Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

A denoising algorithm seeks to remove noise, errors, or perturbations from a signal.
Extensive research has been devoted to this arena over the last several decades, and as a …

We investigate spatially coupled code ensembles. For transmission over the binary erasure
channel, it was recently shown that spatial coupling increases the belief propagation …

In this paper, we construct protograph-based spatially coupled low-density parity-check
(LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner …

This paper presents a framework for compressed sensing that bridges a gap between
existing theory and the current use of compressed sensing in many real-world applications …

We consider a class of approximated message passing (AMP) algorithms and characterize
their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof …

Compressed sensing is a signal processing method that acquires data directly in a
compressed form. This allows one to make fewer measurements than were considered …

Compressed sensing has triggered a major evolution in signal acquisition. It consists of
sampling a sparse signal at low rate and later using computational power for the exact …

We study the compressed sensing reconstruction problem for a broad class of random, band-
diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in …

In the group testing problem, which goes back to the work of Dorfman (1943), we aim to
identify a small set of $ k\sim n^\theta $ infected individuals out of a population size $ n …