This tutorial paper provides a foundation for integrating probabilistic shaping (PS) and
forward error correction (FEC). A layered PS-FEC architecture consisting of a PS encoder …

Autoencoder-based geometric shaping is proposed that includes optimizing bit mappings.
Up to 0.2 bits/QAM symbol gain in GMI is achieved for a variety of data rates and in the …

In this paper, we provide a systematic comparison of distribution matching (DM) and sphere
shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For …

Distribution matching (DM) transforms independent and Bernoulli (1/2) distributed bits into a
sequence of output symbols with a desired distribution. A fixed-to-fixed length, invertible DM …

Nonlinear interference (NLI) generated during the propagation of an optical waveform
through the fiber depends on the fourth order standardized moment of the channel input …

Infrared free-space optics (FSO) provide an attractive solution for ultra-high-capacity
wireless communications. However, the full potential of FSO is still being hindered by the …

The interaction between carrier phase recovery and probabilistic amplitude shaping (PAS)
in the nonlinear regime is investigated. We show that, for sufficiently high signal-to-noise …

To achieve a link budget capable of supporting high capacity free space optical
communication (FSO), a high transmit power is required. However, the transmitter can …

Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic
constellation shaping, which provides nearly optimal energy efficiency at low …

The performance of different probabilistic amplitude shaping (PAS) techniques in the
nonlinear regime is investigated, highlighting its dependence on the PAS block length and …