Lecture Notes for Math 696 Coding Theory Iterative Decoding
نویسنده
چکیده
These notes are my effort to understand several articles concerning decoding of lowdensity parity-check codes. The paper by Aji and McEliece called “The Generalized Distributive Law” [6] gives a clear description of an algorithm that is useful in many areas of applied mathematics including error correction: They cite artificial intelligence, belief propagation algorithms, fast Fourier transforms and several decoding algorithms. The GDL yields a computationally efficient algorithm for computing certain complicated formulas. The algorithm is best understood by looking at a graph that expresses the relationship between the variables and the functions that occur in the formula. The algorithm involves “message passing” between the vertices of the graph. I will actually use the graphical representation from a different article, “Factor Graphs and the SumProduct Algorithm” by Kschischang, Frey and Loeliger. The algorithm is only exact when the underlying graph is a tree, but numerous experiments using these message passing algorithms for decoding have been done, and the performance for non-trees is remarkably good. Theoretical understanding of the algorithm has improved greatly in the last three years, but my impression is that a definitive explanation of the performance is still lacking.
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Coding Theory Lecture Notes
These are the notes for the 2011 Summer Tutorial on Coding Theory. I have not gone through and given citations or references for all of the results given here, but the presentation relies heavily on two sources, van Lint’s Introduction to Coding Theory and the book of Huffman and Pless Fundamentals of Error-Correcting Codes. I also used course notes written by Sebastian Pancratz from a Part II ...
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