@article {27150,
	title = {Adaptive linear programming decoding of nonbinary linear codes over prime fields},
	journal = { IEEE Transactions on Information Theory },
	volume = {66},
	number = {3},
	year = {2020},
	pages = {1281-1317},
	publisher = {IEEE},
	author = {Rosnes, Eirik and Helmling, Michael}
}
@inproceedings {25105,
	title = {On adaptive linear programming decoding of linear codes over GF(8)},
	journal = {Inf. Theory Appl. (ITA)},
	year = {2016},
	month = {02/2016},
	publisher = {IEEE Press},
	abstract = {In this work, we consider adaptive linear programming (LP) decoding of linear codes over GF(8). In particular, we give explicit constructions of valid inequalities (using no auxiliary variables) for the codeword polytope (or the convex hull) of the so-called constant-weight embedding of a single parity-check code over GF(8) that all are facet-defining. We conjecture that these inequalities together with so-called simplex constraints give a complete and irredundant description of the embedded (under the constant-weight embedding) codeword polytope. Furthermore, these sets of inequalities are used to develop an efficient (as compared to a static approach) exact (assuming that the conjecture is true) adaptive LP decoder for linear codes over GF(8). Numerical results show that only a very small subset of these inequalities is necessary for achieving close-to-exact LP decoding performance.},
	author = {Rosnes, Eirik and Helmling, Michael}
}
@inproceedings {25100,
	title = {On adaptive linear programming decoding of nonbinary linear codes over prime fields},
	journal = {9th Int. Symp. Turbo Codes \& Iterative Inf. Processing (ISTC)},
	year = {2016},
	month = {09/2016},
	pages = {106-110},
	publisher = {IEEE Press},
	abstract = {In this work, we study linear programming (LP) decoding of nonbinary linear codes over prime fields. In particular, we develop a novel separation algorithm for valid inequalities describing the codeword polytope of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The algorithm has linear (in the length of the SPC code) complexity, is structurally different from the one for binary codes, and is based on the principle of dynamic programming. Furthermore, it is the basis of the proposed efficient (relaxed) adaptive LP (ALP) decoder for general (non-SPC) linear codes over any prime field, generalizing the well-known ALP decoding algorithm for binary codes. Numerical results show that the ALP decoding algorithm is very efficient compared to a static approach.},
	author = {Rosnes, Eirik and Helmling, Michael}
}
@inproceedings {25104,
	title = {Constructing valid convex hull inequalities for single parity-check codes over prime fields},
	journal = {IEEE International Symposium on Information Theory (ISIT)},
	year = {2016},
	month = {07/2016},
	pages = {1939-1943},
	publisher = {IEEE Press},
	abstract = {In this work, we present an explicit construction of valid inequalities (using no auxiliary variables) for the convex hull of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on classes of building blocks that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining, while we conjecture this to be true if and only if the class is valid and symmetric. Such sets of inequalities have not appeared in the literature before, have a strong theoretical interest, and can be used to develop an efficient (relaxed) adaptive linear programming decoder for general (non-SPC) linear codes over prime fields.},
	author = {Rosnes, Eirik and Helmling, Michael}
}
@inproceedings {23492,
	title = {On adaptive linear programming decoding of ternary linear codes},
	journal = {IEEE Information Theory Workshop},
	year = {2015},
	month = {05/2015},
	publisher = {IEEE Press},
	author = {Rosnes, Eirik and Helmling, Michael}
}
@misc {23506,
	title = {On maximum-likelihood decoding of polar codes},
	howpublished = {Jerusalem, Israel},
	year = {2015},
	type = {Invited talk at the 2015 IEEE Information Theory Workshop},
	author = {Helmling, Michael and Rosnes, Eirik and Ruzika, Stefan}
}
@inproceedings {23504,
	title = {Efficient maximum-likelihood decoding of linear block codes on binary memoryless channels},
	journal = {IEEE International Symposium on Information Theory},
	year = {2014},
	month = {07/2014},
	pages = {2589-2593},
	publisher = {IEEE Press},
	author = {Helmling, Michael and Rosnes, Eirik and Ruzika, Stefan and Scholl, Stefan}
}
@article {23499,
	title = {Minimum pseudoweight analysis of 3-dimensional turbo codes},
	journal = {IEEE Transactions on Communications},
	volume = {62},
	year = {2014},
	month = {07/2014},
	pages = {2170-2182},
	publisher = {IEEE Press},
	author = {Rosnes, Eirik and Helmling, Michael and Alexandre Graell i {Amat}}
}
