Title :
On concentration of measures for LDPC code ensembles
Author :
Sason, Igal ; Eshel, Ronen
Author_Institution :
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel
fDate :
July 31 2011-Aug. 5 2011
Abstract :
This work considers the concentration of measures for low-density parity-check (LDPC) code ensembles. The two results derived in this paper follow from Azuma´s inequality for Doob martingales with bounded differences. The first result is a tightened concentration inequality for the conditional entropy (originally derived by Méasson et al.), and the second result is a concentration inequality for the cardinality of the fundamental systems of cycles of a bipartite graph from the ensemble.
Keywords :
entropy; graph theory; parity check codes; Azuma inequality; Doob martingales; LDPC code ensembles; bipartite graph; cardinality; conditional entropy; fundamental systems; low-density parity-check code ensembles; tightened concentration inequality; Bipartite graph; Channel capacity; Entropy; Iterative decoding; Upper bound; Azuma´s inequality; concentration of measures; low-density parity-check (LDPC) codes; martingales;
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2011.6033740
