RT Conference Proceedings
T1 On the information dimension rate of stochastic processes
A1 Geiger, Bernhard C.
A1 Koch, Tobias Mirco
AB Jalali and Poor ("Universal compressed sensing," arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of Rényi's information dimension to stationary stochastic processes by defining the information dimension of the stochastic process as the information dimension of k samples divided by k in the limit as k →∞  to. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m →∞ ; to. It is demonstrated that both definitions are equivalent for stochastic processes that are ψ*-mixing, but that they may differ in general. In particular, it is shown that for Gaussian processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is 1 if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size.
PB IEEE
SN 978-1-5090-4096-4
YR 2017
FD 2017-08-15
LK https://hdl.handle.net/10016/26234
UL https://hdl.handle.net/10016/26234
LA eng
NO Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June 2017
NO The work of Bernhard C. Geiger has been funded by the Erwin SchrödingerFellowship J 3765 of the Austrian Science Fund and by the German Ministryof Education and Research in the framework of an Alexander von HumboldtProfessorship. The work of Tobias Koch has received funding from theEuropean Research Council (ERC) under the European Union’s Horizon 2020research and innovation programme (grant agreement number 714161), fromthe 7th European Union Framework Programme under Grant 333680, from theSpanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU),and from the Comunidad de Madrid under Grant S2103/ICE-2845.
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