on a
randomly selected subset of the available training data. For this setup, we
present bounds for bounded loss functions in terms of the conditional
information density between the output hypothesis and the random variable
determining the subset choice, given all training data. Through our approach,
we recover the average generalization bound presented by Steinke and
Zakynthinou (2020) and extend it to the PAC-Bayesian and single-draw scenarios.
For the single-draw scenario, we also obtain novel bounds in terms of the
conditional -mutual information and the conditional maximal leakage.Comment: Published in Journal on Selected Areas in Information Theory (JSAIT).
Important note: the proof of the data-dependent bounds provided in the paper
contains an error, which is rectified in the following document:
https://gdurisi.github.io/files/2021/jsait-correction.pd
High-SNR Capacity of Wireless Communication Channels in the Noncoherent Setting: A Primer
This paper, mostly tutorial in nature, deals with the problem of
characterizing the capacity of fading channels in the high signal-to-noise
ratio (SNR) regime. We focus on the practically relevant noncoherent setting,
where neither transmitter nor receiver know the channel realizations, but both
are aware of the channel law. We present, in an intuitive and accessible form,
two tools, first proposed by Lapidoth & Moser (2003), of fundamental importance
to high-SNR capacity analysis: the duality approach and the escape-to-infinity
property of capacity-achieving distributions. Furthermore, we apply these tools
to refine some of the results that appeared previously in the literature and to
simplify the corresponding proofs.Comment: To appear in Int. J. Electron. Commun. (AE\"U), Aug. 201
Bounds on the Per-Sample Capacity of Zero-Dispersion Simplified Fiber-Optical Channel Models
A number of simplified models, based on perturbation theory, have been
proposed for the fiber-optical channel and have been extensively used in the
literature. Although these models are mainly developed for the low-power
regime, they are used at moderate or high powers as well. It remains unclear to
what extent the capacity of these models is affected by the simplifying
assumptions under which they are derived. In this paper, we consider single
channel data transmission based on three continuous-time optical models i) a
regular perturbative channel, ii) a logarithmic perturbative channel, and iii)
the stochastic nonlinear Schr\"odinger (NLS) channel. We apply two simplifying
assumptions on these channels to obtain analytically tractable discrete-time
models. Namely, we neglect the channel memory (fiber dispersion) and we use a
sampling receiver. These assumptions bring into question the physical relevance
of the models studied in the paper. Therefore, the results should be viewed as
a first step toward analyzing more realistic channels. We investigate the
per-sample capacity of the simplified discrete-time models. Specifically, i) we
establish tight bounds on the capacity of the regular perturbative channel; ii)
we obtain the capacity of the logarithmic perturbative channel; and iii) we
present a novel upper bound on the capacity of the zero-dispersion NLS channel.
Our results illustrate that the capacity of these models departs from each
other at high powers because these models yield different capacity pre-logs.
Since all three models are based on the same physical channel, our results
highlight that care must be exercised in using simplified channel models in the
high-power regime
Analysis of Massive MIMO With Hardware Impairments and Different Channel Models
Massive Multiple-Input Multiple-Output (MIMO) is foreseen to be one of the
main technology components in next generation cellular communications (5G). In
this paper, fundamental limits on the performance of downlink massive MIMO
systems are investigated by means of simulations and analytical analysis.
Signal-to-noise-and-interference ratio (SINR) and sum rate for a single-cell
scenario multi-user MIMO are analyzed for different array sizes, channel
models, and precoding schemes. The impact of hardware impairments on
performance is also investigated. Simple approximations are derived that show
explicitly how the number of antennas, number of served users, transmit power,
and magnitude of hardware impairments affect performance.Comment: 5 pages, 5 figure
Improved Sparsity Thresholds Through Dictionary Splitting
Known sparsity thresholds for basis pursuit to deliver the maximally sparse
solution of the compressed sensing recovery problem typically depend on the
dictionary's coherence. While the coherence is easy to compute, it can lead to
rather pessimistic thresholds as it captures only limited information about the
dictionary. In this paper, we show that viewing the dictionary as the
concatenation of two general sub-dictionaries leads to provably better sparsity
thresholds--that are explicit in the coherence parameters of the dictionary and
of the individual sub-dictionaries. Equivalently, our results can be
interpreted as sparsity thresholds for dictionaries that are unions of two
general (i.e., not necessarily orthonormal) sub-dictionaries.Comment: IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct. 2009,
to appea
Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets
We present an uncertainty relation for the representation of signals in two
different general (possibly redundant or incomplete) signal sets. This
uncertainty relation is relevant for the analysis of signals containing two
distinct features each of which can be described sparsely in a suitable general
signal set. Furthermore, the new uncertainty relation is shown to lead to
improved sparsity thresholds for recovery of signals that are sparse in general
dictionaries. Specifically, our results improve on the well-known
-threshold for dictionaries with coherence by up to a factor of
two. Furthermore, we provide probabilistic recovery guarantees for pairs of
general dictionaries that also allow us to understand which parts of a general
dictionary one needs to randomize over to "weed out" the sparsity patterns that
prohibit breaking the square-root bottleneck.Comment: submitted to IEEE Trans. Inf. Theor
Minimum Energy to Send Bits Over Multiple-Antenna Fading Channels
This paper investigates the minimum energy required to transmit
information bits with a given reliability over a multiple-antenna Rayleigh
block-fading channel, with and without channel state information (CSI) at the
receiver. No feedback is assumed. It is well known that the ratio between the
minimum energy per bit and the noise level converges to dB as goes
to infinity, regardless of whether CSI is available at the receiver or not.
This paper shows that lack of CSI at the receiver causes a slowdown in the
speed of convergence to dB as compared to the case of
perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap
to dB is proportional to , whereas when perfect
CSI is available at the receiver, this gap is proportional to . In
both cases, the gap to dB is independent of the number of transmit
antennas and of the channel's coherence time. Numerically, we observe that,
when the receiver is equipped with a single antenna, to achieve an energy per
bit of dB in the no-CSI case, one needs to transmit at least information bits, whereas bits suffice for the case of
perfect CSI at the receiver
Capacity of Underspread Noncoherent WSSUS Fading Channels under Peak Signal Constraints
We characterize the capacity of the general class of noncoherent underspread
wide-sense stationary uncorrelated scattering (WSSUS) time-frequency-selective
Rayleigh fading channels, under peak constraints in time and frequency and in
time only. Capacity upper and lower bounds are found which are explicit in the
channel's scattering function and allow to identify the capacity-maximizing
bandwidth for a given scattering function and a given peak-to-average power
ratio.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2007, Nice, Franc
On the capacity of the block-memoryless phase-noise channel
Bounds are presented on the capacity of the block-memoryless phase-noise channel.
The bounds capture the first two terms in the asymptotic expansion of capacity for SNR going to infinity and turn out to be tight for a large range of SNR values of practical interest.
Through these bounds, the capacity dependency on the coherence time of the phase-noise process is determined
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