Stepanov for providing the matrices of Margulis ,
A mathematical theory of communication, Bell System Technical Journal, vol.27, 1948. ,
Near Shannon limit errorcorrecting coding and decoding: turbo-codes, ICC '93, pp.1064-1070, 1993. ,
Low-density parity-check codes, IEEE Transactions on Information Theory, vol.8, issue.1, 1963. ,
DOI : 10.1109/TIT.1962.1057683
Good error correcting codes based on very sparse matrices, IEEE Trans. Inf. Theory, vol.45, issue.2, pp.399-431, 1999. ,
Design of capacity-approaching irregular low-density parity-check codes, IEEE Transactions on Information Theory, vol.47, issue.2, pp.619-637, 2001. ,
DOI : 10.1109/18.910578
Efficient encoding of low-density parity-check codes, IEEE Transactions on Information Theory, vol.47, issue.2, pp.638-656, 2001. ,
DOI : 10.1109/18.910579
Design of Efficiently Encodable Moderate-Length High-Rate Irregular LDPC Codes, IEEE Transactions on Communications, vol.52, issue.4, pp.564-571, 2004. ,
DOI : 10.1109/TCOMM.2004.826367
Bounds on the performance of belief propagation decoding, IEEE Transactions on Information Theory, vol.48, issue.1, pp.112-122, 2002. ,
DOI : 10.1109/18.971742
Design of capacity-approaching irregular low-density parity-check codes, IEEE Transactions on Information Theory, vol.47, issue.2, pp.619-637, 2001. ,
DOI : 10.1109/18.910578
Expander codes, IEEE Transactions on Information Theory, vol.42, issue.6, pp.1710-1723, 1996. ,
DOI : 10.1109/18.556667
Fast flat histogram algorithm for generalized spin models, Phys. Rev., E, vol.72, issue.56710, 2005. ,
Digital Modulation and Coding A recursive approach to low complexity codes, IEEE Trans. Inf. Theory, vol.27, 1981. ,
Weaknesses of Margulis and Ramanujan LDPC codes, Electronic Nodes in Theoretical Computer Science, vol.74, pp.808-821, 2003. ,
Error floors of LDPC codes, Allerton Conference, 2001. ,
Codes and decoding on general graphs, 1996. ,
Codes and iterative decoding on general graphs, Europ. Trans. Telecommunications, vol.6, issue.513, 1995. ,
On the effective weights of pseudocodewords for codes defined on graphs with cycles " . Codes, Systems and graphical models, IMA Appl, vol.123, pp.101-112, 1999. ,
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs, IEEE Transactions on Information Theory, vol.47, issue.2, pp.736-744, 2001. ,
DOI : 10.1109/18.910585
Spin-glass models as error-correcting codes, Nature, vol.339, issue.6227, pp.693-695, 1989. ,
DOI : 10.1038/339693a0
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988. ,
Iterative decoding of binary block and convolutional codes, IEEE Transactions on Information Theory, vol.42, issue.2, pp.429-445, 1996. ,
DOI : 10.1109/18.485714
Determining Performance of LDPC Codes at Low Error Probability, 2006. ,
An Introduction to LDPC Codes, 2003. ,
DOI : 10.1201/9780203490310.ch36
Iterative reliability based decoding of LDPC codes, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252), pp.908-917, 2001. ,
DOI : 10.1109/ISIT.2001.936096
Efficient implementation of the sum-product algorithm for decoding LDPC codes, IEEE GlobeComm'01, pp.1036-1036, 2001. ,
On importance sampling in digital communications -part I: fundamentals, IEEE JSAC, vol.11, issue.3, pp.289-299, 1993. ,
On large deviations theory and asymptotically efficient Monte Carlo estimation, IEEE Transactions on Information Theory, vol.36, issue.3, pp.579-588, 1990. ,
DOI : 10.1109/18.54903
Modern Coding Theory, 2008. ,
DOI : 10.1017/CBO9780511791338
Unveiling turbo codes: some results on parallel concatenated coding schemes, IEEE Transactions on Information Theory, vol.42, issue.2, p.42, 1996. ,
DOI : 10.1109/18.485713
A heuristic search for good low-density paritycheck codes at short block lengths, IEEE International Conference on Communications, p.41, 2001. ,
Finitelength analysis of LDPC codes on the BEC, IEEE Trans. Inf. Theory, issue.6, pp.481570-1579, 2002. ,
Lower bounds on the minimum pseudo-weight of linear codes, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., p.70, 2004. ,
DOI : 10.1109/ISIT.2004.1365104
Field programmable gate array (FPGA) for iterative code evaluation, IEEE Trans. on Magnetics, vol.42, issue.2, pp.226-231, 2006. ,
Code construction and FGPA implementation of capacity approaching low error-floor LDPC decoder, IEEE Trans. on Circuits and Systems, 2006. ,
Algorithmic and Combinatorial Analysis of Trapping Sets in Structured LDPC Codes, 2005 International Conference on Wireless Networks, Communications and Mobile Computing, 2005. ,
DOI : 10.1109/WIRLES.2005.1549481
Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles, IEEE Transactions on Information Theory, vol.53, issue.1, pp.39-55, 2007. ,
DOI : 10.1109/TIT.2006.887060
Finding All Small Error-Prone Substructures in LDPC Codes, IEEE Transactions on Information Theory, vol.55, issue.5, pp.1976-1998, 2009. ,
DOI : 10.1109/TIT.2009.2015993
Graph-covers and iterative decoding of finitelength codes, 3rd Intl. Symp. on Turbo Codes and Realted Topics, pp.75-82, 2003. ,
Factor graphs and the sum-product algorithm, IEEE Transactions on Information Theory, vol.47, issue.2, pp.498-519, 2001. ,
DOI : 10.1109/18.910572
The capacity of low-density parity-check codes under message-passing decoding, IEEE Transactions on Information Theory, vol.47, issue.2, pp.599-618, 2001. ,
DOI : 10.1109/18.910577
Exact Thresholds and Optimal Codes for the Binary-Symmetric Channel and Gallager's Decoding Algorithm A, IEEE Transactions on Information Theory, vol.50, issue.9, pp.2010-2021, 2004. ,
DOI : 10.1109/TIT.2004.833352
Improved Bit-Flipping Decoding of Low-Density Parity-Check Codes, IEEE Transactions on Information Theory, vol.51, issue.4, pp.1594-1606, 2005. ,
DOI : 10.1109/TIT.2005.844095
Threshold Values and Convergence Properties of Majority-Based Algorithms for Decoding Regular Low-Density Parity-Check Codes, IEEE Transactions on Communications, vol.52, issue.12, pp.2087-2097, 2004. ,
DOI : 10.1109/TCOMM.2004.838738
Estimation of Bit and Frame Error Rates of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels, IEEE Transactions on Communications, vol.55, issue.12, pp.2234-2239, 2007. ,
DOI : 10.1109/TCOMM.2007.910589
An IS Simulation Technique for Very Low BER Performance Evaluation of LDPC Codes, 2006 IEEE International Conference on Communications, pp.1095-1100, 2006. ,
DOI : 10.1109/ICC.2006.254893
Investigation of error floors of structured low-density parity-check codes via hardware simulation, 2006. ,
Analysis of Absorbing Sets for Array-Based LDPC Codes, 2007 IEEE International Conference on Communications, 2007. ,
DOI : 10.1109/ICC.2007.1037
Skewness and pseudocodewords in iterative decoding, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 1998. ,
DOI : 10.1109/ISIT.1998.708741
Pseudocodeword weights and stopping sets, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., p.67, 2004. ,
DOI : 10.1109/ISIT.2004.1365105
Using Linear Programming to Decode Binary Linear Codes, Conference on Information Sciences and Systems, 2003. ,
DOI : 10.1109/TIT.2004.842696
Graph-cover decoding and finite-length analysis of message-passing iterative decoding of LDPC codes, IEEE Trans. Inf. Theory, 2007. ,
A universal theory of decoding and pseudocodewords, Allerton Conference on Communication, Control, and Computing, 2007. ,
Pseudocodewords of Tanner Graphs, IEEE Transactions on Information Theory, vol.53, issue.11, pp.4013-4038, 2007. ,
DOI : 10.1109/TIT.2007.907501
Minimum Pseudoweight and Minimum Pseudocodewords of LDPC Codes, IEEE Transactions on Information Theory, vol.54, issue.1, pp.480-485, 2008. ,
DOI : 10.1109/TIT.2007.911177
Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes, IEEE Transactions on Information Theory, vol.53, issue.7, pp.2376-2393, 2007. ,
DOI : 10.1109/TIT.2007.899563
Pseudocodewords in LDPC convolutional codes, IEEE Intern. Symp. on Inf. Theory, 2006. ,
Using Linear Programming to Decode Binary Linear Codes, IEEE Transactions on Information Theory, vol.51, issue.3, pp.954-972, 2005. ,
DOI : 10.1109/TIT.2004.842696
Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms, IEEE Transactions on Information Theory, vol.51, issue.7, p.51, 2005. ,
DOI : 10.1109/TIT.2005.850085
On the relationship between LP decoding and Min-Sum Algorithms decoding, ISITA, 2004. ,
An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes, IEEE Transactions on Information Theory, vol.54, issue.4, pp.1514-1520, 2006. ,
DOI : 10.1109/TIT.2008.917682
Pseudo-codeword landscape, IEEE Intern. Symp. on Inf. Theory, 2007. ,
Error Correction on a Tree: An Instanton Approach, Physical Review Letters, vol.93, issue.19, p.93, 2004. ,
DOI : 10.1103/PhysRevLett.93.198702
Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics Approach, Physical Review Letters, vol.95, issue.22, p.95, 2005. ,
DOI : 10.1103/PhysRevLett.95.228701
The error floor of LDPC codes in the Laplacian channel, 43rd Allerton Conference on Communication, Control and Computing, 2005. ,
A Guide to Monte Carlo Methods in Statistical Physics, 2000. ,
Importance Sampling -Applications in Communications and Detection, 2002. ,
Quick simulation: a review of importance sampling techniques in communications systems, IEEE Journal on Selected Areas in Communications, vol.15, issue.4, pp.597-613, 1997. ,
DOI : 10.1109/49.585771
Improved importance sampling technique for efficient simulation of digital communication systems, IEEE Journal on Selected Areas in Communications, vol.6, issue.1, pp.67-82, 1988. ,
DOI : 10.1109/49.192731
A new method for Viterbi decoder simulation using importance sampling, IEEE Transactions on Communications, vol.38, issue.9, pp.1341-1351, 1990. ,
DOI : 10.1109/26.61375
Importance sampling simulation of concatenated block codes, IEE Proc. Communications, pp.245-251, 2000. ,
DOI : 10.1049/ip-com:20000662
On importance sampling for linear block codes, Proc. IEEE International Conference on Communications (ICC '03), pp.2904-2908, 2003. ,
Importance sampling for loop-free decoding trees with application to low-density parity-check codes, IEEE International Symposium on Information Theory, 2003. Proceedings., 2003. ,
DOI : 10.1109/ISIT.2003.1228134
A study on importance sampling for turbo codes, IEICE Trans. Fundamentals, issue.10, pp.87-2503, 2004. ,
Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems, IEEE Journal on Selected Areas in Communications, vol.2, issue.1, pp.153-170, 1984. ,
DOI : 10.1109/JSAC.1984.1146031
A Modified Monte-Carlo Simulation Technique for the Evaluation of Error Rate in Digital Communication Systems, IEEE Transactions on Communications, vol.28, issue.11, pp.1916-1924, 1980. ,
DOI : 10.1109/TCOM.1980.1094613
A composite importance sampling technique for digital communication system simulation, IEEE Transactions on Communications, vol.38, issue.4, pp.393-396, 1990. ,
DOI : 10.1109/26.52645
An investigation of Gaussian tail and Rayleigh tail density functions for importance sampling digital communication system simulation, IEEE Transactions on Communications, vol.38, issue.9, pp.1288-1292, 1990. ,
DOI : 10.1109/26.61364
Nonlinear importance sampling techniques for efficient simulation of communication systems, IEEE International Conference on Communications, Including Supercomm Technical Sessions, pp.631-635, 1990. ,
DOI : 10.1109/ICC.1990.117155
Adaptive Monte Carlo methods for rare event simulations, Winter Simulation Conf, 2002. ,
A general method for finding low error rates of LDPC codes, p.605051, 2006. ,
Evaluation of the Low Frame Error Rate Performance of LDPC Codes Using Importance Sampling, 2007 IEEE Information Theory Workshop, 2007. ,
DOI : 10.1109/ITW.2007.4313074
Error rate estimation of finite-length lowdensity parity-check codes on binary symmetric channels using cycle enumeration, IEEE Intern. Symp. on Inf. Theory, 2007. ,
Error rate estimation of finite-length LDPC Codes decoded by soft-decision iterative algorithms, IEEE Intern. Symp. on Inf. Theory, 2008. ,
Spin Glasses, Error-Correcting Codes and Finite-Temperature Decoding, Europhysics Letters (EPL), vol.25, issue.3, pp.159-16414, 1994. ,
DOI : 10.1209/0295-5075/25/3/001
Finite temperature error-correcting codes, Physical Review Letters, vol.70, issue.19, pp.2968-2971, 1993. ,
DOI : 10.1103/PhysRevLett.70.2968
Optimum Decoding Temperature for Error-Correcting Codes, Journal of the Physical Society of Japan, vol.62, issue.9, pp.2973-2975, 1993. ,
DOI : 10.1143/JPSJ.62.2973
Turbo codes: the phase transition, The European Physical Journal B, vol.18, issue.1, pp.121-136, 2000. ,
DOI : 10.1007/s100510070085
The glassy phase of Gallager codes, The European Physical Journal B, vol.23, issue.1, pp.121-136, 2001. ,
DOI : 10.1007/s100510170089
Dynamic phase transition for decoding algorithms, Physical Review E, vol.66, issue.4, pp.461201-461218, 2002. ,
DOI : 10.1103/PhysRevE.66.046120
Energy spectrum structure and quantum states of disordered condensed systems, Uspekhi Fizicheskih Nauk, vol.83, issue.8, pp.617-663, 1964. ,
DOI : 10.3367/UFNr.0083.196408c.0617
Divergence of the perturbation-theory series and the quasiclassical theory, Zh. Eksp. Teor. Fiz, vol.72, issue.2, pp.411-427, 1977. ,
Generalized Belief Propagation, Advances in Neural Information Processing Systems, pp.689-695, 2000. ,
Bethe free energy, Kikuchi approximations and Belief Propagation algorithms, SCTV01, 2001. ,
Pseudoparticle solutions of the Yang-Mills equations, Phys. Rev. Lett, p.59, 1975. ,
Instanton analysis of Low-Density Parity-Check codes in the error-floor regime, 2006 IEEE International Symposium on Information Theory, 2006. ,
DOI : 10.1109/ISIT.2006.261777
A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-313, 1965. ,
DOI : 10.1093/comjnl/7.4.308
Instanton-based techniques for analysis and reduction of error floors of LDPC codes, IEEE Journal on Selected Areas in Communications, vol.27, issue.6, pp.855-865, 2009. ,
DOI : 10.1109/JSAC.2009.090804
Adaptive importance sampling (digital communication), IEEE Journal on Selected Areas in Communications, vol.11, issue.3, pp.309-316, 1993. ,
DOI : 10.1109/49.219545
Kernel method in importance sampling density estimation, ICOSSAR, pp.1193-1200, 1989. ,
Adaptive sampling ??? an iterative fast Monte Carlo procedure, Structural Safety, vol.5, issue.2, pp.119-126, 1988. ,
DOI : 10.1016/0167-4730(88)90020-3
An adaptive importance sampling strategy, Mech. Comput. in 1990's, pp.1288-1292, 1990. ,
An algorithmic approach to the optimization of importance sampling parameters in digital communication system simulation, IEEE Transactions on Communications, vol.41, issue.10, 1991. ,
DOI : 10.1109/26.237881
Evaluation of the very low BER of FEC codes using dual adaptive importance sampling, IEEE Communications Letters, vol.9, issue.2, 2005. ,
DOI : 10.1109/LCOMM.2005.02012
Multicanonical ensemble: A new approach to simulate first-order phase transitions, Physical Review Letters, vol.68, issue.1, pp.9-12, 1992. ,
DOI : 10.1103/PhysRevLett.68.9
Algorithmic aspects of multicanonical Monte Carlo simulations, Nucl. Phys. Proc. Suppl, pp.982-984, 1998. ,
Near Shannon limit performance of low density parity check codes, Electronics Letters, vol.33, issue.6, pp.457-458, 1997. ,
DOI : 10.1049/el:19970362
Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems, Optics Letters, vol.28, issue.20, pp.1894-1896, 2003. ,
DOI : 10.1364/OL.28.001894
Fast Simulation for the Performance Evaluation of LDPC Codes using Fast Flat Histogram Method, 2008 IEEE Sarnoff Symposium, 2008. ,
DOI : 10.1109/SARNOF.2008.4520050
URL : https://hal.archives-ouvertes.fr/hal-00512276
Efficient performance evaluation of Forward Error Correcting codes, 2008 11th IEEE Singapore International Conference on Communication Systems, 2008. ,
DOI : 10.1109/ICCS.2008.4737185
URL : https://hal.archives-ouvertes.fr/hal-00512279
An efficient pseudocodeword search algorithm for belief propagation decoding of LDPC codes, IEEE ICUMT'09, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00531123
New approach to spin-glass simulations, Physical Review Letters, vol.69, issue.15, pp.2292-2295, 1992. ,
DOI : 10.1103/PhysRevLett.69.2292
Multicanonical algorithms for first order phase transitions, Physics Letters B, vol.267, issue.2, p.249, 1991. ,
DOI : 10.1016/0370-2693(91)91256-U
=2 Ising model, Physical Review B, vol.47, issue.1, p.47, 1993. ,
DOI : 10.1103/PhysRevB.47.497
Multioverlap Simulations of the 3D Edwards-Anderson Ising Spin Glass, Physical Review Letters, vol.80, issue.21, pp.4771-4774, 1998. ,
DOI : 10.1103/PhysRevLett.80.4771
Effective way for determination of multicanonical weights, Physical Review E, vol.56, issue.5, pp.6200-6203, 1997. ,
DOI : 10.1103/PhysRevE.56.6200
Monte Carlo simulations in generalized ensemble: Multicanonical algorithm versus simulated tempering, Physical Review E, vol.54, issue.5, 1996. ,
DOI : 10.1103/PhysRevE.54.5863
Multi-overlap simulations of free-energy barriers in the 3D Edwards???Anderson Ising spin glass, Computer Physics Communications, vol.121, issue.122, pp.121-122, 1999. ,
DOI : 10.1016/S0010-4655(99)00306-9
Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram, Physical Review E, vol.64, issue.5, 2001. ,
DOI : 10.1103/PhysRevE.64.056101
Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States, Physical Review Letters, vol.86, issue.10, 2001. ,
DOI : 10.1103/PhysRevLett.86.2050
Performances of Wang-Landau algorithms for continuous systems, Physical Review E, vol.73, issue.5, p.73, 2006. ,
DOI : 10.1103/PhysRevE.73.056704
URL : https://hal.archives-ouvertes.fr/hal-00142107
Flat histogram method of Wang-Landau and N-fold way, Int. J. Mod. Phys, issue.477, p.13, 2002. ,
Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals, Physical Review E, vol.72, issue.3, p.72, 2005. ,
DOI : 10.1103/PhysRevE.72.036702
Understanding and improving the Wang-Landau algorithm, Physical Review E, vol.72, issue.2, p.72, 2005. ,
DOI : 10.1103/PhysRevE.72.025701
Wang-Landau sampling with self-adaptive range, Physical Review E, vol.71, issue.6, 2005. ,
DOI : 10.1103/PhysRevE.71.066705
Wang-Landau Algorithm for Continuous Models and Joint Density of States, Physical Review Letters, vol.96, issue.12, p.96, 2006. ,
DOI : 10.1103/PhysRevLett.96.120201
Optimising the ensemble for equilibrium in broad-histogram Monte Carlo simulations, Phys. Rev, issue.046701, p.70, 2004. ,
Performance Limitations of Flat-Histogram Methods, Physical Review Letters, vol.92, issue.9, p.92, 2004. ,
DOI : 10.1103/PhysRevLett.92.097201
Convergence and refinement of the Wang???Landau algorithm, Computer Physics Communications, vol.175, issue.1, p.175, 2006. ,
DOI : 10.1016/j.cpc.2006.02.009
Analytical study of tunneling times in flat histogram Monte Carlo, Europhys. Lett, vol.72, pp.802-808, 2005. ,
Optimized multicanonical simulations: A proposal based on classical fluctuation theory, Physical Review E, vol.74, issue.4, p.74, 2006. ,
DOI : 10.1103/PhysRevE.74.046702
Wang-Landau algorithm: A theoretical analysis of the saturation of the error, The Journal of Chemical Physics, vol.127, issue.18, p.127, 2007. ,
DOI : 10.1063/1.2803061
Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953. ,
DOI : 10.1063/1.1699114
Weak convergence and optimal scaling of random walk Metropolis algorithms, The Annals of Applied Probability, vol.7, issue.1, pp.110-130, 1997. ,
DOI : 10.1214/aoap/1034625254
Cluster Monte Carlo algorithms " . In New Optimization Algorithms in Physics, 2004. ,
Phase transitions in long-range spin models: the power of generalized ensembles Fast calculation of the density of states of a fluid by Monte Carlo simulations, Phys. Rev. Lett, issue.035701, p.90, 2003. ,
Transition matrix Monte Carlo method, Computer Physics Communications, vol.121, issue.122, 2002. ,
DOI : 10.1016/S0010-4655(99)00270-2
Introduction to Monte Carlo Algorithms Advances in computer simulation, lectures held at Eotvos summer school in Budapest, 1996. ,
Fast simulation of turbo codes over AWGN channels, 2007 International Symposium on Communications and Information Technologies, pp.1176-1181, 2007. ,
DOI : 10.1109/ISCIT.2007.4392195
Non-binary convolutional codes for turbo coding, Electronics Letters, vol.35, issue.1, pp.39-40, 1999. ,
DOI : 10.1049/el:19990059
A new algorithm for Monte Carlo simulation of Ising spin systems, Journal of Computational Physics, vol.17, issue.1, p.17, 1975. ,
DOI : 10.1016/0021-9991(75)90060-1
Numerical integration using Wang???Landau sampling, Computer Physics Communications, vol.177, issue.6, pp.524-529, 2007. ,
DOI : 10.1016/j.cpc.2007.06.001
Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics Approach, Physical Review Letters, vol.95, issue.22, p.95, 2005. ,
DOI : 10.1103/PhysRevLett.95.228701
Explicit constructions of graphs without short cycles and low density codes, Combinatorica, vol.12, issue.1, 1982. ,
DOI : 10.1007/BF02579283
Encyclopedia of sparse graph codes, C ,
Improved impulse method to evaluate the low weight profile of sparse binary linear codes, 2008 IEEE International Symposium on Information Theory, 2008. ,
DOI : 10.1109/ISIT.2008.4595332
URL : https://hal.archives-ouvertes.fr/hal-00522149