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Information Capacity ofNonlinear Fiber-Optical Systems

BernardWu andEvgenii Narimanov

Published Jan 1, 2005• 0 citations

Abstract

edu Abstract: Wedevelop information-theoretical description ofnonlinear optical communication systems. We present a non-perturbative calculation oftheinformation capacity fordifferent modulation formats, anddemonstrate thatfiber nonlinearity leads toexponential suppression ofthechannel capacity. © 2004Optical Society ofAmerica OCIScodes:(060.2330) Fiberoptics communications; (190.4370) Nonlinear optics, fibers; (190.4380) Nonlinear optics, four-wave mixing Theperformance ofanycommunication system isultimately limited bythesignal tonoise ratio ofthe received signal andavailable bandwidth. Thislimitation canbestated moreformally byusing theconcept of information capacity originally introduced within theframework ofinformation theory (1). Theinformation capacity isdefined asthemaximumpossible bitrateforerror-free transmission inthepresence ofnoise. For alinear communication channel withadditive noise, andatotal signal powerconstraint attheinput, the capacity isgiven bythecelebrated Shannon formula (1)

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edu Abstract: Wedevelop information-theoretical description ofnonlinear optical communication systems. We present a non-perturbative calculation oftheinformation capacity fordifferent modulation formats, anddemonstrate thatfiber nonlinearity leads toexponential suppression ofthechannel capacity. © 2004Optical Society ofAmerica OCIScodes:(060.2330) Fiberoptics communications; (190.4370) Nonlinear optics, fibers; (190.4380) Nonlinear optics, four-wave mixing Theperformance ofanycommunication system isultimately limited bythesignal tonoise ratio ofthe received signal andavailable bandwidth. Thislimitation canbestated moreformally byusing theconcept of information capacity originally introduced within theframework ofinformation theory (1). Theinformation capacity isdefined asthemaximumpossible bitrateforerror-free transmission inthepresence ofnoise. For alinear communication channel withadditive noise, andatotal signal powerconstraint attheinput, the capacity isgiven bythecelebrated Shannon formula (1)

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit—the upper bound of regeneration efficiency—is derived. The Shannon limit describes the limit of error-free information transmission and thus the information that can be transmitted in telecommunications. Here, the authors derive the Shannon limit for nonlinear, regenerative systems, expanding on the classical linear case.

We analyze the information-capacity limitations of the optical communication channel, as determined by noise accumulation from optical amplification and nonlinear wave-mixing. We review the concepts of signal-to-noise ratio and entropy for binary-coded and continuous communications, leading to a definition of ultimate capacity for the optically-amplified channel. A unified quantum model, describing both amplification and nonlinearity limitations, makes possible to determine the power transmission window within which the channel capacity can be maximized.

For studying the accurate impacts of nonlinear fiber propagation on channel capacity conveniently, a numerical calculating method derived from signal power transmission property is presented, its dependences on input pulses peak power is obtained, and spontaneous emission noise intensity, nonlinear coefficients and group velocity dispersion of fiber are amplified. It can also conclude that the improvement of nonlinear channel capacity will not go with the improvement of input signal power especially for larger power input case, which can be used as a guideline to calculate nonlinear channel capacity theoretically and improve nonlinear channel capacity in technical application.