Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This 4-neighbourhood topological simplicity makes the application of convolutional masks straightforward for time series data, such as video applications, but many high-dimens...

Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing harmonic motions can all leverage redundancies introduced by convolution. Solving problems involving sparse and convolutional constraints remains a difficult co...

The generalized Singleton bound and MDS-convolutional codes are reviewed. For each n, k and 6 an elementary construction of rate k / n MDS convolutional codes of degree 6 is given.

Using a new parity-check matrix, a class of convolutional codes with a designed free distance is introduced. This new class of codes has many characteristics of BCH block codes, therefore, we call these codes BCH convolutional codes.

In this note we introduce the concept of group convolutional code. We make a complete classification of the minimal S 3-convolutional codes over the field of five elements by means of Jategaonkar's theorems .

Using a new parity-check matrix, a class of convolutional codes with a designed free distance is introduced. This new class of codes has many characteristics of BCH block codes, therefore, we call these codes BCH convolutional codes.

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. Those results are obtained thanks to a module-theoretic framework which has been developed in linear control.

I present a new way to parallelize the training of convolutional neural networks across multiple GPUs. The method scales significantly better than all alternatives when applied to modern convolutional neural

Recently, we proposed a new design technique to construct high-rate convolutional codes based on a structure formed by a block encoder and a simpler convolutional encoder [1]. The search technique was based on the optimization of the output weight enumerating function of the code. Here, we prove that every (n, n − 1) convolutional code can be reduced to this structure. Following this result and...

Compressive sensing (CS), aiming to reconstruct an image/signal from a small set of random measurements has attracted considerable attentions in recent years. Due to the high dimensionality of images, previous CS methods mainly work on image blocks to avoid the huge requirements of memory and computation, i.e., image blocks are measured with Gaussian random matrices, and the whole images are re...