4,583 research outputs found

### Zigzag Codes: MDS Array Codes with Optimal Rebuilding

MDS array codes are widely used in storage systems to protect data against
erasures. We address the \emph{rebuilding ratio} problem, namely, in the case
of erasures, what is the fraction of the remaining information that needs to be
accessed in order to rebuild \emph{exactly} the lost information? It is clear
that when the number of erasures equals the maximum number of erasures that an
MDS code can correct then the rebuilding ratio is 1 (access all the remaining
information). However, the interesting and more practical case is when the
number of erasures is smaller than the erasure correcting capability of the
code. For example, consider an MDS code that can correct two erasures: What is
the smallest amount of information that one needs to access in order to correct
a single erasure? Previous work showed that the rebuilding ratio is bounded
between 1/2 and 3/4, however, the exact value was left as an open problem. In
this paper, we solve this open problem and prove that for the case of a single
erasure with a 2-erasure correcting code, the rebuilding ratio is 1/2. In
general, we construct a new family of $r$-erasure correcting MDS array codes
that has optimal rebuilding ratio of $\frac{e}{r}$ in the case of $e$ erasures,
$1 \le e \le r$. Our array codes have efficient encoding and decoding
algorithms (for the case $r=2$ they use a finite field of size 3) and an
optimal update property.Comment: 23 pages, 5 figures, submitted to IEEE transactions on information
theor

### Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data

### Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for
innovative and large-scale signal processing algorithms, complemented by
collaborative and adaptive sensing platforms to accomplish the objectives of
layered sensing and control. Towards this goal, the present paper develops a
spline-based approach to field estimation, which relies on a basis expansion
model of the field of interest. The model entails known bases, weighted by
generic functions estimated from the field's noisy samples. A novel field
estimator is developed based on a regularized variational least-squares (LS)
criterion that yields finitely-parameterized (function) estimates spanned by
thin-plate splines. Robustness considerations motivate well the adoption of an
overcomplete set of (possibly overlapping) basis functions, while a sparsifying
regularizer augmenting the LS cost endows the estimator with the ability to
select a few of these bases that ``better'' explain the data. This parsimonious
field representation becomes possible, because the sparsity-aware spline-based
method of this paper induces a group-Lasso estimator for the coefficients of
the thin-plate spline expansions per basis. A distributed algorithm is also
developed to obtain the group-Lasso estimator using a network of wireless
sensors, or, using multiple processors to balance the load of a single
computational unit. The novel spline-based approach is motivated by a spectrum
cartography application, in which a set of sensing cognitive radios collaborate
to estimate the distribution of RF power in space and frequency. Simulated
tests corroborate that the estimated power spectrum density atlas yields the
desired RF state awareness, since the maps reveal spatial locations where idle
frequency bands can be reused for transmission, even when fading and shadowing
effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin

### Incremental Relaying for the Gaussian Interference Channel with a Degraded Broadcasting Relay

This paper studies incremental relay strategies for a two-user Gaussian
relay-interference channel with an in-band-reception and
out-of-band-transmission relay, where the link between the relay and the two
receivers is modelled as a degraded broadcast channel. It is shown that
generalized hash-and-forward (GHF) can achieve the capacity region of this
channel to within a constant number of bits in a certain weak relay regime,
where the transmitter-to-relay link gains are not unboundedly stronger than the
interference links between the transmitters and the receivers. The GHF relaying
strategy is ideally suited for the broadcasting relay because it can be
implemented in an incremental fashion, i.e., the relay message to one receiver
is a degraded version of the message to the other receiver. A
generalized-degree-of-freedom (GDoF) analysis in the high signal-to-noise ratio
(SNR) regime reveals that in the symmetric channel setting, each common relay
bit can improve the sum rate roughly by either one bit or two bits
asymptotically depending on the operating regime, and the rate gain can be
interpreted as coming solely from the improvement of the common message rates,
or alternatively in the very weak interference regime as solely coming from the
rate improvement of the private messages. Further, this paper studies an
asymmetric case in which the relay has only a single single link to one of the
destinations. It is shown that with only one relay-destination link, the
approximate capacity region can be established for a larger regime of channel
parameters. Further, from a GDoF point of view, the sum-capacity gain due to
the relay can now be thought as coming from either signal relaying only, or
interference forwarding only.Comment: To appear in IEEE Trans. on Inf. Theor

### A Game-Theoretic View of the Interference Channel: Impact of Coordination and Bargaining

This work considers coordination and bargaining between two selfish users
over a Gaussian interference channel. The usual information theoretic approach
assumes full cooperation among users for codebook and rate selection. In the
scenario investigated here, each user is willing to coordinate its actions only
when an incentive exists and benefits of cooperation are fairly allocated. The
users are first allowed to negotiate for the use of a simple Han-Kobayashi type
scheme with fixed power split. Conditions for which users have incentives to
cooperate are identified. Then, two different approaches are used to solve the
associated bargaining problem. First, the Nash Bargaining Solution (NBS) is
used as a tool to get fair information rates and the operating point is
obtained as a result of an optimization problem. Next, a dynamic
alternating-offer bargaining game (AOBG) from bargaining theory is introduced
to model the bargaining process and the rates resulting from negotiation are
characterized. The relationship between the NBS and the equilibrium outcome of
the AOBG is studied and factors that may affect the bargaining outcome are
discussed. Finally, under certain high signal-to-noise ratio regimes, the
bargaining problem for the generalized degrees of freedom is studied.Comment: 43 pages, 11 figures, to appear on Special Issue of the IEEE
Transactions on Information Theory on Interference Networks, 201

### Geographic Gossip: Efficient Averaging for Sensor Networks

Gossip algorithms for distributed computation are attractive due to their
simplicity, distributed nature, and robustness in noisy and uncertain
environments. However, using standard gossip algorithms can lead to a
significant waste in energy by repeatedly recirculating redundant information.
For realistic sensor network model topologies like grids and random geometric
graphs, the inefficiency of gossip schemes is related to the slow mixing times
of random walks on the communication graph. We propose and analyze an
alternative gossiping scheme that exploits geographic information. By utilizing
geographic routing combined with a simple resampling method, we demonstrate
substantial gains over previously proposed gossip protocols. For regular graphs
such as the ring or grid, our algorithm improves standard gossip by factors of
$n$ and $\sqrt{n}$ respectively. For the more challenging case of random
geometric graphs, our algorithm computes the true average to accuracy
$\epsilon$ using $O(\frac{n^{1.5}}{\sqrt{\log n}} \log \epsilon^{-1})$ radio
transmissions, which yields a $\sqrt{\frac{n}{\log n}}$ factor improvement over
standard gossip algorithms. We illustrate these theoretical results with
experimental comparisons between our algorithm and standard methods as applied
to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin

### Block-Sparse Recovery via Convex Optimization

Given a dictionary that consists of multiple blocks and a signal that lives
in the range space of only a few blocks, we study the problem of finding a
block-sparse representation of the signal, i.e., a representation that uses the
minimum number of blocks. Motivated by signal/image processing and computer
vision applications, such as face recognition, we consider the block-sparse
recovery problem in the case where the number of atoms in each block is
arbitrary, possibly much larger than the dimension of the underlying subspace.
To find a block-sparse representation of a signal, we propose two classes of
non-convex optimization programs, which aim to minimize the number of nonzero
coefficient blocks and the number of nonzero reconstructed vectors from the
blocks, respectively. Since both classes of problems are NP-hard, we propose
convex relaxations and derive conditions under which each class of the convex
programs is equivalent to the original non-convex formulation. Our conditions
depend on the notions of mutual and cumulative subspace coherence of a
dictionary, which are natural generalizations of existing notions of mutual and
cumulative coherence. We evaluate the performance of the proposed convex
programs through simulations as well as real experiments on face recognition.
We show that treating the face recognition problem as a block-sparse recovery
problem improves the state-of-the-art results by 10% with only 25% of the
training data.Comment: IEEE Transactions on Signal Processin

- …