Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Modern optical fiber networks transmit data at astonishingly high rates—at leasta hundred billion (1011) bits per second in a single optical fiber. The error rates causedby physical phenomena are amazingly low—in the range of one error per trillion (1012)bits or lower—but still need to be detected and corrected. How can one simulatesuch a system effectively and efficiently to understand and deal with the transmissionerrors? Not by a straightforward Monte Carlo simulation; the number of sample pointswould be prohibitively high. This is an example of the type of problem addressed inthis issue’s SIGEST paper, “A Method to Compute Statistics of Large, Noise-InducedPerturbations of Nonlinear Schrodinger Solitons” by R. O. Moore, G. Biondini, andW. L. Kath, originally published in 2007 in the SIAM Journal on Applied Mathematics.

As the paper’s title suggests, the type of communication network that it considersis a soliton-based transmission system. (Solitons are wave pulses that maintain theirshapes while traveling at constant speed.) The mathematical model that is used is thenonlinear Schrodinger equation, which governs the propagation of optical pulses undersimplified conditions. The authors’ approach is not limited to this simplified model,however, as they have shown in subsequent work.

The key technique that is used by the authors to conduct effective and efficientsimulations is importance sampling. This technique does what the words connote:concentrate the sample points in regions that are most consequential. Of course, thisis much easier said than done. In this instance, the authors accomplish this by usingapproximate analytical knowledge about the behavior of the transmission system thatcomes from soliton perturbation theory to bias the sampling to regions where events ofinterest occur. Importance sampling is an important technique in general, and one of thebonus aspects of this paper is that it provides readers with a nice general introductionto importance sampling as well as a specific application.

A consequence of this research is the ability to effectively simulate soliton-basedoptical transmission networks governed by the nonlinear Schrodinger equation severalorders of magnitude more quickly than by standard Monte Carlo simulations. Thenumerical simulations towards the end of the paper illustrate this. The overall resultis a very nice demonstration of the use of sophisticated and deep mathematics to aidin the understanding of an important practical problem, written in a very accessiblemanner that should interest a broad range of SIAM readers.

The Editors

521

Dow

nloa

ded

11/2

3/14

to 1

34.7

1.13

5.13

4. R

edis

trib

utio

n su

bjec

t to

SIA

M li

cens

e or

cop

yrig

ht; s

ee h

ttp://

ww

w.s

iam

.org

/jour

nals

/ojs

a.ph

p