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 D, 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 t=D. 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 D is registered as the instants {tk} of emission of photoelectrons at the detector. If H denotes the D and Q, the expected number of photoelectrons is 2D, and DT, then the mutual information between the D 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 |D|T, this is maximized by H = ln2T, for uniformly distributed D, 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 D, 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.

© 1973 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Resolution, Optical-Channel Capacity and Information Theory*

Neil J. Bershad
J. Opt. Soc. Am. 59(2) 157-163 (1969)

Capacity and Nonuniform Signaling for Discrete-Time Poisson Channels

Jihai Cao, Steve Hranilovic, and Jun Chen
J. Opt. Commun. Netw. 5(4) 329-337 (2013)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (1)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (47)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription