Information in the time of arrival of a photon packet: capacity of PPM channels*
- 1 February 1973
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America
- Vol. 63 (2) , 166-170
- https://doi.org/10.1364/josa.63.000166
Abstract
Expressions for the information rate and capacity of amplitude-modulated photon beams are available in literature. Recent interest in position-modulated laser pulses has motivated the investigation of the following model: A random variable , which can take on values in the interval (−T, T), is transmitted by centering a narrow, coherent, single-mode light pulse of duration 2D and constant irradiance at . It is assumed that no other than quantum fluctuations, of the otherwise stable source, disturb the transmission. The information that the received photon packet carries about is registered as the instants {tk} of emission of photoelectrons at the detector. If H denotes the and Q, the expected number of photoelectrons is 2D, and D≪T, then the mutual information between the and {tk} ensembles is, for large Q, approximately H−ln(2D/ρQ). Here, ρ = exp(γ − 1) and γ is Euler’s constant. Under the peak-excursion constraint , this is maximized by H = ln2T, for uniformly distributed , so that for large Q the capacity C = ln(ρQT/D). The accurate expression, valid for all Q, involves the exponential integral E1(Q). The value of C is used to derive a lower bound on the mean-square error of any estimator of , by the rate-distortion method. The bound, which decreases as Q2, is compared with the variance of maximum-a-posteriori-probability estimators of delay which, in the case of differentiable pulses, decreases only as Q.
Keywords
This publication has 7 references indexed in Scilit:
- Information in a Photon Beam vs Modulation-Level SpacingJournal of the Optical Society of America, 1971
- Information Rate in an Optical Communication Channel*Journal of the Optical Society of America, 1971
- On the extension of the discrete model for optical detectionProceedings of the IEEE, 1971
- Communication theory for the free-space optical channelProceedings of the IEEE, 1970
- Phenomenological Theory of Laser Beam Fluctuations and Beam MixingPhysical Review B, 1965
- Coherence Properties of Optical FieldsReviews of Modern Physics, 1965
- A Mathematical Theory of CommunicationBell System Technical Journal, 1948