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Graphcover decoding and finitelength analysis of messagepassing iterative decoding of LDPC codes
 IEEE TRANS. INFORM. THEORY
, 2005
"... The goal of the present paper is the derivation of a framework for the finitelength analysis of messagepassing iterative decoding of lowdensity paritycheck codes. To this end we introduce the concept of graphcover decoding. Whereas in maximumlikelihood decoding all codewords in a code are comp ..."
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Cited by 114 (16 self)
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The goal of the present paper is the derivation of a framework for the finitelength analysis of messagepassing iterative decoding of lowdensity paritycheck codes. To this end we introduce the concept of graphcover decoding. Whereas in maximumlikelihood decoding all codewords in a code are competing to be the best explanation of the received vector, under graphcover decoding all codewords in all finite covers of a Tanner graph representation of the code are competing to be the best explanation. We are interested in graphcover decoding because it is a theoretical tool that can be used to show connections between linear programming decoding and messagepassing iterative decoding. Namely, on the one hand it turns out that graphcover decoding is essentially equivalent to linear programming decoding. On the other hand, because iterative, locally operating decoding algorithms like messagepassing iterative decoding cannot distinguish the underlying Tanner graph from any covering graph, graphcover decoding can serve as a model to explain the behavior of messagepassing iterative decoding. Understanding the behavior of graphcover decoding is tantamount to understanding
Course Outline for CS 236610: Recent Advances in Algebraic and Combinatorial Coding Theory
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Two methods for reducing . . .
, 2006
"... We investigate two techniques for reducing the errorfloor of lowdensity paritycheck codes under iterative decoding. Both techniques are developed based on comprehensive analytical and simulation studies of combinatorial properties of trapping sets in codes on graphs. The first technique represent ..."
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We investigate two techniques for reducing the errorfloor of lowdensity paritycheck codes under iterative decoding. Both techniques are developed based on comprehensive analytical and simulation studies of combinatorial properties of trapping sets in codes on graphs. The first technique represents an algorithmic modification of beliefpropagation based on data fusion principles and specialized message averaging methods. The second technique relies on identifying redundant paritycheck matrices of codes that do not contain small trapping sets. In the latter context we introduce the notion of the trapping redundancy of a code and show how decoding with redundant paritycheck matrices can lead to reductions of error rates exceeding an order of magnitude. Our findings are described on the well known [2640,1320] Margulis code.