On Probabilistic Shaping and Learned Decoders with Application to Fiber-Optic Communications

Doctoral thesis, 2020

We live in an ubiquitously connected world whose backbone are optical fibers. Achieving high spectral efficiencies and hence high transmission rates requires a careful combination of forward error correction (FEC) and higher-order modulation. This is referred to as coded modulation. In this thesis, we focus on probabilistic shaping which aims to shape the distribution of the transmitted symbols to the capacity-achieving distribution. For symmetric distributions, probabilistic amplitude shaping (PAS) has been proposed by Böcherer et al.. Certain fiber-optic systems, however, have non-symmetric capacity-achieving distributions and hence, PAS can not be applied.
In the first part of this thesis, we focus on probabilistic shaping for asymmetric distributions. For a nonlinear Fourier transform-based transmission scheme, we introduce probabilistic eigenvalue shaping, where the coded symbols are partially distributed according to the capacity-achieving distribution and partially uniformly distributed. Further, for an intensity modulation with direct-detection (IM/DD) system, we uncover a hidden symmetry of the capacity-achieving distribution. We propose to extend the PAS scheme with a compound construction of a low-density generator matrix code and a low-density parity-check code (LDGM/LDPC) to incorporate this hidden symmetry. For both shaping schemes, we demonstrate significant improvements over the state of the art.
In the second part of this thesis, we address low-complexity, near-maximum-likelihood (ML) decoding of short linear block codes, which play an important role in FEC in fiber-optic communication systems as component codes in staircase codes or generalized LDPC codes. Our work extends neural belief propagation (NBP) introduced by Nachmani et al. where belief propagation decoding is unrolled and weights are placed on the edges. In particular, we consider NBP decoding over an overcomplete parity-check matrix and use the weights of NBP as a measure of the importance of the check nodes (CNs) to decoding. Unimportant CNs are successively pruned. This typically results in a different parity-check matrix in each iteration. We demonstrate that for codes with a dense parity-check matrix such as algebraic codes, our proposed decoder performs close to ML decoding. To further improve the decoding of short LDPC codes, we introduce a two-stage decimation process to NBP decoding. First, we create a list by iterating between a conventional NBP decoder and guessing the least reliable bit. This is followed by iterating between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For short LDPC codes, this results in a significant performance gain.