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Generalized Stopping Sets and Stopping Redundancy [PDF]
Iterative decoding for linear block codes over erasure channels may be much simpler than optimal decoding but its performance is usually not as good. Here, we present a general iterative decoding technique that gives a more refined trade-off between complexity and performance. In each iteration, a system of equations is solved.
Khaled A.S. Abdel-Ghaffar, Jos H. Weber
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Pseudocodeword weights and stopping sets [PDF]
We examine the structure of pseudocodewords in Tanner graphs and derive lower bounds of pseudocodeword weights. The weight of a pseudocodeword is related to the size of its support set, which forms a stopping set in the Tanner graph.
Kelley, C +3 more
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Stopping Sets of Hermitian Codes
IEEE Transactions on Information Theory, 2016Combinatorial structures called stopping sets are useful in analyzing the performance of a linear code when coupled with an iterative decoding algorithm over an erasure channel. In this paper, we consider stopping sets of Hermitian codes.
Gretchen L Matthews
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Stopping set elimination for LDPC codes [PDF]
This work studies the Stopping-Set Elimination Problem, namely, given a stopping set, how to remove the fewest erasures so that the remaining erasures can be decoded by belief propagation in k iterations (including k =∞). The NP-hardness of the problem is proven. An approximation algorithm is presented for k = 1.
Anxiao Andrew Jiang +6 more
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Small stopping sets in Steiner triple systems
Cryptography and Communications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Charles J Colbourn, Colbourn Charles J
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Stopping sets for physical-layer security
2010 IEEE Information Theory Workshop, 2010Physical-layer security based on wiretap codes can be used to complement cryptographic applications at higher layers of the protocol stack. We assume a passive eavesdropper that has access to noise-corrupted codewords with erasures that are statistically independent to those of the legitimate communication partners.
Willie K. Harrison +4 more
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Stopping set analysis for Hamming codes
IEEE Information Theory Workshop, 2005., 2005In the 2004 Shannon Lecture, McEliece presented an expression for the number of stopping sets of size three in a Hamming code. In this paper, we investigate how this number depends on the parity-check matrix used in the decoding process. First, we present basic results on stopping set enumerators for block codes in general.
Jos H. Weber, Khaled A. S. Abdel-Ghaffar
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Stopping Set Distribution of LDPC Code Ensembles
IEEE Transactions on Information Theory, 2003Stopping sets determine the performance of low-density parity-check (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical
Alon Orlitsky +2 more
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