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6 papers · 2 filters
Group representation design of digital signals and sequences
Shamgar Gurevich, Ronny Hadani, Nir Sochen
In this survey a novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_{p}, is described and studied. The new functions a…
Incoherent dictionaries and the statistical restricted isometry property
Shamgar Gurevich, Ronny Hadani
In this article we present a statistical version of the Candes-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a dis…
Lower Bounds on the Rate-Distortion Function of LDGM Codes
A. G. Dimakis, M. J. Wainwright, K. Ramchandran
A recent line of work has focused on the use of low-density generator matrix (LDGM) codes for lossy source coding. In this paper, wedevelop a generic technique for deriving lower b…
On the diagonalization of the discrete Fourier transform
Shamgar Gurevich, Ronny Hadani
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime nu…
On some deterministic dictionaries supporting sparsity
Shamgar Gurevich, Ronny Hadani, Nir Sochen
We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups…
The Case for Structured Random Codes in Network Capacity Theorems
Bobak Nazer, Michael Gastpar
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for prov…