Partial Enumerative Sphere Shaping

The dependency between the Gaussianity of the input distribution for the additive white Gaussian noise (AWGN) channel and the gap-to-capacity is discussed. We show that a set of particular approximations to the Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap. We relate these symbol-level distributions to bit-level distributions, and demonstrate that they correspond to keeping some of the amplitude bit-levels uniform and independent of the others. Then we propose partial enumerative sphere shaping (P-ESS) to realize such distributions in the probabilistic amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit that shaping 2 amplitude bits of 16-ASK have almost the same performance as shaping 3 bits, which is 1.3 dB more power-efficient than uniform signaling at a rate of 3 bit/symbol. In this way, required storage and computational complexity of shaping are reduced by factors of 6 and 3, respectively.Comment: 6 pages, 6 figure

Diffusion Variational Autoencoders

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.Comment: 10 pages, 8 figures Added an appendix with derivation of asymptotic expansion of KL divergence for heat kernel on arbitrary Riemannian manifolds, and an appendix with new experiments on binarized MNIST. Added a previously missing factor in the asymptotic expansion of the heat kernel and corrected a coefficient in asymptotic expansion KL divergence; further minor edit

Scanner Invariant Representations for Diffusion MRI Harmonization

Purpose: In the present work we describe the correction of diffusion-weighted MRI for site and scanner biases using a novel method based on invariant representation. Theory and Methods: Pooled imaging data from multiple sources are subject to variation between the sources. Correcting for these biases has become very important as imaging studies increase in size and multi-site cases become more common. We propose learning an intermediate representation invariant to site/protocol variables, a technique adapted from information theory-based algorithmic fairness; by leveraging the data processing inequality, such a representation can then be used to create an image reconstruction that is uninformative of its original source, yet still faithful to underlying structures. To implement this, we use a deep learning method based on variational auto-encoders (VAE) to construct scanner invariant encodings of the imaging data. Results: To evaluate our method, we use training data from the 2018 MICCAI Computational Diffusion MRI (CDMRI) Challenge Harmonization dataset. Our proposed method shows improvements on independent test data relative to a recently published baseline method on each subtask, mapping data from three different scanning contexts to and from one separate target scanning context. Conclusion: As imaging studies continue to grow, the use of pooled multi-site imaging will similarly increase. Invariant representation presents a strong candidate for the harmonization of these data

Near-capacity dirty-paper code design : a source-channel coding approach

This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity

Miniaturized modular manipulator design for high precision assembly and manipulation tasks

In this paper, design and control issues for the development of miniaturized manipulators which are aimed to be used in high precision assembly and manipulation tasks are presented. The developed manipulators are size adapted devices, miniaturized versions of conventional robots based on well-known kinematic structures. 3 degrees of freedom (DOF) delta robot and a 2 DOF pantograph mechanism enhanced with a rotational axis at the tip and a Z axis actuating the whole mechanism are given as examples of study. These parallel mechanisms are designed and developed to be used in modular assembly systems for the realization of high precision assembly and manipulation tasks. In that sense, modularity is addressed as an important design consideration. The design procedures are given in details in order to provide solutions for miniaturization and experimental results are given to show the achieved performances