R. G. Gallager, Low-density parity-check codes, IEEE Transactions on Information Theory, vol.8, issue.1, 1963.
DOI : 10.1109/TIT.1962.1057683

D. J. Mackay and R. M. Neal, Good codes based on very sparse matrices, Proc. 5th IMA Conference, 1995.
DOI : 10.1007/3-540-60693-9_13

J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988.

F. R. Kschischang, B. J. Frey, and H. A. Loeliger, Factor graphs and the sum-product algorithm, IEEE Transactions on Information Theory, vol.47, issue.2, 2001.
DOI : 10.1109/18.910572

S. Chung, T. J. Richardson, and R. L. Urbanke, Analysis of Sum- Product Decoding of Low-Density Parity-Check Codes Using a Gaussian Approximation, IEEE Transactions on Information Theory, vol.47, issue.2, 2001.

T. J. Richardson and R. L. Urbanke, The capacity of low-density parity-check codes under message-passing decoding, IEEE Transactions on Information Theory, vol.47, issue.2, 2001.
DOI : 10.1109/18.910577

T. Heskes, Stable fixed points of loopy belief propagation are minima of the Bethe free energy, Advances in Neural Information Processing Systems, pp.359-366, 2003.

K. P. Murphy, Y. Weiss, and M. I. Jordan, Loopy belief propagation for approximate inference: an empirical study, Proc. Uncertainty in Artificial Intelligence, 1999.

X. Zheng, F. C. Lau, C. K. Tse, and S. C. Wong, STUDY OF BIFURCATION BEHAVIOR OF LDPC DECODERS, International Journal of Bifurcation and Chaos, vol.16, issue.11, pp.3435-3449, 2005.
DOI : 10.1142/S0218127406016926

J. Sibel, S. Reynal, and D. Declercq, Evidence of chaos in the Belief Propagation for LDPC codes, Chaotic Modeling and Simulations Journal, vol.6, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00736202

T. J. Richardson, Error floors of LDPC codes, Proc. 41st Annual Allerton Conference on Communication, Control and Computing, 2003.

S. Sankaranarayanan, S. K. Chilappagari, R. Radhakrishnan, and B. Vasic, Failures of the Gallager B Decoder: Analysis and Applications, Proc. Information Theory and Applications Workshop UCSD, 2006.

B. Vasic, S. K. Chilappagari, D. V. Nguyen, and S. K. Planjery, Trapping set ontology, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2009.
DOI : 10.1109/ALLERTON.2009.5394825

S. K. Planjery, D. Declercq, L. Danjean, and B. Vasic, Finite alphabet iterative decoders for LDPC codes surpassing floating-point iterative decoders, Electronics Letters, vol.47, issue.16, 2011.
DOI : 10.1049/el.2011.1184
URL : https://hal.archives-ouvertes.fr/hal-00670723

D. Declercq, E. Li, S. K. Planjery, and B. Vasic, Approaching maximum likelihood decoding of finite length LDPC codes via FAID diversity, 2012 IEEE Information Theory Workshop, 2012.
DOI : 10.1109/ITW.2012.6404721
URL : https://hal.archives-ouvertes.fr/hal-00764115

S. K. Planjery, D. Declercq, S. K. Chilappagari, and B. Vasic, Multilevel decoders surpassing belief propagation on the binary symmetric channel, 2010 IEEE International Symposium on Information Theory, 2010.
DOI : 10.1109/ISIT.2010.5513620
URL : https://hal.archives-ouvertes.fr/hal-00531127

J. S. Yedidia, Generalized Belief Propagation and Free Energy Minimization, Proc. Neural Information Processing System, 2002.

J. S. Yedidia, W. T. Freeman, and Y. Weiss, Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms, IEEE Transactions on Information Theory, vol.51, issue.7, pp.2282-2312, 2005.
DOI : 10.1109/TIT.2005.850085

M. Mezard and A. Montanari, Information, Physics, and Computation, 2006.
DOI : 10.1093/acprof:oso/9780198570837.001.0001

H. Nishimori, Statistical physics of spin glasses and information processing an introduction, 2001.

M. Welling, On the Choice of Regions for Generalized Belief Propagation, Proc. 20th Conference on Uncertainty in Artificial Intelligence, 2004.

P. Pakzad and V. Anantharam, Estimation and Marginalization Using the Kikuchi Approximation Methods, Neural Computation, vol.17, issue.8, pp.1836-1873, 2003.
DOI : 10.1162/08997660260028674

R. M. Tanner, R. Michael, D. Sridhara, and T. Fuja, A Class of Group- Structured LDPC Codes, 2001.

R. Koetter and P. Vontobel, Graph-covers and Iterative Decoding of Finite Length Codes, Proc. Int. Symp. on Turbo codes and Iterative Inform. Process, 2003.

A. Morello and V. Mignone, DVB-S2: The Second Generation Standard for Satellite Broad-Band Services, Proc. IEEE, 2006.
DOI : 10.1109/JPROC.2005.861013

D. V. Nguyen, S. H. Chilappagari, M. W. Marcellin, and B. Vasic, On the Construction of Structured LDPC Codes Free of Small Trapping Sets, IEEE Transactions on Information Theory, vol.58, issue.4, 2012.
DOI : 10.1109/TIT.2011.2173733

S. Kullback, Information Theory and Statistics, 1968.

H. A. Bethe, Statistical Theory of Superlattices, Proc. Royal Society of London, 1935.

R. Kikuchi, A Theory of Cooperative Phenomena, Physical Review, vol.81, issue.6, pp.988-1003, 1951.
DOI : 10.1103/PhysRev.81.988

J. Sibel, S. Reynal, and D. Declercq, A novel region graph construction based on trapping sets for the Generalized Belief Propagation, 2012 IEEE International Conference on Communication Systems (ICCS), 2012.
DOI : 10.1109/ICCS.2012.6406159
URL : https://hal.archives-ouvertes.fr/hal-00736234