Multi-dimensional permutation-modulation format for coherent optical communications

Abstract

We introduce the multi-dimensional permutation-modulation format in coherent optical communication systems and analyze its performance, focusing on the power efficiency and the spectral efficiency. In the case of four-dimensional (4D) modulation, the polarization-switched quadrature phase-shift keying (PS-QPSK) modulation format and the polarization quadrature-amplitude modulation (POL-QAM) format can be classified into the permutation modulation format. Other than these well-known modulation formats, we find novel modulation formats trading-off between the power efficiency and the spectral efficiency. With the increase in the dimension, the spectral efficiency can more closely approach the channel capacity predicted from the Shannon's theory. We verify these theoretical characteristics through computer simulations of the symbol-error rate (SER) and bit-error rate (BER) performances. For example, the newly-found eight-dimensional (8D) permutation-modulation format can improve the spectral efficiency up to 2.75 bit/s/Hz/pol/channel, while the power penalty against QPSK is about 1 dB at BER=10(-3).

50 Years of Permutation, Spatial and Index Modulation: From Classic RF to Visible Light Communications and Data Storage

“…2013 Mittelholzer et al [46] Patented a PM concept applied to a solid-state storage device to mitigate the effects of drift noise. 2015 Ishimura and Kikuchi [66] Applied the PM concept to coherent optical communications.…”

Constructive Methods for the Design and Labeling of Four-Dimensional Modulations

“…• The design of 4D modulations using Hopf fibres is a constructive method that differs from other approaches based solely on permutation of vector coordinates [5], [6], [2]. An advantage of the method presented here is the direct relation between the projected modulations and the physical characteristics of the signal to be transmitted in both the optical domain (Stokes parameters) and in the electrical domain (voltages as coordinates of 4D vectors);…”

“…I N the recent scenario of coherent optical communications the design of uncoded modulations has been performed mainly through the permutation of vector coordinates [1], [2]. The simplicity and efficiency explains why this method has gained great prominence in optical communication systems.…”

Optimized Eight-Dimensional Lattice Modulation Format for IM-DD 56 Gb/s Optical Interconnections Using 850 nm VCSELs

“…Besides, formats optimized with D 4 lattice can be equivalently obtained from the conventional PDM-mQAM by applying a four-dimensional set partitioning scheme [15]. Eight-dimensional formats have also been investigated recently [16]- [18]. A higher dimensional one, binary 24-dimensional modulation format, is also discussed in [19].…”