Petabyte-scale distributed storage systems are currently transitioning to erasure codes to
achieve higher storage efficiency. Classical codes, such as Reed-Solomon (RS), are highly …

This paper studies the problem of recovering a sparse signal x∈ ℝ n from highly corrupted
linear measurements y= Ax+ e∈ ℝ m, where e is an unknown error vector whose nonzero …

We present a mathematical connection between channel coding and compressed sensing.
In particular, we link, on the one hand, channel coding linear programming decoding (CC …

Mathematical programming is a branch of applied mathematics and has recently been used
to derive new decoding approaches, challenging established but often heuristic algorithms …

Detectability of failures of linear programming (LP) decoding and the potential for
improvement by adding new constraints motivate the use of an adaptive approach in …

This paper provides a link between matroid theory and locally repairable codes (LRCs) that
are either linear or more generally almost affine. Using this link, new results on both LRCs …

The Highly Connected Matroids in Minor-Closed Classes Page 1 Ann. Comb. 19 (2015) 107–123
DOI 10.1007/s00026-015-0251-3 Published online January 15, 2015 © Springer Basel …

This is a tale of two linear programming decoders, namely channel coding linear
programming decoding (CC-LPD) and compressed sensing linear programming decoding …

We relate the notion of matroid pathwidth to the minimum trellis state-complexity (which we
term trellis-width) of a linear code and to the pathwidth of a graph. By reducing from the …

Matroids provide one of the most elegant structures for algorithm design. This is best
identified by the Edmonds-Rado theorem relating the success of the simple greedy …