Outage probability for soliton transmission

– We study the interplay between amplifier noise and birefringent disorder in the case of strongly nonlinear (soliton) type of transmission in optical fibers. Assuming both noise and disorder to be weak, we evaluate the probability distribution function (PDF) of the Bit-Error-Rate (BER) for the values of BER that are much larger than the typical (average) value. The PDF tail that describes probability of the system outage shows log-normal shape, strongly dependent on the fiber length. We also discuss a simple timing shift technique capable of the outage compensation. Nonlinear information transmission in optical fibers when elementary bits are represented by optical solitons constitutes a promising technology that has been a subject of intensive research over the past decades [1, 2]. In ideal fibers, the information carried by the solitons would be transmitted without any loss. In practice, however, various impairments lead to information loss. Amplifier noise and birefringent disorder represent the two major impairments in both linear and nonlinear transmission regimes. The noise generated by spontaneous emission in optical amplifiers is, therefore, short-correlated both in space and time. Birefringence that stems from variations of the optical fiber core degree of ellipticity is sensitive to external stresses and temperature changes, which leads to its substantial changes along the fiber line. Birefringence is practically frozen, i.e. the typical time scale of the birefringence variations is long compared to the time it takes for a pulse to pass the entire fiber line [3]. Therefore, birefringence can be treated as time-independent disorder, short-correlated in space. The optical communication system performance is usually measured by Bit-Error-Rate (BER) that represents the probability of an incorrect bit identification at the system output. However, because of the quasi-static nature of the birefringent disorder, the system performance may not be characterized in terms of a single number, e.g. some BER averaged over disorder realizations. BER should be rather considered as a number, dependent on a given realization of birefringent disorder, whereas the system performance should be characterized in terms of the Probability Distribution Function (PDF) of BER, with the statistics being collected by averaging over a large number of birefringent-disorder realizations. Note that the co-existence of two very different randomness sources constitutes a common feature of many problems in