Transmission of information via the non-linear Scroedinger equation: The random Gaussian input case

Abstract

The explosion of demand for ultra-high information transmission rates over the last decade has necessitated the usage of increasingly high light intensities for fiber optical transmissions. As a result, the fiber non-linearities need to be treated non-perturbatively. Similar analyses in the past have focused on the effects of non-linearities on existing transmission technologies, e.g. WDM.In this paper we take advantage of the fact that, under certain assumptions, light transmission through optical fibers can be described using the non-linear Schroedinger equation, which is exactly integrable. As a particular example, we show that in the low Gaussian noise limit, the Gaussian input distribution has a higher mutual information than the transmission using WDM over the same available bandwidth.

The Asymptotic Capacity of the Optical Fiber

“…There is a good review in [15, Section I-A]. The achievable rates of 1-and multi-solitons is studied, respectively, in [3], [16]- [18] and [19]- [21]. There is also a myriad of lower bounds that hold good in the low power regime; see, e.g., [22]- [27].…”