TY - GEN
T1 - Signal representations with minimum ℓ∞-norm
AU - Studer, Christoph
AU - Yin, Wotao
AU - Baraniuk, Richard G.
PY - 2012
Y1 - 2012
N2 - Maximum (or ℓ∞) norm minimization subject to an underdetermined system of linear equations finds use in a large number of practical applications, such as vector quantization, peak-to-average power ratio (PAPR) (or 'crest factor') reduction in wireless communication systems, approximate neighbor search, robotics, and control. In this paper, we analyze the fundamental properties of signal representations with minimum ℓ∞-norm. In particular, we develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, 2010, and we characterize the limits of ℓ∞-norm-based PAPR reduction. Our results show that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the efficient computation of so-called democratic representations, which have both provably small ℓ∞-norm and low PAPR.
AB - Maximum (or ℓ∞) norm minimization subject to an underdetermined system of linear equations finds use in a large number of practical applications, such as vector quantization, peak-to-average power ratio (PAPR) (or 'crest factor') reduction in wireless communication systems, approximate neighbor search, robotics, and control. In this paper, we analyze the fundamental properties of signal representations with minimum ℓ∞-norm. In particular, we develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, 2010, and we characterize the limits of ℓ∞-norm-based PAPR reduction. Our results show that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the efficient computation of so-called democratic representations, which have both provably small ℓ∞-norm and low PAPR.
UR - http://www.scopus.com/inward/record.url?scp=84875734283&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84875734283&partnerID=8YFLogxK
U2 - 10.1109/Allerton.2012.6483364
DO - 10.1109/Allerton.2012.6483364
M3 - Conference contribution
AN - SCOPUS:84875734283
SN - 9781467345385
T3 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
SP - 1270
EP - 1277
BT - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
T2 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
Y2 - 1 October 2012 through 5 October 2012
ER -