An Energy Efficient QAM Modulation with Multidimensional Signal Constellation

Packing constellations points in higher dimensions, the concept of multidimensional modulation exploits the idea drawn from geometry for searching dense sphere packings in a given dimension, utilising it to minimise the average energy of the underlying constellations. The following work analyses the impactof spherical shaping of the constellations bound instead of the traditional, hyper-cubical bound. Balanced constellation schemes are obtained with the N -dimensional simplex merging algorithm. The performance of constellations of dimensions 2, 4 and 6 is compared to the performance of QAM modulations of equivalent throughputs in the sense of bits transmitted per complex (two- dimensional) symbols. The considered constellations give an approximately 0.7 dB to 1 dB gain in terms of BER over a standard QAM modulation

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

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

Bases équilibrées et signalisation multidimensionnelle

On envisage ici le problème de la construction d'une base orthonormée, relativement au produit scalaire euclidien, dont les éléments ont tous la même norme vis à vis d'un autre produit scalaire. On propose un algorithme itératif pour réaliser cette opération. Une application possible de cette méthode vise à construire des bases de signalisation pour les modulations numériques multi-dimensionnelles possédant une proportion d'énergie bornée hors d'une bande de fréquences prescrite. Par ailleurs, pour quantifier le gain lié à l'augmentation de dimensionnallité des modulations PSK, on propose une nouvelle formule asymptotique de probabilité d'erreur pour de telles modulations

Design and Software Validation of Coded Communication Schemes using Multidimensional Signal Sets without Constellation Expansion Penalty in Band-Limited Gaussian and Fading Channels

It has been well reported that the use of multidimensional constellation signals can help to reduce the bit error rate in Additive Gaussian channels by using the hyperspace geometry more efficiently. Similarly, in fading channels, dimensionality provides an inherent signal space diversity (distinct components between two constellations points), so the amplitude degradation of the signal are combated significantly better. Moreover, the set of n-dimensional signals also provides great compatibility with various Trellis Coded modulation schemes: N-dimensional signaling joined with a convolutional encoder uses fewer redundant bits for each 2D signaling interval, and increases intra-subset minimum squared Euclidean distance (MSED) to approach the ultimate capacity limit predicted by Shannon\u27s theory. The multidimensional signals perform better for the same complexity than two-dimensional schemes. The inherent constellation expansion penalty factor paid for using classical mapping structures can be decreased by enlarging the constellation\u27s dimension. In this thesis, a multidimensional signal set construction paradigm that completely avoids the constellation expansion penalty is used in Band-limited channels and in fading channels. As such, theoretical work on performance analysis and computer simulations for Quadrature-Quadrature Phase Shift Keying (Q2PSK), Constant Envelope (CE) Q2PSK, and trellis-coded 16D CEQ2PSK in ideal band-limited channels of various bandwidths is presented along with a novel discussion on visualization techniques for 4D Quadrature-Quadrature Phase Shift Keying (Q2PSK), Saha\u27s Constant Envelope (CE) Q2PSK, and Cartwright\u27s CEQ2PSK in ideal band-limited channels. Furthermore, a metric designed to be used in fading channels, with Hamming Distance (HD) as a primary concern and Euclidean distance (ED) as secondary is also introduced. Simulation results show that the 16D TCM CEQ2PSK system performs well in channels with AWGN and fading, even with the simplest convolutional encoder tested; achievable coding gains using 16-D CEQ2PSK Expanded TCM schemes under various conditions are finally reported

Sequential decoding of trellis codes through ISI channels

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 56-57).by Patrick M. Maurer.M.S

Investigation of coding and equalization for the digital HDTV terrestrial broadcast channel

Includes bibliographical references (p. 241-248).Supported by the Advanced Telecommunications Research Program.Julien J. Nicolas