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—We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Lévy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; moreover, the Lévy family also contains other interesting members exhibiting heavy-tail statistics… (More)

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of lo-calization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet frame. Based on these calculations, we design the variance-optimal wavelet (VOW). Finally, we demonstrate… (More)

In this paper we introduce a new class of codes for overloaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for… (More)

In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple Access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain and the… (More)

—In this paper, we introduce a new class of codes for overloaded synchronous wireless and optical code-division multiple access (CDMA) systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently , the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink… (More)

overloaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally… (More)

— It is known that the Karhunen-Lò eve transform (KLT) of Gaussian first-order auto-regressive (AR (1)) processes results in sinusoidal basis functions. The same sinusoidal bases come out of the independent-component analysis (ICA) and actually correspond to processes with completely independent samples. In this paper , we relax the Gaussian hypothesis and… (More)