Influence of Behavioral Models on Multiuser Channel Capacity

Abstract

Abstract-In order to characterize the channel capacity of a wavelength channel in a wavelength-division multiplexed (WDM) system, statistical models are needed for the transmitted signals on the other wavelengths. For example, one could assume that the transmitters for all wavelengths are configured independently of each other, that they use the same signal power, or that they use the same modulation format. In this paper, it is shown that these so-called behavioral models have a profound impact on the singlewavelength achievable information rate. This is demonstrated by establishing, for the first time, upper and lower bounds on the maximum achievable rate under various behavioral models, for a rudimentary WDM channel model. Index Terms-Achievable information rate, behavioral models, channel capacity, multiuser communications, mutual information, network information theory, nonlinear interference, wavelengthdivision multiplexing.

Capacity estimates for optical transmission based on the nonlinear Fourier transform

“… 5 , that the case of COI with no side information corresponds to the worst case scenario capacity wise. We note that different assumptions for the input statistics can affect the capacity estimates 50 . We are assuming here that all channels are transmitting symbols with the same statistics and input power that is known at the receiver.…”

“…We are assuming here that all channels are transmitting symbols with the same statistics and input power that is known at the receiver. According to the recently proposed classification of work 50 , this corresponds to the so-called adaptive interferer distribution. To avoid a possible confusion, one should notice that the result given by equation (11) does not conflict with the lower-bound estimation for the zero-dispersion channel obtained in ref 39 : when the dispersion β 2 goes to 0, the window of applicability of the result (11), given by two formulas above, closes, such that one cannot perform a correct comparison.…”

Information-Theoretic Tools for Optical Communications Engineers

“…Even the very existence of an AIR maximum at some finite optimum power is related to the suboptimum choice of p(x) and q(y|x), as channel capacity is a monotonic function of average power [23]. In fact, the unbounded capacity (growing to infinity for infinite power) of many simplified opticallyrelated nonlinear channels has been demonstrated [19], [24], [25].…”

Scope and Limitations of the Nonlinear Shannon Limit

“…These effects, however, have a negligible impact on the performance of conventional WDM systems and, as discussed before, are often neglected in the computation of the NSL. Finally, we make the additional assumptions (typical in optical networks and corresponding to the behavioral model (c) described in [24]) that {x k } and {w k } are independently drawn from the same alphabet with equal distribution and same average power E{|X k | 2 } = E{|W k | 2 } = P s (fairness and independence among channels) and that {w k } are unknown to the receiver.…”

“…There are also some theoretical arguments against the NSL: in [22] it was demonstrated that the capacity of a static discrete-time channel, even when defined using an equality constraint on the average power, cannot decrease when the input power increases, as instead predicted by the NSL. For example, in [23] and [24] it is shown that ever-increasing bounds on the capacity (per symbol) can be obtained in the presence of, respectively, nonlinear phase-noise and four-wave mixing in non-dispersive fibers, exactly in the cases where the typical approach used to compute the NSL would provide the usual behavior with a finite maximum. As a matter of fact, all papers that take into account realistic fiber models only obtain lower bounds (or approximations) on the capacity with a finite maximum.…”