S. Yang and J. Belfiore, Distributed rotation recovers spatial diversity, 2010 IEEE International Symposium on Information Theory, 2010.
DOI : 10.1109/ISIT.2010.5513461

URL : https://hal.archives-ouvertes.fr/hal-00528200

W. Hachem, P. Bianchi, and P. Ciblat, Outage Probability-Based Power and Time Optimization for Relay Networks, IEEE Transactions on Signal Processing, vol.57, issue.2, pp.764-782, 2009.
DOI : 10.1109/TSP.2008.2008245

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

B. Nazer and M. Gastpar, Compute-and-forward: Harnessing interference through structured codes, " iEEE Transaction on Information Theory available on arxiv http, 2009.
DOI : 10.1109/tit.2011.2165816

URL : http://arxiv.org/abs/0908.2119

O. L. Pedarsani and S. Yang, On the DMT optimality of the rotate-and-forward scheme in a two-hop MIMO relay channel, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2011.
DOI : 10.1109/ALLERTON.2010.5706891

URL : https://hal.archives-ouvertes.fr/hal-00528221

U. Niesen and P. Whiting, The degrees of freedom of compute-and-forward, 2011.

A. Sendonaris, E. Erkip, and B. Aazhang, User cooperation diversity-part I: system description, IEEE Transactions on Communications, vol.51, issue.11, pp.1927-1938, 2003.
DOI : 10.1109/TCOMM.2003.818096

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. N. Laneman, D. Tse, and G. W. , Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior, IEEE Transactions on Information Theory, vol.50, issue.12, pp.3062-3080, 2004.
DOI : 10.1109/TIT.2004.838089

J. N. Laneman and G. W. , Distributed space-time-coded protocols for exploiting cooperative diveristy in wireless networks, IEEE Transactions on Communications, vol.49, issue.10, pp.2415-2425, 2003.

K. Azarian, H. E. Gamal, and P. Schniter, On the Achievable Diversity???Multiplexing Tradeoff in Half-Duplex Cooperative Channels, IEEE Transactions on Information Theory, vol.51, issue.12, pp.4152-4172, 2005.
DOI : 10.1109/TIT.2005.858920

R. U. Nabar, H. Bolcskei, and F. W. Kneubuhler, Fading Relay Channels: Performance Limits and Space???Time Signal Design, IEEE Journal on Selected Areas in Communications, vol.22, issue.6, pp.1099-1109, 2004.
DOI : 10.1109/JSAC.2004.830922

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

S. Yang and J. Belfiore, Towards the Optimal Amplify-and-Forward Cooperative Diversity Scheme, IEEE Transactions on Information Theory, vol.53, issue.9, pp.3114-3126, 2007.
DOI : 10.1109/TIT.2007.903133

URL : https://hal.archives-ouvertes.fr/hal-00021690

T. M. Cover and A. A. Gamal, Capacity theorems for the relay channel, IEEE Transactions on Information Theory, vol.25, issue.5, pp.572-584, 1979.
DOI : 10.1109/TIT.1979.1056084

M. Yukusel and E. Erkip, Multiple-antenna cooperative wireless systems: A diversitymultiplexing tradeoff perspective, IEEE Transactions on Information Theory, vol.5, issue.12, pp.3371-3393, 2007.

K. Sreeram, P. V. Birenjith, and . Kumar, Dmt of multi-hop cooperative networks - Part I: Basic results, note = available on arxiv http

C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

G. J. Foschini, Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas, Bell Labs Technical Journal, vol.1, issue.2, pp.41-59, 1996.
DOI : 10.1002/bltj.2015

L. Zheng and D. Tse, Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels, IEEE Transactions on Information Theory, vol.49, issue.5, pp.1073-1096, 2003.
DOI : 10.1109/TIT.2003.810646

E. Lawler, Combinatorial Optimization: Networks and Matroids, 2001.

S. Yang and J. Belfiore, Diversity of MIMO multihop relay channels

Y. Jing and B. Hassibi, Distributed Space-Time Coding in Wireless Relay Networks, IEEE Transactions on Wireless Communications, vol.5, issue.12, pp.3524-3536, 2006.
DOI : 10.1109/TWC.2006.256975

URL : http://authors.library.caltech.edu/7270/1/JINieeetwc06.pdf

C. Rao and B. Hassibi, Diversity-Multiplexing Gain Trade-off of a MIMO System with Relays, 2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks, 2007.
DOI : 10.1109/ITWITWN.2007.4318029

S. Borade, L. Zheng, and R. Gallager, Amplify-and-Forward in Wireless Relay Networks: Rate, Diversity, and Network Size, IEEE Transactions on Information Theory, vol.53, issue.10, pp.3302-3335, 2007.
DOI : 10.1109/TIT.2007.904774

S. O. Gharan, A. Bayesteh, and A. K. Khandani, Diversity multiplexing tradeoff in multi-antenna multi-relay networks: Improvements and some optimality results

A. S. Avestimehr, S. N. Diggavi, and D. Tse, Wireless Network Information Flow: A Deterministic Approach, IEEE Transactions on Information Theory, vol.57, issue.4
DOI : 10.1109/TIT.2011.2110110

URL : http://arxiv.org/abs/0906.5394

S. Yang, Cooperative diversity of MIMO channels with Amplify-and-Forward, 2007.

W. Zeng, M. Wang, C. Xiao, and J. Lu, On the Power Allocation for Relay Networks with Finite-Alphabet Constraints, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010, 2010.
DOI : 10.1109/GLOCOM.2010.5684332

J. M. Paredes and A. B. Gershman, Relay network beamforming and power control using maximization of mutual information, 2010.

W. T. Wells, R. L. Anderson, and J. W. , The Distribution of the Product of Two Central or Non-Central Chi-Square Variates, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1016-1020, 1962.
DOI : 10.1214/aoms/1177704469

L. S. Gradshteyn and I. M. Ryzbik, Tables of Integrals. Series and Products, 2000.

R. Ahlswede, N. Cai, S. R. Li, and R. W. Yeung, Network information flow, IEEE Transactions on Information Theory, vol.46, issue.4, pp.1204-1216, 2000.
DOI : 10.1109/18.850663

K. Menger, Zur allgemeinen kurventheorie, Fundamenta Mathematicae, vol.10, pp.95-115, 1927.
DOI : 10.1007/bf02307626

L. R. Jr and D. R. Fulkerson, Maximal flow through a network, Canadian Journal of Mathematics, vol.8, pp.399-404, 1956.

P. Elias, A. Feinstein, and C. E. Shannon, A note on the maximum flow through a network, IEEE Transactions on Information Theory, vol.2, issue.4, pp.117-119, 1956.
DOI : 10.1109/TIT.1956.1056816

S. R. Li, R. W. Yeung, and N. Cai, Linear network coding, IEEE Transactions on Information Theory, vol.49, issue.2, pp.371-381, 2003.
DOI : 10.1109/TIT.2002.807285

URL : https://hal.archives-ouvertes.fr/hal-01327498

C. Fragouli and E. Soljanin, Foudations and Trends on Networking: Network Coding Fundamentals, 2007.

S. Zhang, S. Liew, and P. P. Lam, Physical-layer network coding, p.2475

P. Popovski and H. Yomo, The anti-packets can increase the achievable throughput of a wireless multihop network, IEEE Intenrational Conference on Communications, pp.11-15, 2006.

P. Popovski and T. Koike-akino, Coded Bidirectional Relaying in Wireless Networks, New Directions in Wireless Communications Research, pp.291-316, 2009.
DOI : 10.1007/978-1-4419-0673-1_11

M. P. Wilson, K. Narayanan, H. Pfister, and A. Sprintson, Joint Physical Layer Coding and Network Coding for Bidirectional Relaying, IEEE Transactions on Information Theory, vol.56, issue.11, pp.5641-5654, 2010.
DOI : 10.1109/TIT.2010.2068750

URL : http://arxiv.org/abs/0805.0012

T. Koike-akino, P. Popovski, and V. Tarokh, Optimized constellations for two-way wireless relaying with physical network coding, IEEE Journal on Selected Areas in Communications, vol.27, issue.5, pp.773-787, 2009.
DOI : 10.1109/JSAC.2009.090617

B. Hern and K. Narayanan, Multilevel coding schemes for computeand-forward, 2010.
DOI : 10.1109/isit.2011.6033840

URL : http://arxiv.org/abs/1010.1016

R. Koetter and M. Medard, An algebraic approach to network coding, IEEE/ACM Transactions on Networking, vol.11, issue.5, pp.782-795, 2003.
DOI : 10.1109/TNET.2003.818197

S. Katti, S. Gollakota, and D. Katabi, Embracing wireless interference: Analog network coding, ACM SIGCOMM, 2007.
DOI : 10.1145/1282427.1282425

S. H. Lim, Y. Kim, A. E. Gamal, and S. Chung, Noisy Network Coding, IEEE Transactions on Information Theory, vol.57, issue.5, pp.3132-3152, 2011.
DOI : 10.1109/TIT.2011.2119930

C. Feng, D. Silva, and F. R. Kschischang, An algebraic approach to Physical-Layer Network Coding, ISIT 2010, 2010.
DOI : 10.1109/isit.2010.5513739

URL : http://arxiv.org/abs/1005.2646

B. Nazer and M. Gastpar, The case for structured random codes in network capacity theorems, European Transactions on Telecommunications, vol.11, issue.4, 2008.
DOI : 10.1002/ett.1284

J. H. Conway and N. J. Sloane, Sphere Packings, Lattices and Groups, 1998.

H. Cohen, A Course in Computational Algebraic Number Theory, Pages 103-105. Section 2.7.3: Finding Small Vectors in Lattices, 1993.
DOI : 10.1007/978-3-662-02945-9

U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Mathematics of Computation, vol.44, issue.170, pp.463-471, 1985.
DOI : 10.1090/S0025-5718-1985-0777278-8

R. L. Cormen, C. E. Leiserson, and C. Stein, Introduction to Algorithms. Third Edition, 2009.

D. Micciancio and O. Regev, Worst???Case to Average???Case Reductions Based on Gaussian Measures, SIAM Journal on Computing, vol.37, issue.1, pp.267-302, 2007.
DOI : 10.1137/S0097539705447360

J. W. Cassels, Introduction to Algorithms. An Introduction to Diophantine Approximation, 1957.

S. V. Clarkson, Approximation of linear forms by lattice points with applications to signal processing, 1997.

G. Poltyrev, On coding without restrictions for the AWGN channel, IEEE Transactions on Information Theory, vol.40, issue.2, pp.409-417, 1994.
DOI : 10.1109/18.312163

A. Osmane-was-born-in-lebanon, He received his engineering diploma from Telecom ParisTech former Ecole Nationale Supérieure des Télécommunications de Paris in 2008 and his master degree from, 1985.

A. Osmane and J. Belfiore, Publications The content of this thesis was submitted to the following conferences and journal papers The Compute-and-Forward Protocol: Implementation and Practical Aspects, Journal papers

J. Osmane and . Belfiore, Practical Constraints on Lattice Codes for the Computeand-Forward Protocol: The Flatness Factor, preparation to be submitted to IEEE Transactions on Wireless Communications

S. Osmane, J. Yang, and . Belfiore, On the performance of the Rotate-and-Forward protocol in the two-hop relay channels, 2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications
DOI : 10.1109/SPAWC.2011.5990473

URL : https://hal.archives-ouvertes.fr/hal-00628539

. Conference-papers-a, S. Osmane, J. Yang, and . Belfiore, On the Performance of the Rotate-and-Forward Protocol in the Two-Hop Relay Channels, ICC, 2011.

S. Osmane, J. Yang, and . Belfiore, Two-Hop Relay Channels with Limited Feed- Back, PIMRC, 2010.
DOI : 10.1109/pimrc.2010.5671726

URL : http://hal.upmc.fr/hal-00628535/file/Osmane_Yang_Belfiore_PIMRC_2010.pdf