  Decoding error-correctiong codes by methods of mathematical optimization,
most importantly linear programming, has become an important alternative
approach to both algebraic and iterative decoding methods since its
introduction by Feldman et al. At first celebrated mainly for its analytical
powers, real-world applications of LP decoding are now within reach thanks to
most recent research. This document gives an elaborate introduction into both
mathematical optimization and coding theory as well as a review of the
contributions by which these two areas have found common ground.
