Several approximate non-linear fiber propagation models have been proposed over the years. Recent re-consideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.
A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit. The proposed system is based on probabilistically shaped 64-QAM modulation formats. Adjustable shaping is combined with a fixed-QAM modulation and a fixed forward-error correction code to realize a system with adjustable net data rate that can operate over a large reach range. At the transmitter, an adjustable distribution matcher performs the shaping. At the receiver, an inverse distribution matcher is used. Probabilistic shaping is implemented into a coherent optical transmission system for 64-QAM at 32 Gbaud to realize adjustable operation modes for net data rates ranging from 200 to 300 Gb/s. It is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16-QAM and regular 64-QAM signals by more than 40% in the transmission reach.
A new coded modulation scheme is proposed. At the transmitter, the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding. At the receiver, the output of a bitwise demapper is fed to a binary decoder. No iterative demapping is performed. Rate adaption is achieved by adjusting the input distribution and the transmission power. The scheme is applied to bipolar amplitudeshift keying (ASK) constellations with equidistant signal points and it is directly applicable to two-dimensional quadrature amplitude modulation (QAM). The scheme is implemented by using the DVB-S2 low-density parity-check (LDPC) codes. At a frame error rate of 10 -3 , the new scheme operates within less than 1.1 dB of the AWGN capacity 1/2 log 2 (1 + SNR) at any spectral efficiency between 1 and 5 bits/s/Hz by using only 5 modes, i.e., 4-ASK with code rate 2/3, 8-ASK with 3/4, 16-ASK and 32-ASK with 5/6, and 64-ASK with 9/10.
Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented. The encoder achieves the maximum rate, namely, the entropy of the desired distribution, asymptotically in the blocklength. Furthermore, the normalized divergence of the encoder output and the desired distribution goes to zero in the blocklength.
The GN-model has been proposed as an approximate but sufficiently accurate tool for predicting uncompensated optical coherent transmission system performance, in realistic scenarios. For this specific use, the GN-model has enjoyed substantial validation, both simulative and experimental. Recently, however, it has been pointed out that its predictions, when used to obtain a detailed picture of non-linear interference (NLI) noise accumulation along a link, may be affected by a substantial NLI overestimation error, especially in the first spans of the link. In this paper we analyze in detail the GN-model errors. We discuss recently proposed formulas for correcting such errors and show that they neglect several contributions to NLI, so that they may substantially underestimate NLI in specific situations, especially over low-dispersion fibers. We derive a complete set of formulas accounting for all single, cross, and multi-channel effects, This set constitutes what we have called the enhanced GN-model (EGN-model). We extensively validate the EGN model by comparison with accurate simulations in several different system scenarios. The overall EGN model accuracy is found to be very good when assessing detailed span-by-span NLI accumulation and excellent when estimating realistic system maximum reach. The computational complexity vs. accuracy trade-offs of the various versions of the GN and EGN models are extensively discussed.