Abstract
The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with $2n$ degrees of freedom, where $n=2$ and $n=3$ correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary $n$ and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of $n$. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for $n=1,2,3$. At an SNR of $25$ dB, the best lower bounds we developed are approximately $3.68$ bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of $25$ dB, a $16$-ASK constellation yields a rate of approximately $3.45$ bit per channel use.
Highlights
O PTICAL fibre transmission systems carrying the overwhelming bulk of the world’s telecommunication trafficManuscript received April 1, 2017; revised September 8, 2017 and January 31, 2018; accepted February 12, 2018
Our results showed that a lower bound for the capacity per channel use of such a model grows unbounded with the effective signal-to-noise ratio (SNR)
We will show results as a function of the effective SNR defined as ρ σS2/σN2, where σS2 is the second moment of the input distribution pX and σN2 is given by (16)
Summary
O PTICAL fibre transmission systems carrying the overwhelming bulk of the world’s telecommunication traffic. SHEVCHENKO et al.: CAPACITY LOWER BOUNDS OF THE NONCENTRAL CHI-CHANNEL overcoming the effects of nonlinearity has been receiving increased attention This approach relies on the fact that both the ME and NSE in the absence of losses and noise are exactly integrable [22], [23]. Achievable information rates for multi-eigenvalue transmission systems utilising all four degrees of freedom of each scalar soliton in NSE were analytically obtained in [46]. These results were obtained within the framework of a Gaussian noise model provided in [29] and [47] (non-Gaussian models have been presented in [51] and [52]) and assuming a continuous uniform input distribution subject to peak power constraints. This asymptotic expression shows that the MI grows unbounded and at the same rate, independently of the number of degrees of freedom
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