15,390 research outputs found
Highly Robust Error Correction by Convex Programming
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x ∈ ℝ^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g., quantization errors).
We show that if one encodes the information as Ax where A ∈
ℝ^(m x n) (m ≥ n) is a suitable coding matrix, there are two decoding schemes that allow the recovery of the block of n pieces of information x with nearly the same accuracy as if no gross errors occurred upon transmission (or equivalently as if one had an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well
Highly robust error correction by convex programming
This paper discusses a stylized communications problem where one wishes to
transmit a real-valued signal x in R^n (a block of n pieces of information) to
a remote receiver. We ask whether it is possible to transmit this information
reliably when a fraction of the transmitted codeword is corrupted by arbitrary
gross errors, and when in addition, all the entries of the codeword are
contaminated by smaller errors (e.g. quantization errors).
We show that if one encodes the information as Ax where A is a suitable m by
n coding matrix (m >= n), there are two decoding schemes that allow the
recovery of the block of n pieces of information x with nearly the same
accuracy as if no gross errors occur upon transmission (or equivalently as if
one has an oracle supplying perfect information about the sites and amplitudes
of the gross errors). Moreover, both decoding strategies are very concrete and
only involve solving simple convex optimization programs, either a linear
program or a second-order cone program. We complement our study with numerical
simulations showing that the encoder/decoder pair performs remarkably well.Comment: 23 pages, 2 figure
MAGMA: Multi-level accelerated gradient mirror descent algorithm for large-scale convex composite minimization
Composite convex optimization models arise in several applications, and are
especially prevalent in inverse problems with a sparsity inducing norm and in
general convex optimization with simple constraints. The most widely used
algorithms for convex composite models are accelerated first order methods,
however they can take a large number of iterations to compute an acceptable
solution for large-scale problems. In this paper we propose to speed up first
order methods by taking advantage of the structure present in many applications
and in image processing in particular. Our method is based on multi-level
optimization methods and exploits the fact that many applications that give
rise to large scale models can be modelled using varying degrees of fidelity.
We use Nesterov's acceleration techniques together with the multi-level
approach to achieve convergence rate, where
denotes the desired accuracy. The proposed method has a better
convergence rate than any other existing multi-level method for convex
problems, and in addition has the same rate as accelerated methods, which is
known to be optimal for first-order methods. Moreover, as our numerical
experiments show, on large-scale face recognition problems our algorithm is
several times faster than the state of the art
Channel-Optimized Quantum Error Correction
We develop a theory for finding quantum error correction (QEC) procedures
which are optimized for given noise channels. Our theory accounts for
uncertainties in the noise channel, against which our QEC procedures are
robust. We demonstrate via numerical examples that our optimized QEC procedures
always achieve a higher channel fidelity than the standard error correction
method, which is agnostic about the specifics of the channel. This demonstrates
the importance of channel characterization before QEC procedures are applied.
Our main novel finding is that in the setting of a known noise channel the
recovery ancillas are redundant for optimized quantum error correction. We show
this using a general rank minimization heuristic and supporting numerical
calculations. Therefore, one can further improve the fidelity by utilizing all
the available ancillas in the encoding block.Comment: 12 pages, 9 figure
Sparse Signal Processing Concepts for Efficient 5G System Design
As it becomes increasingly apparent that 4G will not be able to meet the
emerging demands of future mobile communication systems, the question what
could make up a 5G system, what are the crucial challenges and what are the key
drivers is part of intensive, ongoing discussions. Partly due to the advent of
compressive sensing, methods that can optimally exploit sparsity in signals
have received tremendous attention in recent years. In this paper we will
describe a variety of scenarios in which signal sparsity arises naturally in 5G
wireless systems. Signal sparsity and the associated rich collection of tools
and algorithms will thus be a viable source for innovation in 5G wireless
system design. We will discribe applications of this sparse signal processing
paradigm in MIMO random access, cloud radio access networks, compressive
channel-source network coding, and embedded security. We will also emphasize
important open problem that may arise in 5G system design, for which sparsity
will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces
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