Title | Codes, Systems, and Graphical Models [electronic resource] / edited by Brian Marcus, Joachim Rosenthal |
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Imprint | New York, NY : Springer New York, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0165-3 |
Descript | XIII, 513 p. 18 illus. online resource |
1. Overviews -- An introduction to the analysis of iterative coding systems -- Connections between linear systems and convolutional codes -- Multi-dimensional symbolic dynamical systems -- 2. Codes on Graphs -- Linear-congruence constructions of low-density parity-check codes -- On the effective weights of pseudocodewords for codes defined on graphs with cycles -- Evaluation of Gallager codes for short block length and high rate applications -- Two small Gallager codes -- Mildly non-linear codes -- Capacity-achieving sequences -- Hypertrellis: A generalization of trellis and factor graph -- 3: Decoding Techniques -- BSC thresholds for code ensembles based on โtypical pairsโ decoding -- Properties of the tailbiting BCJR decoder -- Iterative decoding of tail-biting trellises and connections with symbolic dynamics -- Algorithms for decoding and interpolation -- An algebraic description of iterative decoding schemes -- Recursive construction of Grรถbner bases for the solution of polynomial congruences -- On iterative decoding of cycle codes of graphs -- 4. Convolutional Codes and Codes Over Rings -- Convolutional codes over finite Abelian groups: Some basic results -- Symbolic dynamics and convolutional codes -- Linear codes and their duals over artinian rings -- Unit memory convolutional codes with maximum distance -- Basic properties of multidimensional convolutional codes -- 5. Symbolic Dynamics and Automata Theory -- Length distributions and regular sequences -- Handelmanโs theorem on polynomials with positive multiples -- Topological dynamics of cellular automata -- A spanning tree invariant for Markov shifts -- List of workshop participants