Multidimensional Optimized Optical Modulation Formats

Abstract

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Two-Stage Coded Modulation for Hurwitz Constellations in Fiber-Optical Communications

“…2) D 4 Lattice: If N > 1, the packing of Z N is not optimal. Considering N = 4, the checkerboard lattice D 4 (aka Schläfli lattice) is the densest packing with a packing gain 1 of 3 dB over Z 4 [3], [10], [24]. It can, e.g., be defined as a subset of Z 4 where the sum of all coordinates is even (even parity); the minimum distance between the lattice points then reads d min = 2, cf.…”

“…In fiber-optical transmission, D 4 -based constellations have already been considered and are well-known as M -ary SP-QAM formats [10], [25], [26]. In order to understand the relation between the SP-QAM formats and the proposed Hurwitz constellations, it is instructive to review the well-known binary partitioning chain 2 of 4D lattices [24, P. 436], which takes the following form 3 .…”

“…for the chain given in (1). The considered SP-QAM formats are typically based on a construction technique called reduction [10], [25], where starting from a Z 4 -based constellation (i.e., DP square QAM) the number of signal points is halved. Thereby, the minimum Euclidean distance d min is effectively increased by a factor of √ 2 while maintaining the same hypercubic bound.…”

“…In fact, the (re-)discovery of higher-dimensional modulation has triggered considerable effort in identifying novel modulation formats and their characterization in simulations [5], [6] and system experiments [7]- [9]. A comprehensive summary can be found in [10]; an online database of 4D packings is available at [11].…”

“…In this contribution, we consider the coded-modulation scheme from [19] that employs a set of 4D modulation formats based on the D 4 lattice-termed Hurwitz constellations-using binary SD-FEC. Hurwitz constellations belong to a subset of the well-known set-partitioned (SP)-QAM formats [10]. To utilize the packing gain of the proposed D 4 -based signal sets, a suited coded-modulation scheme must be designed.…”