.. The-randpeg-algorithm, 84 3.2.2.1 Truncated spanning tree, p.86

.. Performance-of-the-randpeg-algorithm, 87 3.2.3.1 Design of ultra-sparse graphs (d v =2), p.89

L. Review-of-structured and .. , 89 3.3.1 LDPC codes constructed from protographs

[. Bibliography, S. Andrews, D. Dolinar, J. Divsalar, and . Thorpe, Design of low-density parity-check (LDPC) codes for deep-space applications, JPL Interplanetary Network Progress (INP), 2004.

[. Amraoui, S. Dusad, and R. Urbanke, Achieving general points in the 2-user gaussian mac without time sharing or rate splitting by means of iterative decoding, Proc. of IEEE Int. Symp. on Inform. Theory (ISIT), p.334, 2002.

A. Abbasfar, D. Divsalar, and K. Yao, Accumulate repeat accumulate codes, Proc. of GLOBECOM, pp.509-513, 2004.
DOI : 10.1109/isit.2004.1365542
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.5661

A. Abbasfar, D. Divsalar, and K. Yao, Accumulate repeat accumulate codes, Proc. of IEEE Int. Symp. on Inform. Theory (ISIT), p.505, 2004.
DOI : 10.1109/isit.2004.1365542
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.5661

[. Ardakani and F. R. Kschischang, A More Accurate One-Dimensional Analysis and Design of Irregular LDPC Codes, IEEE Transactions on Communications, vol.52, issue.12, pp.2106-2114, 2004.
DOI : 10.1109/TCOMM.2004.838718

[. Ardakani and F. R. Kschischang, Properties of Optimum Binary Message-Passing Decoders, IEEE Transactions on Information Theory, vol.51, issue.10, pp.3658-3665, 2005.
DOI : 10.1109/TIT.2005.855611

S. Abu-surra, W. E. Ryan, and D. Divsalar, Ensemble trapping set enumerators for protograph-based LDPC codes, Proc. of 44th Allerton Conf, 2007.
DOI : 10.1109/glocom.2007.287
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.321.6663

. [. Bahl, . Cocke, R. Jelinek, and . Raviv, Optimal decoding of linear codes for minimizing symbol error rate (Corresp.), IEEE Transactions on Information Theory, vol.20, issue.2, pp.284-287, 1974.
DOI : 10.1109/TIT.1974.1055186

C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon limit error-correcting codes and decoding, Proc. of International Conference on Communications (ICC), pp.1064-1070, 1993.
DOI : 10.1109/icc.1993.397441

N. Biggs, Constructions for cubic graphs with large girths. The electronic journal of Combinatorics, 1988.

J. Byers, M. Luby, and M. Mitzenmacher, A digital fountain approach to asynchronous reliable multicast, IEEE Journal on Selected Areas in Communications, vol.20, issue.8, pp.1528-1540, 2002.
DOI : 10.1109/JSAC.2002.803996

J. Byers, M. Luby, M. Mitzenmacher, and A. Rege, A digital fountain approach to reliable distribution of bulk data, Proc. of ACM SIGCOMM, pp.56-67, 1998.

. Bri01-]-stephan-ten and . Brinck, Convergence behavior of iteratively decoded parallel concatenated codes, IEEE Trans. Commun, vol.49, issue.10, pp.1727-1737, 2001.

[. Bazzi, T. Richardson, and R. Urbanke, 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

S. Chung, D. Forney, T. J. Richardson, and R. Urbanke, On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit, IEEE Communications Letters, vol.5, issue.2, pp.58-60, 2001.
DOI : 10.1109/4234.905935

J. Castura and Y. Mao, On Rateless Coding over Fading Channels with Delay Constraints, 2006 IEEE International Symposium on Information Theory, 2006.
DOI : 10.1109/ISIT.2006.261959

J. Castura and Y. Mao, Rateless coding over fading channels, IEEE Communications Letters, vol.10, issue.1, 2006.
DOI : 10.1109/LCOMM.2006.1576565

[. Chung, T. J. Richardson, and R. 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, pp.657-670, 2001.
DOI : 10.1109/18.910580

[. Divsalar, S. Dolinar, and C. Jones, Construction of Protograph LDPC Codes with Linear Minimum Distance, 2006 IEEE International Symposium on Information Theory, pp.664-668, 2006.
DOI : 10.1109/ISIT.2006.261868

[. Divsalar, S. Dolinar, and C. Jones, Short protographbased LDPC codes, Proc. of IEEE MILCOM, pp.1-6, 2007.

[. Divsalar, S. Dolinar, and J. Thorpe, Accumulate-repeataccumulate-accumulate codes, Proc. of 60th Vehicular Technology Conf. (VTC), pp.2292-2296, 2004.
DOI : 10.1109/vetecf.2004.1400450
URL : https://trs.jpl.nasa.gov/bitstream/2014/41117/1/04-2990.pdf

[. Declercq, David declercq's homepage

[. Declercq, Optimisation et performances des codes LDPC pour des canaux non-standards, 2003.

D. Declercq and M. Fossorier, Decoding Algorithms for Nonbinary LDPC Codes Over GF<formula formulatype="inline"><tex>$(q)$</tex></formula>, IEEE Transactions on Communications, vol.55, issue.4, pp.633-643, 2005.
DOI : 10.1109/TCOMM.2007.894088

[. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, Protograph based LDPC codes with minimum distance linearly growing with block size, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005., pp.1152-1156, 2005.
DOI : 10.1109/GLOCOM.2005.1577834
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.464.3456

[. Divsalar, H. Jin, and R. J. Mceliece, Coding theorems for 'turbo-like' codes, Proc. of 36th Allerton Conf. on Communication, Control, and Computing, pp.201-210, 1998.

S. Dolinar, A rate-compatible family of protograph-based LDPC codes built by expurgation and lengthening, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., pp.1627-1631, 2005.
DOI : 10.1109/ISIT.2005.1523620

D. Di, I. E. Proietti, T. J. Telatar, U. Richardson, and . Rudiger, Finite length analysis of low-density parity-check codes on the binary erasure channel, IEEE Trans. Inform. Theory, issue.6, pp.481570-1579, 2002.

[. Ts, v1.2.1 DVBH. Technical specification group services and system aspects, p.472, 2006.

[. Etesami and A. Shokrollahi, Raptor codes on binary memoryless symmetric channels, IEEE Transactions on Information Theory, vol.52, issue.5, pp.2033-2051, 2006.
DOI : 10.1109/TIT.2006.872855

B. J. Frey, F. R. Kschischang, H. Loeliger, and N. Wiberg, Factor graphs and algorithms, Proc. of 35th Allerton Conf. on Communications, Control and Computing, pp.666-680, 1997.

M. Fossorier, Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices, IEEE Transactions on Information Theory, vol.50, issue.8, pp.1788-1793, 2004.
DOI : 10.1109/TIT.2004.831841
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.320.7109

[. Gallager, Low-density parity-check codes, IEEE Transactions on Information Theory, vol.8, issue.1, pp.21-28, 1962.
DOI : 10.1109/TIT.1962.1057683

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

[. Hu and E. Eleftheriou, Cycle Tanner-graph codes over GF(2/sup b/), IEEE International Symposium on Information Theory, 2003. Proceedings., p.87, 2003.
DOI : 10.1109/ISIT.2003.1228101

[. Hu, E. Eleftheriou, M. Dieter, and . Arnold, Regular and irregular progressive edge-growth tanner graphs, IEEE Transactions on Information Theory, vol.51, issue.1, pp.386-398, 2005.
DOI : 10.1109/TIT.2004.839541

[. Ha, J. Kim, D. Klinc, and S. W. Mclaughlin, Rate-compatible punctured low-density parity-check codes with short block lengths, IEEE Trans. Inform. Theory, vol.52, issue.2, pp.728-738, 2006.

[. Ha and S. W. Mclaughlin, Low-density parity-check codes over gaussian channels with erasures, IEEE Trans. Inform. Theory, vol.49, issue.7, pp.1801-1809, 2003.

J. Ha and S. W. Mclaughlin, Rate-Compatible Puncturing of Low-Density Parity-Check Codes, IEEE Transactions on Information Theory, vol.50, issue.11, pp.2824-2836, 2004.
DOI : 10.1109/TIT.2004.836667

J. Hou, P. H. Siegel, and L. B. Milstein, Performance analysis and code optimization of low-density parity-check codes on rayleigh fading channels, IEEE J. Select. Areas Commun, vol.19, 2001.

A. Hagedorn, D. Starobinski, and A. Trachtenberg, Rateless Deluge: Over-the-Air Programming of Wireless Sensor Networks Using Random Linear Codes, 2008 International Conference on Information Processing in Sensor Networks (ipsn 2008), pp.457-466, 2008.
DOI : 10.1109/IPSN.2008.9

H. Jin, A. Khandekar, and R. J. Mceliece, Irregular repeataccumulate codes, Proc. of Int. Symp. on Turbo codes and Related Topics, pp.1-8, 2000.

H. Jin and T. Richardson, A new fast density evolution, Proc. of IEEE ITW, 2006.

R. Frank, B. J. Kschischang, H. Frey, and . Loeliger, Factor graphs and the sum-product algorithm, IEEE Trans. Inform. Theory, vol.47, issue.2, pp.498-519, 2001.

[. Kim, W. Hur, A. Ramamoorthy, and S. W. Mclaughlin, Design of Rate-Compatible Irregular LDPC Codes for Incremental Redundancy Hybrid ARQ Systems, 2006 IEEE International Symposium on Information Theory, pp.1139-1143, 2006.
DOI : 10.1109/ISIT.2006.261962

[. Kou, S. Lin, and M. Fossorier, Low-density parity-check codes based on finite geometries: a rediscovery and new results, IEEE Transactions on Information Theory, vol.47, issue.7, pp.2711-2736, 2001.
DOI : 10.1109/18.959255

R. Karp, M. Luby, and A. Shokrollahi, Finite length analysis of LT codes, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., 2004.
DOI : 10.1109/ISIT.2004.1365074

[. Kim, J. No, H. Chung, and D. Shin, Cycle Analysis and Construction of Protographs for QC LDPC Codes With Girth Larger Than 12, 2007 IEEE International Symposium on Information Theory, pp.2256-2260, 2007.
DOI : 10.1109/ISIT.2007.4557555

[. Kim, J. No, H. Chung, and D. Shin, Quasi-cyclic low-density parity-check codes with girth larger than 12, IEEE Trans. Inform. Theory, issue.8, pp.532885-2891, 2007.

L. López and A. Fernández, A Game Theoretic Analysis of Protocols Based on Fountain Codes, 10th IEEE Symposium on Computers and Communications (ISCC'05), pp.625-630, 2005.
DOI : 10.1109/ISCC.2005.11

[. Li, B. V. Vijaya, and . Kumar, A class of good quasi-cyclic lowdensity parity check codes based on progressive edge growth graph, Proc. of 38 th Asilomar Conference on Signals, Systems and Computers (ACSSC), 2004.

K. S. Jason, B. Lee, J. Lee, K. Thorpe, S. Andrews et al., A scalable architecture of a structured LDPC decoder, Proc. of IEEE Int. Symp. on Inform. Theory (ISIT), p.296, 2004.

[. Luby, M. Mitzenmacher, and A. Shokrollahi, Practical loss-resilent codes, Proc. of 29th ACM Symp. on Theory of Computing (STOC), pp.150-159, 1997.
DOI : 10.1145/258533.258573
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.5754

[. Luby, M. Mitzenmacher, and A. Shokrollahi, Analysis of random process via and-or tree evaluation, Proc. of 9th symp. on ACM-SIAM Symposium on Discrete Algorithms, pp.364-373, 1998.

[. Luby, M. Mitzenmacher, A. Shokrollahi, and D. Spielman, Improved low-density parity-check codes using irregular graphs and belief propagation, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), p.117, 1998.
DOI : 10.1109/ISIT.1998.708706
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.6926

[. Luby, M. Mitzenmacher, A. Shokrollahi, and D. A. Spielman, Efficient erasure correcting codes, IEEE Transactions on Information Theory, vol.47, issue.2, pp.569-584, 2001.
DOI : 10.1109/18.910575

[. Luby, M. Mitzenmacher, A. Shokrollahi, and D. A. Spielman, Improved low-density parity-check codes using irregular graphs, IEEE Transactions on Information Theory, vol.47, issue.2, pp.585-598, 2001.
DOI : 10.1109/18.910576

S. Liva, L. Song, Y. Lan, S. Zhang, W. E. Lin et al., Design of LDPC Codes: A Survey and New Results, for publication in J. Comm. Software and Systems, 2006.
DOI : 10.24138/jcomss.v2i3.283

. Mackay, Encyclopedia of sparse graph codes

]. Mac99, . J. David, and . Mackay, Good error correcting codes based on very sparse matrices, IEEE Trans. Inform. Theory, vol.45, issue.2, pp.399-431, 1999.

[. Maymounkov, Online codes, 2002.

[. Mannoni, D. Declercq, and G. Gelle, Optimized Irregular Low-Density Parity-Check Codes for Multicarrier Modulations over Frequency-Selective Channels, Proc., special issue on 'Multicarrier Communication Systems, pp.1546-1556, 2004.
DOI : 10.1155/S1110865704312199

M. Mitzenmacher, A note on low-density parity-check codes for erasures and errors. SRC Technical Note, 1998.

[. Maymounkov and D. Eres, Rateless Codes and Big Downloads, Proc. of the 2nd Int. Workshop Peer-to-Peer Systems (IPTPS), 2003.
DOI : 10.1007/978-3-540-45172-3_23
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.5054

C. Measson, A. Montanari, and R. Urbanke, Maxwell's construction: the hidden bridge between maximum-likelihood and iterative decoding, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., p.225, 2004.
DOI : 10.1109/ISIT.2004.1365262

D. Mackay and M. Post, Weakness of margulis and ramanujanmargulis low-density parity-check codes, Proc of MFCSIT2002, 2003.

N. Elitza, A. Maneva, and . Shokrollahi, New model for rigorous analysis of LT codes, Proc. of IEEE Int. Symp. on Inform. Theory (ISIT), 2006.

A. Mohajer and . Shokrollahi, Raptor Codes with Fast Hard Decision Decoding Algorithms, 2006 IEEE Information Theory Workshop, ITW '06 Chengdu, pp.56-60, 2006.
DOI : 10.1109/ITW2.2006.323756

[. Okamura, Designing LDPC odes using cyclic shifts, Proc. of IEEE Int. Symp. on Inform. Theory (ISIT), p.151, 2003.

P. Oswald and A. Shokrollahi, Capacity-achieving sequences for the erasure channel, Proc. of IEEE Int. Symp. on Inform. Theory (ISIT), p.48, 2001.

P. Oswald and A. Shokrollahi, Capacity-achieving sequences for the erasure channel, IEEE Transactions on Information Theory, vol.48, issue.12, pp.3017-3028, 2002.
DOI : 10.1109/TIT.2002.805067

[. Poulliat, M. Fossorier, and D. Declercq, Design of regular (2, d c ) LDPC codes over GF(q) using their binary image. accepted for publication in IEEE Trans, 2007.

P. Piantanida, Multi-user Information Theory: State Information and Imperfect Channel Knowledge, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00168330

[. Piantanida, P. Matz, and . Duhamel, Outage behavior of discrete memoryless channels under channel estimation errorsl, 2006.

[. Pishro-nik and F. Fekri, On Raptor Codes, 2006 IEEE International Conference on Communications, pp.1137-1141, 2006.
DOI : 10.1109/ICC.2006.254900

[. Piantanida, S. Sadough, and P. Duhamel, On the Outage Capacity of a Practical Decoder Using Channel Estimation Accuracy, 2007 IEEE International Symposium on Information Theory, 2007.
DOI : 10.1109/ISIT.2007.4557559

W. Peterson and E. J. Weldon, Error Correcting Codes, 1972.

A. Roumy and D. Declercq, Characterization and Optimization of LDPC Codes for the 2-User Gaussian Multiple Access Channel, EURASIP Journal on Wireless Communications and Networking, vol.2007, issue.1, 2007.
DOI : 10.1109/18.910578

A. Roumy, S. Guemghar, G. Caire, and S. Verdú, Design Methods for Irregular Repeat???Accumulate Codes, IEEE Transactions on Information Theory, vol.50, issue.8, pp.1711-1727, 2004.
DOI : 10.1109/TIT.2004.831778
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.4116

T. Richardson, Error floors of LDPC codes, Proc. of 41st Allerton Conf, 2003.

T. J. Richardson, A. Shokrollahi, and R. Urbanke, 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

J. Thomas, R. Richardson, and . Urbanke, The capacity of low-density parity-check codes under message-passing decoding, IEEE Trans. Inform. Theory, vol.47, issue.2, pp.599-618, 2001.

[. Richardson and R. Urbanke, Multi-edge type LDPC codes, 2004.

[. Richardson and R. Urbanke, Modern Coding Theory, 2007.
DOI : 10.1017/CBO9780511791338

[. Sankaranarayanan, R. Shashi-kiran-chilappagari, B. Radhakrishnan, and . Vasi´cvasi´c, Failures of the gallager b decoder: Analysis and applications, Proc. of UCSD Workshop on Information Theory and Its Applications, 2006.

[. Sesia, G. Caire, and G. Vivier, Incremental Redundancy Hybrid ARQ Schemes Based on Low-Density Parity-Check Codes, IEEE Transactions on Communications, vol.52, issue.8, pp.1311-1321, 2004.
DOI : 10.1109/TCOMM.2004.833022

[. Shokrollahi, Raptor codes, SVW05] Emina Soljanin, Nedeljko Varnica, and Philip Whiting, pp.2551-2567, 2005.
DOI : 10.1109/TIT.2006.874390

[. Soljanin, N. Varnica, and P. Whiting, Punctured vs rateless codes for hybrid ARQ, Proc. of IEEE ITW, pp.155-159, 2006.

J. Thorpe, K. Andrews, and S. Dolinar, Methodologies for designing LDPC codes using protographs and circulants, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., p.236, 2004.
DOI : 10.1109/ISIT.2004.1365273

M. Tanner, A recursive approach to low complexity codes, IEEE Transactions on Information Theory, vol.27, issue.5, pp.533-547, 1981.
DOI : 10.1109/TIT.1981.1056404

J. Thorpe, Low-density parity-check (LDPC) codes constructed from protographs, JPL Interplanetary Network Progress (INP), 2003.

[. Tian, C. R. Jones, J. D. Villasenor, and R. D. Wesel, Construction of irregular LDPC codes with low error floors, IEEE International Conference on Communications, 2003. ICC '03., pp.3125-3129, 2004.
DOI : 10.1109/ICC.2003.1203996

[. Tian, C. R. Jones, J. D. Villasenor, and R. D. Wesel, Selective Avoidance of Cycles in Irregular LDPC Code Construction, IEEE Transactions on Communications, vol.52, issue.8, pp.1242-1247, 2004.
DOI : 10.1109/TCOMM.2004.833048

R. Michael, D. Tanner, T. Sridhara, and . Fuja, A class of groupstructured LDPC codes, Proc. of ISTA, 2001.

D. Tse and P. Viswanath, Fundamentals of Wireless Communications, 2005.
DOI : 10.1017/CBO9780511807213

A. J. Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Transactions on Information Theory, vol.13, issue.2, pp.260-269, 1937.
DOI : 10.1109/TIT.1967.1054010

[. Xiao, H. Amir, and . Banihashemi, Improved Progressive-Edge-Growth (PEG) Construction of Irregular LDPC Codes, IEEE Communications Letters, vol.8, issue.12, pp.715-717, 2004.
DOI : 10.1109/LCOMM.2004.839612

[. Yao, L. Chen, H. Li, and H. Xu, Research on Fountain Codes in Deep Space Communication, 2008 Congress on Image and Signal Processing, pp.219-224, 2008.
DOI : 10.1109/CISP.2008.59