Fogal, S. L. and McEliece, Robert and Thorpe, Jeremy (2005) Enumerators for protograph ensembles of LDPC codes. In: 2005 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, pp. 2156-2160. ISBN 0-7803-9150-0 http://resolver.caltech.edu/CaltechAUTHORS:20110810-094621665
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This paper considers the problem of finding average enumerators for the class of protograph ensembles, which are related in a certain way to quasi-cyclic codes. Our methods, which are necessarily different from those used to compute enumerators for classical irregular ensembles, can be applied to both codeword and stopping set weight enumerators. The method divides codewords into types based on their partial weight enumerator. For each type, an exponent can be computed for the average number of codewords of that type. Maximizing over types of fixed average weight gives the average enumerator which we seek. Although this maximization step is in general difficult because of non-unique local maxima, we can compute it for simple cases. We show that certain ensembles exist which have a linearly growing minimum distance with high probability, while others have at most sublinearly growing minimum distance with high probability.
|Item Type:||Book Section|
|Additional Information:||© 2005 IEEE. Issue Date: 4-9 Sept. 2005. Date of Current Version: 31 October 2005.|
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|Official Citation:||Fogal, S.L.; McEliece, R.; Thorpe, J.; , "Enumerators for protograph ensembles of LDPC codes," Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on , vol., no., pp.2156-2160, 4-9 Sept. 2005 doi: 10.1109/ISIT.2005.1523728 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1523728&isnumber=32581|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||12 Sep 2011 15:52|
|Last Modified:||12 Sep 2011 15:52|
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