Conditional entropy of non-binary LDPC codes over the BEC
Rathi, V.
Sch. of Comput. & Commun. Sci., EPFL, Zurich;
This paper appears in: Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Publication Date: 6-11 July 2008
On page(s): 945-949
Location: Toronto, ON,
ISBN: 978-1-4244-2256-2
INSPEC Accession Number: 10156546
Digital Object Identifier: 10.1109/ISIT.2008.4595126
Current Version Published: 2008-08-08
Abstract
We consider transmission over the binary erasure channel (BEC) using non-binary LDPC codes. We generalize the concept of stopping sets to non-binary LDPC codes. We give a combinatorial characterization of decoding failures for non-binary LDPC codes decoded via Belief Propagation (BP). Using the density evolution analysis, we compute the asymptotic residual degree distribution for non-binary LDPC codes. In order to show that asymptotically almost every code in the non-binary LDPC ensemble has a rate equal to the design rate, we generalize the arguments of Measson, Montanari, and Urbanke to the non-binary setting. This generalization enables us to compute the conditional entropy of non-binary LDPC codes. We observe that the Maxwell construction of Measson, Montanari, and Urbanke relating the performance of MAP and BP decoding, holds in the setting of non-binary LDPC codes.
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