Michael Helmling

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Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions(More)
It has been shown that non-binary LDPC codes have a better error correction performance than binary codes for short block lengths. However, this advantage was up to now only shown under belief propagation decoding. To gain new insights, we investigate binary and non-binary codes under ML decoding. Our analysis includes different modulation schemes and(More)
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE Trans. Inf. Theory, 2012) for obtaining lower bounds. We have compared our proposed algorithm to the state-of-the-art(More)
In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs), recently introduced by Berrou et al.. Here, we consider binary 3D-TCs while the original work of Berrou et al. considered double-binary codes. We present a relaxed LP decoder for 3D-TCs, which is an adaptation of the relaxed LP(More)
We present a novel algorithm that solves the turbo code LP decoding problem in a finite number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the turbo code. Previous attempts to exploit the combinatorial graph structure only led to algorithms which are either of(More)
In this work, we consider adaptive linear programming (LP) decoding of ternary linear codes, i. e., linear codes over the finite field F<sub>q</sub> with q = 3 elements. In particular, we characterize completely the codeword polytope (or the convex hull) of the binary image, under Flanagan's embedding, of a ternary single parity-check code. Then, this(More)
In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and C-symmetric, and make a connection to finite(More)
Channel coding and mathematical optimization— two omnipresent branches of science which heavily influence our everyday life, which is certainly unimaginable without the epochal achievements of each of the two disciplines since they affect nearly every communication system as well as every transportation, manufacturing, and organization process. The(More)