459 research outputs found
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
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 of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
Efficient Maximum-Likelihood Decoding of Linear Block Codes on Binary Memoryless Channels
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 commercial integer program
solver CPLEX, and for all considered codes our approach is faster for both low
and high signal-to-noise ratios. For instance, for the benchmark (155,64)
Tanner code our algorithm is more than 11 times as fast as CPLEX for an SNR of
1.0 dB on the additive white Gaussian noise channel. By a small modification,
our algorithm can be used to calculate the minimum distance, which we have
again verified to be much faster than using the CPLEX solver.Comment: Submitted to 2014 International Symposium on Information Theory. 5
Pages. Accepte
Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes
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 -symmetric, and make a connection to finite graph covers of the
3D-TC factor graph. This connection is used to show that the support set of any
pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum
a posteriori constituent decoders on the binary erasure channel. Furthermore,
we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a
finite-length minimum pseudoweight analysis for small cover degrees. Also, an
explicit description of the fundamental cone of the 3D-TC polytope is given.
Finally, we present an extensive numerical study of small-to-medium block
length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the
minimum distance and/or the stopping distance is
high, the minimum pseudoweight (on the additive white Gaussian noise channel)
is strictly smaller than both the and the , and 2)
the minimum pseudoweight grows with the block length, at least for
small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication
Introduction to Mathematical Programming-Based Error-Correction Decoding
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.Comment: LaTeX sources maintained here: https://github.com/supermihi/lpdintr
Pseudocodewords of linear programming decoding of 3-dimensional turbo codes
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 decoder for conventional turbo codes proposed by Feldman in his thesis. The vertices of this relaxed polytope are the pseudocodewords. We show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we present a numerical study of small block length 3D-TCs, which shows that typically the minimum pseudoweight (on the additive white Gaussian noise (AWGN) channel) is smaller than both the minimum distance and the stopping distance. In particular, we performed an exhaustive search over all interleaver pairs in the 3D-TC (with input block length K = 128) based on quadratic permutation polynomials over integer rings with a quadratic inverse. The search shows that the best minimum AWGN pseudoweight is strictly smaller than the best minimum/stopping distance
Peergruppenarbeit
In diesem Beitrag werde ich mich mit den Spezifika der Peergruppenarbeit beschäftigen. Unter diesem Begriff
verstehen wir einen strukturierten Austausch in einer Gruppe von Lernenden, bei dem jeder Lernende die
Möglichkeit bekommt, von der Kompetenz und der Erfahrung anderer Sprachlerner zu profitieren, um für sich
selbst passende Lösungen zu finden. In der Peergruppenarbeit "beraten" Lernende unter der Leitung eines
geschulten Moderators andere Lernende und werden somit als "Experten", mit ihren Kompetenzen und ihrer
Erfahrung beim Lernen, ernst genommen. In der Fachliteratur finden sich für ähnliche Konzepte die
unterschiedlichsten Bezeichnungen, wie Kooperative Beratung, Kollegiale Supervision, peer coaching und peer
consultation
Transformation und Ausmittelung bestimmter Integrale : Abhandlung welche mit Genehmigung einer hochverordneten physiko-mathematischen Fakultät der Kaiserlichen Universität Dorpat pro venia legendi öffentlich vertheidigen wird
http://tartu.ester.ee/record=b1973357~S1*es
Untersuchungen über die lineären Differentialgleichungen der zweiten und dritten Ordnung
http://tartu.ester.ee/record=b1867935~S1*es
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