Shannon Capacity of Nonlinear Communication Channels

Abstract

We compute Shannon capacity of nonlinear channels with regenerative elements. Conditions are found under which capacity of such nonlinear channels is higher than the Shannon capacity of the classical linear additive white Gaussian noise channel. We develop a general scheme for designing the proposed channels and apply it to the particular nonlinear sine-mapping. The upper bound for regeneration efficiency is found and the asymptotic behavior of the capacity in the saturation regime is derived.

Performance limits in optical communications due to fiber nonlinearity

“…For memoryless systems employing matched filters to optimize the trade of between inter-symbol interference [131] and noise [132] is of significant benefit, whilst correlated signaling, which deliberately introduces controlled inter-symbol interference [133] or cancelation of intentionally induced inter-symbol interference by maximum likelihood sequence estimation [134] may be used to trade off total capacity and required signal to noise ratio. Modulation formats and coding should be optimized including bi-polar formats to maximize use of the transmitted energy and adapting the constellation to the almost [135] Gaussian noise of the linear optically amplified channel [136]. Having developed a strategy to optimize the per channel performance, it remains to fully exploit the available spectrum by adding additional channels.…”

“…Table 1 therefore lists a selection of alternative models which the reader will find useful in these circumstances. It is useful to note at this point that if memory is included in a formal calculation of the maximum information spectral density, then performance slightly above the optimum predicted by equations 30 and 32 may be possible using, for example, Satellite [180] or Ripple [136] constellations respectively, provided any additional assumptions are satisfied. In addition accurate channel modelling can be used as a basis for advanced methods of nonlinearity mitigation [192][193][194].…”

Sparse identification for nonlinear optical communication systems: SINO method

“…There is an enormous pressure on the fiber-optic communication industry to deal with the exponentially increasing capacity demands from data traffic [1,2] driven by the existing and constantly emerging internet and broadband services as well as the fast growing machine-tomachine traffic. Current technological solutions suggest a combination of advanced modulation formats and space division multiplexing to achieve substantial enhancement of the spectral efficiency [3][4][5][6], while fiber remains a nonlinear medium leading to signal being strongly degraded by nonlinear impairments.…”

Nonlinear signal transformations: path to capacity above the linear AWGN Shannon limit

“…1a), which creates attractive regions around the alphabet -a set of points used for signal modulation. Therefore, the alphabet points are required [11][12] to be stationary ܶሺ‫ݔ‬ ‫כ‬ ሻ ൌ ‫ݔ‬ ‫כ‬ and stable ȁܶ ᇱ ሺ‫ݔ‬ ‫כ‬ ሻȁ ͳ. Finally, the optimum positioning of the alphabet point is in the center of the attraction region ܶԢԢሺ‫ݔ‬ ‫כ‬ ሻ ൌ ͲǤ…”

“…The analytical formula for the regenerative limit were derived [11], in particular at high SNR one can observe the constant gap between the ݊-dimensional linear Shannon limit and the regenerative capacity:…”