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Comptes Rendus Physique

Quantum and nonlinearity limitations of the optical communication channel

E. Desurvire

Published Jan 1, 2003• 2 citations
Publisher

Abstract

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.

DOI
10.1016/s1631-0705(02)00002-6

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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.
This tutorial reviews the Holevo capacity limit as a universal tool to analyze the ultimate transmission rates in a variety of optical communication scenarios, ranging from conventional optically amplified fiber links to free-space communication with power-limited optical signals. The canonical additive white Gaussian noise model is used to describe the propagation of the optical signal. The Holevo limit exceeds substantially the standard Shannon limit when the power spectral density of noise acquired in the course of propagation is small compared to the energy of a single photon at the carrier frequency per unit time-bandwidth area. General results are illustrated with a discussion of efficient communication strategies in the photon-starved regime.
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)
The optical signal transmitted on a fiber with thermal noise, attenuation and amplification is studied. The channel is considered as a quantum channel while the signal to be transmitted is classical. The classical information is encoded in a quantum state then it is transmitted in optical fiber. At the receiving end, measurement is performed on the output quantum state to retrieve the classical information. The optimal distribution of the input quantum state achieving the channel capacity is Gaussian. The capacity is characterized by the attenuation/amplification coefficient and thermal noise in the transmission and at the measurement process together by the power of the input. The loss (or attenuation) of an optical fiber usually should be compensated by the amplification. We show that when they coexist, additional noise occurs
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.