Geometrically shaped multi-dimensional modulation formats designed by deep learning

Abstract

Geometrically shaped multi-dimensional modulation formats are designed by a bit-wise autoencoder (AE), which is one of the deep learning applications. The optimized four-dimensional (4-D) modulation constellation diagrams in two-dimensional (2-D) projection have highly unique symmetrical constellations with clever labeling. In addition, the numerically evaluated BER performances show that the receiver sensitivities of the optimally shaped multi-dimensional modulation format are equivalent to or better than those of the conventional 4-D and 2-D formats with the same transmission capacity.

Geometrically Shaped Four-Dimensional Modulation Formats for 5–7 Bits/Symbol Designed by Autoencoder

“…Figure 1 shows a communication system over AWGN as an AE to obtain 4D modulation formats. Its configuration is exactly equivalent to the one described in [14], configured with reference to [15]. In the mapper section, a m-th length binary bit vector b is encoded as a one-hot vector, i.e., 2 mdimensional vector, the one element of which is equal to one and zero otherwise.…”

“…Several iterations of mini-batch training with a size proportional to 2 m are performed using the Adam optimization algorithm to minimize the total binary categorical cross entropy calculated from b and a set of p(b j | y). Note that log-likelihood ratio (LLR) of each binary bit is obtained before sigmoid function layer, which leads to optimization of not only the position of constellation points but also labeling of binary bit to each point [14,15].…”

“…Recently, the extension of GS from two dimensions to multi-dimension has been reported for optical fiber transmission systems [13,14]. An autoencoder (AE), a deep learning technique, has been attempted to perform complicated computations to optimize the positions of many constellation points for GS [14,15].…”

“…Recently, the extension of GS from two dimensions to multi-dimension has been reported for optical fiber transmission systems [13,14]. An autoencoder (AE), a deep learning technique, has been attempted to perform complicated computations to optimize the positions of many constellation points for GS [14,15]. The layered configuration for the AE shown in [15] allows us to optimize not only a position of constellation points but also labeling of binary bit to each point simultaneously.…”

An Optimal Adaptive Constellation Design Utilizing an Autoencoder-Based Geometric Shaping Model Framework

“…Based on end-to-end communication, novel autoencoder-based learning of joint geometric and probabilistic constellation shaping for coded modulation systems was proposed [22]. Geometrically shaped multi-dimensional modulation formats are designed via deep learning methods [23], and an end-to-end-based multi-dimensional GS strategy is proposed to achieve phase noise robustness [24]. Additionally, a differentiable GS method based on a blind phase search was also proposed for phase noise channels [25].…”