Log-log growth of channel capacity for nondispersive nonlinear optical fiber channel in intermediate power range

Abstract

We consider a model nondispersive nonlinear optical fiber channel with an additive Gaussian noise. Using Feynman path-integral technique, we find the optimal input signal distribution maximizing the channel's per-sample mutual information at large signal-to-noise ratio in the intermediate power range. The optimal input signal distribution allows us to improve previously known estimates for the channel capacity. We calculate the output signal entropy, conditional entropy, and per-sample mutual information for Gaussian, half-Gaussian, and modified Gaussian input signal distributions. We demonstrate that in the intermediate power range the capacity (the per-sample mutual information for the optimal input signal distribution) is greater than the per-sample mutual information for half-Gaussian input signal distribution considered previously as the optimal one. We also show that the capacity grows as loglogP in the intermediate power range, where P is the signal power.

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

“…We have also shown that our result for the spectral efficiency (50) for nonzero dispersion approaches the expression (52) derived in Ref. [12] in the case when β tends to zero.…”

“…It has been observed that the spectral efficiency of the nonlinear channel decreases with increasing SNR at high enough values of SNR [3][4][5]7]. This analysis certainly provides only a lower bound on channel capacity and does not prove that the Shannon nonlinear fiber channel capacity is decreasing with power; see, for example, discussions in [8][9][10][11][12]. As a matter of fact, the decrease of the spectral efficiency can be linked to different effects.…”

“…Also for the nondispersive nonlinear channel it was shown that the channel capacity is growing with increasing SNR, see Refs. [11,12,15]. However, the capacity of nonlinear fiber channels is still an open problem of great practical and fundamental importance.…”

“…For the nondispersive case the result for the per-sample mutual information was obtained in Ref. [12]:…”

Next-to-leading-order corrections to capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region

“…Therefore as the first step in understanding of the effects of nonlinearity impact in the channel one can consider the nonlinear channel with zero average dispersion. The nonlinear nondispersive optical fiber channels are also considered in numerous papers, see, e.g., * Electronic address: panarin.a.a@mail.ru † Electronic address: a.v.reznichenko@inp.nsk.su ‡ Electronic address:i.s.terekhov@gmail.com [13][14][15][16][17][18]. Of course, the problem of capacity calculation for these channels is simpler than the problem with dispersion.…”