In this paper, we show that the nonlinear parametric gain (PG) interaction between signal and noise is a nonnegligible factor in the design and analysis of long-haul dispersion-managed optical 10-Gb/s on-off keying nonreturn to zero transmission systems operated at small signal-to-noise ratios (OSNRs) such as those employing forward-error correction (FEC) coding. In such a regime, we show that the in-phase noise spectrum exhibits a large gain close to the carrier frequency, which is due to the higher order noise terms accounting for the noise-noise beating during propagation that is usually neglected in the nonlinear Schrödinger equation. With a novel stochastic analysis that keeps such higher order terms, we are able to analytically quantify the maximum tolerable signal power after which PG unacceptably degrades system performance. We verify such an analytical power threshold by both simulation and experiment. We finally quantify the needed extra OSNR, or equivalently FEC coding gain, required when taking PG into account.
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