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The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over…
We consider transmission over a binary-input additive white Gaussian noise channel using low-density parity-check codes. One of the most popular techniques for decoding low-density parity-check codes is the linear programming decoder. In…
Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational…
Network coding enhances performance in network communications and distributed storage by increasing throughput and robustness while reducing latency. Batched Sparse (BATS) codes are a class of capacity-achieving network codes, but their…
Convolutional sparse coding (CSC) is an important building block of many computer vision applications ranging from image and video compression to deep learning. We present two contributions to the state of the art in CSC. First, we…
A recent line of work has shown promise in using sparse autoencoders (SAEs) to uncover interpretable features in neural network representations. However, the simple linear-nonlinear encoding mechanism in SAEs limits their ability to perform…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
The \emph{index coding} problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad-hoc networks. An instance of the index coding problem includes a…
Autoencoding has achieved great empirical success as a framework for learning generative models for natural images. Autoencoders often use generic deep networks as the encoder or decoder, which are difficult to interpret, and the learned…
This letter considers a network comprising a transmitter, which employs random linear network coding to encode a message, a legitimate receiver, which can recover the message if it gathers a sufficient number of linearly independent coded…
We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors. By deriving improved variance bounds related to binary Gaussian…
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…
The vast existing wireless infrastructure features a variety of systems and standards. It is of significant practical value to introduce new features and devices without changing the physical layer/hardware infrastructure, but upgrade it…
We focus on designing error-correcting codes for the symmetric Gaussian broadcast channel with feedback. Feedback not only expands the capacity region of the broadcast channel but also enhances transmission reliability. In this work, we…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
In this paper, we propose \textit{coded compressive sensing} that recovers an $n$-dimensional integer sparse signal vector from a noisy and quantized measurement vector whose dimension $m$ is far-fewer than $n$. The core idea of coded…