Optical Channel Capacity

Chapter

Abstract

Given the fact that LDPC-coded turbo equalizer described in  Chap. 7 is an excellent candidate to deal with both linear and nonlinear channel impairments, there naturally raises the question about fundamental limits on channel capacity. There have been numerous attempts to determine the channel capacity of a nonlinear fiber optics communication channel [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. The main approach, until recently, was to consider ASE noise as a predominant effect and to observe the fiber nonlinearities as the perturbation of linear case or as the multiplicative noise. In this chapter, which is based on a series of articles by authors [14, 15, 16, 17, 18, 19, 20], we describe how to determine the true fiber-optics channel capacity. Because in most of the practical applications the channel input distribution is uniform, we also describe how to determine the achievable information rates (AIRs) or uniform information capacity, which represent the lower bound on channel capacity [14, 15, 16, 17, 18, 19, 20]. This method consists of two steps (1) approximating probability density functions (PDFs) for energy of pulses, which is done by (a) evaluation of histograms [14, 15, 16, 17, 18, 19, 20], (b) instanton approach [15], or (c) edgeworth expansion [21], and (2) estimating AIRs by applying a method originally proposed by Arnold and Pfitser [22, 23, 24]. In most of the publications that are related to the channel capacity, it was assumed that fiber-optics channel is memoryless [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], while in reality the fiber-optics channel is the channel with memory [14, 15, 16, 17, 18, 19, 20]. An interesting approach to reduce the fiber-optics channel memory, introduced recently [25, 26], is the backpropagation method. Namely, in point-to-point links, the receiver knows the dispersion map configuration and can propagate the received signal through the fictive dispersion map with fiber parameters [group velocity dispersion (GVD), second-order GVD, and nonlinearity coefficient] of opposite signs to that used in original map. However, the nonlinear interaction of ASE noise and Kerr nonlinearities cannot be compensated for and someone should use the method introduced in this chapter in information capacity calculation to account for this effect.

Keywords

Entropy Microwave Attenuation Covariance Coherence 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Electrical & Computer EngineeringUniversity of ArizonaTucsonUSA

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