Abstract
The last two decades have witnessed a full revival of graph based codes. The advent of Turbo codes [1] in the early 1990’s, the revival of Gallager’s LDPC codes in the 1990’s [12,11,7,8], and a decade long research on their properties [16] have brought fundamental changes to coding theory in general, and to the practical design of codes in particular. Today, a number of international standards such as DVB-S2, ITU-T G.hn, or 10 GBase-T use LDPC codes for the transmission of signals.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berrou, C., Glavieux, A., Thitimajshima, P.: Near Shannon limit error-correcting coding and decoding. In: Proceedings of ICC 1993, Geneva, Switzerland, pp. 1064–1070 (May 1993)
Byers, J., Luby, M., Mitzenmacher, M., Rege, A.: A digital fountain approach to reliable distribution of bulk data. In: proceedings of ACM SIGCOMM 1988 (1998)
Etesami, O., Shokrollahi, A.: Raptor codes on binary memoryless symmetric channels. IEEE Trans. Inform. Theory 52(5), 2033–2051 (2006)
Kolchin, V.: Random Graphs. Encyclopedia of Mathematics and its Applications, vol. 53. Cambridge University Press, Cambridge (1999)
Kumar, K., Pakzad, P., Salavati, A., Shokrollahi, A.: Phase transitions for mutual information. In: 2010 6th International Symposium on Turbo Codes and Iterative Information Processing (ISTC), pp. 137–141 (2010)
Luby, M.: LT-codes. In: Proceedings of the 43rd Annual IEEE Symposium on the Foundations of Computer Science (FOCS), pp. 271–280 (2002)
Luby, M., Mitzenmacher, M., Shokrollahi, A., Spielman, D.: Analysis of low density codes and improved designs using irregular graphs. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pp. 249–258 (1998)
Luby, M., Mitzenmacher, M., Shokrollahi, A., Spielman, D.: Improved low-density parity-check codes using irregular graphs and belief propagation. In: Proceedings 1998 IEEE International Symposium on Information Theory, p. 117 (1998)
Luby, M., Mitzenmacher, M., Shokrollahi, A., Spielman, D.: Efficient erasure correcting codes. IEEE Trans. Inform. Theory 47, 569–584 (2001)
Luby, M.G.: Lt codes. In: Proceedings of 43rd IEEE Symposium Foundations of Computer Science, p. 10 (2002)
MacKay, D.: Good error-correcting codes based on very sparse matrices. IEEE Trans. Inform. Theory 45, 399–431 (1999)
MacKay, D., Neal, R.: Good codes based on very sparse matrices. In: Boyd, C. (ed.) Cryptography and Coding 1995. LNCS, vol. 1025, pp. 100–111. Springer, Heidelberg (1995)
Measson, C., Montanari, A., Urbanke, R.: Maxwell Construction: The Hidden Bridge Between Iterativew and Maximum a Posteriori Decoding. IEEE Transansactions on Information Theory 54(12), 5277–5307 (2008)
Montanari, A.: Tight bounds for ldpc and ldgm codes under map decoding. IEEE Transactions on Information Theory 51(9), 3221–3246 (2005)
Pakzad, P., Shokrollahi, A.: EXIT functions for LT and raptor codes, and asymptotic ranks of random matrices. In: Proc. of the IEEE International Symposium on Information Theory (ISIT), 2007, pp. 411–415 (June 2007)
Richardson, T., Urbanke, R.: Modern Coding Theory. Cambridge University Press, Cambridge (2008)
Shokrollahi, A.: Raptor codes. IEEE Trans. Inform. Theory 52(6), 2551–2567 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shokrollahi, A. (2011). LT-Codes and Phase Transitions for Mutual Information. In: Fehr, S. (eds) Information Theoretic Security. ICITS 2011. Lecture Notes in Computer Science, vol 6673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20728-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-20728-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20727-3
Online ISBN: 978-3-642-20728-0
eBook Packages: Computer ScienceComputer Science (R0)