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Demixing is the task of identifying multiple signals given only their sum and prior information about their structures. Examples of demixing problems include (i) separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis; (ii) decomposing an observed matrix into low-rank and sparse components;… (More)

We consider a flexible greedy approach to wavelength assignment in an optical network with the goal of minimizing the cost incurred by wavelength conversions and fiber deployment. The greedy approach processes demands one by one in a certain order and makes a locally optimal choice for each demand. We address several heuristics for creating desirable demand… (More)

We derive an explicit lower bound on the capacity of the discrete amplitude–constrained Gaussian channel by proving the existence of tight frames that permit redundant vector representations with small coefficients. Our method encodes the information in subspaces that are optimal in terms of the power to amplitude ratio. In a recent paper, Lyubarskii and… (More)

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on Lp(H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α1δ + f , f ∈ L 1 v(H), is invertible with respect to convolution over H, then (α1δ + f) −1 = α2δ + g, g ∈ L 1… (More)

- BRENDAN FARRELL
- 2013

We address the local spectral behavior of the random matrix Π1U ⊗kΠ2U ⊗k∗Π1, where U is a Haar distributed unitary matrix of size n×n, the factor k is at most c0 logn for a small constant c0 > 0, and Π1,Π2 are arbitrary projections on l n k 2 of ranks proportional to n. We prove that in this setting the k-fold Kronecker product behaves similarly to the… (More)

- Holger Boche, Brendan Farrell
- Journal of Approximation Theory
- 2014

- Holger Boche, Brendan Farrell
- EURASIP J. Adv. Sig. Proc.
- 2011

We address the peak-to-average power ratio (PAPR) of transmission signals in OFDM and consider the performance of tone reservation for reduction of the PAPR. Tone reservation is unique among methods for reducing PAPR, because it does not affect information bearing coefficients and involves no additional coordination of transmitter and receiver. It is shown… (More)

- Holger Boche, Brendan Farrell
- Internet Mathematics
- 2013

High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and out-of-band radiation. However, reducing peak values generally comes at the cost some other resource. We provide a theoretical contribution towards understanding the relationship between peak value reduction and the resulting cost in… (More)

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on Lp(H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α1I+Sf , where Sf is the operator given by convolution with f , f ∈ Lv(H), is invertible in B(Lp(H)), then (α1I +… (More)

- Holger Boche, Brendan Farrell, Michel Ledoux, Moritz Wiese
- ArXiv
- 2011

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order √ log n, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order log log n. This is a noteworthy difference to… (More)