New Lower Bounds on the Capacity of Optical Fiber Channels via Optimized Shaping and Detection

TL;DR

This paper introduces a novel optimization technique for constellation shaping in optical fiber channels, significantly improving capacity bounds by accounting for nonlinear effects and long memory, with potential for unbounded capacity growth.

Contribution

It presents a new method to optimize shaping distributions in high-dimensional nonlinear optical channels, providing analytical bounds and practical algorithms for capacity enhancement.

Findings

Capacity lower bound can grow unbounded with power in simplified models.

Rejection sampling algorithm effectively estimates achievable rates.

Enhanced decoding metrics improve capacity bounds for dual-polarization channels.

Abstract

Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly increasing the information rate beyond the current limit dictated by fiber nonlinearity. However, this appealing idea is frustrated by the difficulty of designing an effective shaping strategy that takes into account the nonlinearity and long memory of the fiber channel, as well as the possible interplay with other nonlinearity mitigation strategies. As a result, only little progress has been made so far, while the optimal shaping distribution and the ultimate channel capacity remain unknown. In this work, we describe a novel technique to optimize the shaping distribution in a very general setting and high-dimensional space. For a simplified block-memoryless nonlinear optical channel, the capacity lower bound obtained by the proposed technique can be expressed analytically, establishing the conditions for an unbounded growth of capacity with power. In a more realistic scenario, the technique can be implemented by a rejection sampling algorithm driven by a suitable cost function, and the corresponding achievable information rate estimated numerically. The combination of the proposed technique with an improved (non-Gaussian) decoding metric yields a new capacity lower bound for the dual-polarization WDM channel.