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- Brendan Farrell, Yi Huang, Mark Iwen, Ting Wang, Lisa Zhang, Jintong Zheng
- 2007

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)

- BRENDAN FARRELL
- 2012

We study invertibility of matrices of the form D + R where D is an arbitrary symmetric deterministic matrix, and R is a symmetric random matrix whose independent entries have continuous distributions with bounded densities. We show that (D + R) −1 = O(n 2) with high probability. The bound is completely independent of D. No moment assumptions are placed on… (More)

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

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)

- Holger Boche, Brendan Farrell, Michel Ledoux, Moritz Wiese
- ArXiv
- 2012

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)

- 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 L p (H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α 1 I + S f , where S f is the operator given by convolution with f , f ∈ L 1 v (H), is invertible in B(L p… (More)

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on L p (H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α 1 δ + f , f ∈ L 1 v (H), is invertible with respect to convolu-tion over H, then (α 1 δ + f) −1 = α 2 δ + g, g… (More)