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

Sequential photon-counting statistics and maximum-likelihood estimation techniques for gaussian optical fields*

F. Davidson and J. Amoss
J. Opt. Soc. Am. 63(1) 30-37 (1973)

Resolution distribution and information capacity of a hologram*

Stephen S. Hsiao
J. Opt. Soc. Am. 63(9) 1108-1119 (1973)

Statistics of photoelectron counting with a rectangular spectral profile

M. L. Mehta and C. L. Mehta
J. Opt. Soc. Am. 63(7) 826-831 (1973)

Limitations of fringe-parameter estimation at low light levels*

J. F. Walkup and J. W. Goodman
J. Opt. Soc. Am. 63(4) 399-407 (1973)

Photocounting Array Receivers for Optical Communication Through the Lognormal Atmospheric Channel. 1: Optimum and Suboptimum Receiver Structures

M. C. Teich and S. Rosenberg
Appl. Opt. 12(11) 2616-2624 (1973)