Ultra-Sparse Non-Binary LDPC Codes for Probabilistic Amplitude Shaping

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for power-efficient communication. Ultra-sparse low-density parity-check codes over GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary LDPC codes at a spectral efficiency of 1.5 bits per channel use and a blocklength of 576 bits. The simulation results are compared to finite length coding bounds and complemented by density evolution analysis.Comment: Accepted for Globecom 201

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Probabilistic Shaping for Multidimensional Signals with Autoencoder-based End-to-end Learning

This work proposes a system that optimises multidimensional signal transmission, utilising signals with probabilistic shaping designed with the aid of end-to-end learning of an autoencoder-based architecture. For the first time, this work reports bit mapping optimisation for multidimensional signals and applied the newly derived optimised signals to the probabilistic shaping system. The autoencoder employs two neural networks for the transceiver, separated by the embedded channel. The optimisation of the autoencoder configuration is implemented for probabilistic shaping for n-dimensional signals. Specifically, We investigate a 4-dimensional (4D) signal employing 2 successive time slots that has better noise immunity relative to regular 2-dimensional quadrature amplitude modulation (QAM) signals. We propose a new application of autoencoders in communication systems based on 4D signals and apply machine learning to optimise the 4D probabilistic shaping on the basis of receiver signal-to-noise-ratio (SNR). The performance of the optimised probabilistically shaped 4D signals is evaluated in terms of the bit error rate (BER) and mutual information. Simulation results show that the proposed probabilistically shaped 4D signal achieves better BER performance relative to the unshaped 4D and regular 2D QAM. We demonstrate the mutual information of the proposed signal with varying SNR, showing its improved capacity in comparison with other constellations