Capacity of a Nonlinear Optical Channel With Finite Memory

Abstract

The channel capacity of a nonlinear, dispersive fiberoptic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for independent input in a coded (i.e., dependent) scenario.

Perturbative discrete-time multivariate fiber channel model with finite memory

“…Namely, the class of infinite-memory Gaussian noise models ( [2,5] and references therein) can be received from Eq. 2 after averaging the nonlinear interference term, whereas the finite memory model developed in [6] can be received by averaging of the coupling matrix while keeping the information about interfering symbols.…”

“…Existing channel models [2][3][4][5] are based on averaging signal distortions via an infinite memory approximation [6] of the signal interactions, where they are considered to be nonlinear noise. As averaging leads to information loss about the signal interference, it results in a degraded lower bound of the system capacity in the highly nonlinear regime.…”

“…More accurate channel capacity estimations will require accurate modelling approaches that take into account the finite response of the nonlinear channel [7][8]. These can be also used for other applications such as coding [6] or pre/post-distortion [9-10] compensation, and suggest system designs that can improve significantly the transmission capacity [11][12].…”

“…More accurate channel capacity estimations will require accurate modelling approaches that take into account the finite response of the nonlinear channel [7][8]. These can be also used for other applications such as coding [6] or pre/post-distortion [9-10] compensation, and suggest system designs that can improve significantly the transmission capacity [11][12].Here we developed a perturbative discrete-time channel model with finite memory based on the nonlinearity compensation technique proposed in [10] and experimentally demonstrated in [11][12]. The resulted multivariate channel model allows us to describe memory effects analytically, including both signal-signal and signal-noise effects.…”

Implications of information theory in optical fibre communications

“…The past 15 years have witnessed an intense research in the area of optical fibre capacity. For extensive literature surveys, see [3][4][5][6] and [7,§VI].…”