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Probabilistic Shaping Distributions for Optical Communications | IEEE Journals & Magazine | IEEE Xplore

Probabilistic Shaping Distributions for Optical Communications


Abstract:

Probabilistic shaping is widely employed in local oscillator-based coherent optical systems to improve receiver sensitivity and provide rate adaptation. This widespread a...Show More

Abstract:

Probabilistic shaping is widely employed in local oscillator-based coherent optical systems to improve receiver sensitivity and provide rate adaptation. This widespread adoption has been enabled, in part, by simple closed-form solutions for the optimal input distribution and channel capacity for these standard coherent channels. By contrast, the optimal input distributions and channel capacities for many direct-detection optical channels remain open problems. The lack of non-negative root-Nyquist pulses, signal-dependent noise, and the possible discreteness of the capacity-achieving input distribution have historically prevented standard information-theoretic techniques from obtaining simple closed-form solutions for these channels. In this tutorial, we review a high-rate continuous approximation (HCA) for analytically approximating the optimal input distribution. HCA, which was first developed in the context of source coding and later extended to channel coding for standard coherent channels, approximates the input constellation by a dense high-dimensional coset code that can be approximated well by a continuum, transforming the problem of computing the optimal input distribution subject to an average-power constraint to a problem of finding a minimum-energy shaping region in a high-dimensional continuous space. HCA yields closed-form continuous approximations to the capacity-achieving input distributions and shaping gains at high signal-to-noise ratio. We explain how enumerating a coset code in natural coordinates enables extension of HCA to direct-detection optical channels, allowing one to obtain closed-form approximations for the capacity-achieving input distributions and shaping gains for a variety of direct-detection systems that detect the intensity or Stokes vector and are limited by thermal or optical amplifier noise. We also discuss the implementation of probabilistic shaping in direct-detection systems.
Published in: Journal of Lightwave Technology ( Early Access )
Page(s): 1 - 24
Date of Publication: 14 January 2025

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