@. Consider and N. Combined, the interesting result in Chapter 3 is that the asymptotic outage probability of MRS does not depend on the relay channels This result can be extended to study different aspects, for example , effects of the number of relays and their location. In homogeneous relay networks, the relays are randomly generated according to some random processes , e.g., Poisson point process and their location is uniform distributed over the surface

E. V. Meulen, Three-Terminal Communication Channels, Advances in Applied Probability, vol.3, issue.1, pp.120-154, 1971.
DOI : 10.2307/1426331

T. Cover and 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

A. Wyner, On source coding with side information at the decoder Information Theory, IEEE Transactions on, vol.21, issue.3, pp.294-300, 1975.

A. Host-madsen and J. Zhang, Capacity bounds and power allocation for wireless relay channels Information Theory, IEEE Transactions on, vol.51, issue.6, pp.2020-2040, 2005.

R. Nabar, H. Bolcskei, and F. Kneubuhler, Fading Relay Channels: Performance Limits and Space???Time Signal Design, Selected Areas in Communications, pp.1099-1109, 2004.
DOI : 10.1109/JSAC.2004.830922

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.988

E. Gamal, A. , and S. Zahedi, Capacity of a class of relay channels with orthogonal components Information Theory, IEEE Transactions on, vol.51, issue.5, pp.1815-1817, 2005.

Y. Liang and V. Veeravalli, Gaussian Orthogonal Relay Channels: Optimal Resource Allocation and Capacity Information Theory, IEEE Transactions on, vol.51, issue.9, pp.3284-3289, 2005.
DOI : 10.1109/tit.2005.853305

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.332.1693

E. Gamal, A. , M. Mohseni, and S. Zahedi, Bounds on capacity and minimum energy-per-bit for AWGN relay channels Information Theory, IEEE Transactions on, vol.52, issue.4, pp.1545-1561, 2006.

A. Dana and B. Hassibi, On the power efficiency of sensory and ad hoc wireless networks Information Theory, IEEE Transactions on, vol.52, issue.7, pp.2890-2914, 2006.

A. Nosratinia, T. Hunter, and A. Hedayat, Cooperative communication in wireless networks, IEEE Communications Magazine, vol.42, issue.10, pp.42-74, 2004.
DOI : 10.1109/MCOM.2004.1341264

T. Hunter and A. Nosratinia, Diversity through coded cooperation, IEEE Transactions on Wireless Communications, vol.5, issue.2, pp.283-289, 2006.
DOI : 10.1109/TWC.2006.1611050

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.419.2315

M. Janani, A. Hedayat, T. E. Hunter, and A. Nosratinia, Coded Cooperation in Wireless Communications: Space-Time Transmission and Iterative Decoding, IEEE Transactions on Signal Processing, vol.52, issue.2, pp.362-371, 2004.
DOI : 10.1109/TSP.2003.821100

G. Kramer, M. Gastpar, and P. Gupta, Cooperative Strategies and Capacity Theorems for Relay Networks Information Theory, IEEE Transactions on, vol.51, issue.9, pp.3037-3063, 2005.

G. Kramer and A. Van-wijngaarden, On the white Gaussian multiple-access relay channel, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060), p.40, 2000.
DOI : 10.1109/ISIT.2000.866330

L. Sankaranarayanan, G. Kramer, and N. B. Mandayam, Hierarchical sensor networks: capacity bounds and cooperative strategies using the multiple-access relay channel model, 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2004. IEEE SECON 2004., pp.191-199, 2004.
DOI : 10.1109/SAHCN.2004.1381917

D. Chen, K. Azarian, and J. Laneman, A Case for Amplify–Forward Relaying in the Block-Fading Multiple-Access Channel, IEEE Transactions on Information Theory, vol.54, issue.8, pp.3728-3733, 2008.
DOI : 10.1109/TIT.2008.926336

Y. Liang and G. Kramer, Rate Regions for Relay Broadcast Channels Information Theory, IEEE Transactions on, vol.53, issue.10, pp.3517-3535, 2007.

R. Ahlswede, C. Ning, S. Y. Li, and R. W. Yeung, Network information flow Information Theory, IEEE Transactions on, vol.46, issue.4, pp.1204-1216, 2000.

T. Ho, R. Koetter, M. Medard, D. Karger, and M. Effros, The benefits of coding over routing in a randomized setting, IEEE International Symposium on Information Theory, 2003. Proceedings., p.442, 2003.
DOI : 10.1109/ISIT.2003.1228459

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. Jaggi, P. Sanders, P. Chou, M. Effros, S. Egner et al., Polynomial time algorithms for multicast network code construction Information Theory, IEEE Transactions on, issue.6, pp.51-1973, 2005.
DOI : 10.1109/tit.2005.847712

URL : http://authors.library.caltech.edu/1814/1/JAGieeetit05.pdf

T. Ho, M. Medard, R. Koetter, D. Karger, M. Effros et al., A Random Linear Network Coding Approach to Multicast Information Theory, IEEE Transactions on, issue.10, pp.52-4413, 2006.

T. Ho, M. Mdard, M. Effros, and R. Koetter, Network Coding for Correlated Sources, CISS, 2004.

J. Barros and S. Servetto, Network information flow with correlated sources Information Theory, IEEE Transactions on, vol.52, issue.1, pp.155-170, 2006.

X. Zhang, G. Neglia, J. Kurose, and D. Towsley, On the Benefits of Random Linear Coding for Unicast Applications in Disruption Tolerant Networks, Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks 4th International Symposium on, pp.1-7, 2006.

S. Katti, H. Rahul, W. Hu, D. Katabi, M. Medard et al., XORs in the Air: Practical Wireless Network Coding, IEEE/ACM Transactions on Networking, vol.16, issue.3, pp.497-510, 2008.
DOI : 10.1109/TNET.2008.923722

S. Zhang, S. C. Liew, and P. P. Lam, Hot topic, Proceedings of the 12th annual international conference on Mobile computing and networking , MobiCom '06, pp.358-365, 2006.
DOI : 10.1145/1161089.1161129

P. Popovski and H. Yomo, Bi-directional Amplification of Throughput in a Wireless Multi-Hop Network, 2006 IEEE 63rd Vehicular Technology Conference, pp.588-593, 2006.
DOI : 10.1109/VETECS.2006.1682892

S. Katti, S. Gollakota, and D. Katabi, Embracing wireless interference, ACM SIGCOMM Computer Communication Review, vol.37, issue.4, pp.397-408, 2007.
DOI : 10.1145/1282427.1282425

B. Nazer and M. Gastpar, Computing over Multiple-Access Channels with Connections to Wireless Network Coding, 2006 IEEE International Symposium on Information Theory, 2006.
DOI : 10.1109/ISIT.2006.262047

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.7909

M. Wilson, K. Narayanan, H. Pfister, and A. Sprintson, Joint Physical Layer Coding and Network Coding for Bidirectional Relaying Information Theory, IEEE Transactions on, issue.11, pp.56-5641, 2010.

T. Duc and C. Jinho, Convolutional Codes in Two-Way Relay Networks with Physical-Layer Network Coding, Wireless Communications IEEE Transactions on, vol.9, issue.9, pp.2724-2729, 2010.

M. C. Castro, B. F. Uchoa-filho, T. T. Vinhoza, M. Noronha-neto, and J. Barros, Improved joint turbo decoding and physical-layer network coding, 2012 IEEE Information Theory Workshop, pp.2012-532
DOI : 10.1109/ITW.2012.6404731

J. Liu, T. Meixia, and X. Youyun, Pairwise Check Decoding for LDPC Coded Two-Way Relay Block Fading Channels, IEEE Transactions on Communications, vol.60, issue.8, pp.60-2065, 2012.
DOI : 10.1109/TCOMM.2012.050812.110187

URL : http://arxiv.org/abs/1106.6174

C. Hausl, F. Schreckenbach, I. Oikonomidis, and G. Bauch, Iterative network and channel decoding on a tanner graph, Proc. Allerton Conf. on Commun., Control and Computing, 2005.

C. Hausl and P. Dupraz, Joint Network-Channel Coding for the Multiple-Access Relay Channel, Sensor and Ad Hoc Communications and Networks, 2006. SECON '06. 2006 3rd Annual IEEE Communications Society on, pp.817-822, 2006.

D. Duyck, D. Capirone, J. Boutros, and M. Moeneclaey, Analysis and Construction of Full-Diversity Joint Network-LDPC Codes for Cooperative Communications, EURASIP Journal on Wireless Communications and Networking, vol.2010, issue.1, pp.2010-805216, 2010.
DOI : 10.1109/TIT.2005.856942

X. Xiaoyan, M. F. Flanagan, N. Goertz, and J. Thompson, Joint Channel and Network Coding for Cooperative Diversity in a Shared- Relay Environment, Wireless Communications IEEE Transactions on, vol.9, issue.8, pp.2420-2423, 2010.

A. Hatefi, Distributed coding for Wireless Cooperative Networks, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00829100

Y. Li, B. Vucetic, T. Wong, and M. Dohler, Distributed Turbo Coding With Soft Information Relaying in Multihop Relay Networks, Selected Areas in Communications, pp.2040-2050, 2006.
DOI : 10.1109/JSAC.2006.881630

P. Weitkemper, D. Wuebben, V. Kuehn, and K. Kammeyer, Soft Information Relaying for Wireless Networks with Error-Prone Source-Relay Link, Source and Channel Coding (SCC), pp.1-6, 2008.

H. H. Sneesens and L. Vandendorpe, Soft decode and forward improves cooperative communications, 6th IEE International Conference on 3G and Beyond (05/11182), pp.157-160, 2005.
DOI : 10.1049/cp:20050196

G. Al-habian, A. Ghrayeb, and M. Hasna, Controlling Error Propagation in Network-Coded Cooperative Wireless Systems, 2009 IEEE International Conference on Communications, pp.1-6, 2009.
DOI : 10.1109/ICC.2009.5198855

N. Sinh-le-hong, A. Ghrayeb, G. Al-habian, and M. Hasna, Mitigating Error Propagation in Two-Way Relay Channels with Network Coding, Wireless Communications IEEE Transactions on, vol.9, issue.11, pp.3380-3390, 2010.

L. Ying, S. Guanghui, and W. Lili, Analysis of the joint network LDPC codes over orthogonal multi-access relay channel, Communications Letters IEEE, vol.14, issue.2, pp.184-186, 2010.

A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, A simple Cooperative diversity method based on network path selection, IEEE Journal on Selected Areas in Communications, vol.24, issue.3, pp.659-672, 2006.
DOI : 10.1109/JSAC.2005.862417

Y. Li, R. H. Louie, and B. Vucetic, Relay Selection With Network Coding in Two-Way Relay Channels, IEEE Transactions on Vehicular Technology, vol.59, issue.9, pp.4489-4499, 2010.
DOI : 10.1109/TVT.2010.2070817

Y. Jing and H. Jafarkhani, Single and multiple relay selection schemes and their achievable diversity orders, IEEE Transactions on Wireless Communications, vol.8, issue.3, pp.1414-1423, 2009.
DOI : 10.1109/TWC.2008.080109

C. Peng, Q. Zhang, M. Zhao, Y. Yao, and W. Jia, On the Performance Analysis of Network-Coded Cooperation in Wireless Networks, IEEE INFOCOM 2007, 26th IEEE International Conference on Computer Communications, pp.3090-3097, 2008.
DOI : 10.1109/INFCOM.2007.172

X. Ming and T. Aulin, Optimal Decoding and Performance Analysis of a Noisy Channel Network with Network Coding, Communications, IEEE Transactions on, vol.57, issue.5, pp.1402-1412, 2009.

M. D. Renzo, M. Iezzi, and F. Graziosi, Error Performance and Diversity Analysis of Multi-Source Multi-Relay Wireless Networks with Binary Network Coding and Cooperative MRC, IEEE Transactions on Wireless Communications, vol.12, issue.6, 2013.
DOI : 10.1109/TWC.2013.042413.121194

URL : https://hal.archives-ouvertes.fr/hal-00829269

H. H. Sneessens, J. Louveaux, and L. Vandendorpe, Turbocoded decode-and-forward strategy resilient to relay errors, Acoustics, Speech and Signal Processing IEEE International Conference on, pp.3213-3216, 2008.
DOI : 10.1109/icassp.2008.4518334

L. Sungeun, H. Myeongsu, and H. Daesik, Average SNR and Ergodic Capacity Analysis for Proactive and Reactive DF Relaying over Rayleigh Fading Channels, Vehicular Technology Conference, pp.1-5, 2009.

T. Yune, D. Kim, and G. Im, Opportunistic Network-Coded Cooperative Transmission with Demodulate-and-Forward Protocol in Wireless Channels, IEEE Transactions on Communications, vol.59, issue.7, pp.1-5, 2011.
DOI : 10.1109/TCOMM.2011.050911.090660

X. Vu, M. Direnzo, and P. Duhamel, Multiple-access relaying with network coding: iterative network/channel decoding with imperfect CSI, EURASIP Journal on Advances in Signal Processing, vol.2013, issue.1, 2013.
DOI : 10.1016/j.simpat.2010.10.001

URL : https://hal.archives-ouvertes.fr/hal-00933798

X. Vu, M. D. Renzo, and P. Duhamel, Iterative network/channel decoding for the noisy multiple-access relay channel (MARC), 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2901-2904, 2012.
DOI : 10.1109/ICASSP.2012.6288523

URL : https://hal.archives-ouvertes.fr/hal-00714408

X. Vu, M. Direnzo, and P. Duhamel, Improved receiver for cooperative wireless communication systems using QAM and Galois Field network coding, Advanced Technologies for Communications (ATC), p.2012, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00732636

X. Vu, M. D. Renzo, and P. Duhamel, Optimal and lowcomplexity iterative joint network/channel decoding for the multiple-access relay channel, Acoustics, Speech and Signal Processing (ICASSP) IEEE International Conference on, pp.3312-3315, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00661315

X. Vu, M. Direnzo, and P. Duhamel, BER Analysis of Joint Network/Channel decoding in Block Rayleigh fading channels, Personal, Indoor and Mobile Radio Communications, 2013. PIMRC'13., 24th IEEE International Symposium on, pp.698-702, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00839529

X. Vu, P. Duhamel, and M. D. Renzo, Performance analysis for Network Coding Cooperation with Channel coding and Selection DF in Rayleigh Fading channels, Communications, IEEE Letters on, 2013.

X. Vu, M. D. Renzo, and P. Duhamel, Outage and Diversity analysis of Network Coding with Single and Multiple Relay Selection, IEEE Transactions on Communications

X. Vu, N. Vo, M. D. Renzo, and P. Duhamel, Performance analysis of relay networks with channel code in low SNR regime, 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC), pp.575-579, 2013.
DOI : 10.1109/SPAWC.2013.6612115

URL : https://hal.archives-ouvertes.fr/hal-00816682

X. Vu, P. Duhamel, V. N. Bao, and M. D. Renzo, Partial Relaying in Channel-coded Relay Networks with Relay Selection, IEEE Transactions on Communications

T. T. Kim, G. Caire, and M. Skoglund, Decode-and-Forward Relaying With Quantized Channel State Feedback: An Outage Exponent Analysis, IEEE Transactions on Information Theory, vol.54, issue.10, pp.4548-4564, 2008.
DOI : 10.1109/TIT.2008.928978

D. Zhiguo and K. K. Leung, Impact of Imperfect Channel State Information on Bi-Directional Communications With Relay Selection, IEEE Transactions on Signal Processing, vol.59, issue.11, pp.59-5657, 2011.
DOI : 10.1109/TSP.2011.2163403

R. Knopp and P. A. Humblet, On coding for block fading channels Information Theory, IEEE Transactions on, vol.46, issue.1, pp.189-205, 2000.

J. K. Cavers, An analysis of pilot symbol assisted modulation for Rayleigh fading channels (mobile radio), IEEE Transactions on Vehicular Technology, vol.40, issue.4, pp.686-693, 1991.
DOI : 10.1109/25.108378

J. G. Proakis, Digital communications, McGraw-Hill series in electrical and computer engineering, 2001.

A. Glavieux, Channel Coding in Communication Networks: From Theory to Turbo Codes, 2007.
DOI : 10.1002/9780470612422

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate (Corresp.), " Information Theory, IEEE Transactions on, vol.20, issue.2, pp.284-287, 1974.

A. Nasri, R. Schober, and M. Uysal, Performance and Optimization of Network-Coded Cooperative Diversity Systems, IEEE Transactions on Communications, vol.61, issue.3, pp.1-12, 2013.
DOI : 10.1109/TCOMM.2012.122112.110814

G. Zheng, H. Jie, W. Bing, Z. Shengli, C. Jun-hong et al., A Practical Joint Network-Channel Coding Scheme for Reliable Communication in Wireless Networks, IEEE Transactions on Wireless Communications, vol.11, issue.6, pp.2084-2094, 2012.
DOI : 10.1109/TWC.2012.050112.110395

Y. Li, R. H. Louie, and B. Vucetic, Relay Selection With Network Coding in Two-Way Relay Channels, IEEE Transactions on Vehicular Technology, vol.59, issue.9, pp.4489-4499, 2010.
DOI : 10.1109/TVT.2010.2070817

M. L. Cedervall and R. Johannesson, A fast algorithm for computing distance spectrum of convolutional codes Information Theory, IEEE Transactions on, vol.35, issue.6, pp.1146-1159, 1989.

M. Chiani, D. Dardari, and M. K. Simon, New exponential bounds and approximations for the computation of error probability in fading channels, IEEE Transactions on Wireless Communications, vol.24, issue.5, pp.840-845, 2003.
DOI : 10.1109/TWC.2003.814350

S. Atapattu, Y. Jing, H. Jiang, and C. Tellambura, Relay Selection Schemes and Performance Analysis Approximations for Two-Way Networks, IEEE Transactions on Communications, vol.61, issue.3, pp.61-987, 2013.
DOI : 10.1109/TCOMM.2012.010313.100669

H. Topakkaya and W. Zhengdao, Wireless Network Code Design and Performance Analysis Using Diversity-Multiplexing Tradeoff, IEEE Transactions on Communications, vol.59, issue.2, pp.488-496, 2011.
DOI : 10.1109/TCOMM.2011.111710.100233

W. Guan and K. Liu, Diversity Analysis of Analog Network Coding with Multi-User Interferences, IEEE Transactions on Wireless Communications, vol.12, issue.2, pp.668-679, 2013.
DOI : 10.1109/TWC.2012.121712.112232

M. K. Simon and M. Alouini, Digital communication over fading channels, Wiley series in telecommunications and signal processing, 2005.

R. C. Singleton, Maximum distance q -nary codes Information Theory, IEEE Transactions on, vol.10, issue.2, pp.116-118, 1964.

D. H. Woldegebreal and H. Karl, Multiple-Access Relay Channel with Network Coding and Non-Ideal Source-Relay Channels, 2007 4th International Symposium on Wireless Communication Systems, pp.732-736, 2007.
DOI : 10.1109/ISWCS.2007.4392437

T. Wang, A. Cano, G. B. Giannakis, and J. N. Laneman, High-Performance Cooperative Demodulation With Decode-and-Forward Relays, IEEE Transactions on Communications, vol.55, issue.7, pp.1427-1438, 2007.
DOI : 10.1109/TCOMM.2007.900631

S. Benedetto, R. Garello, and G. Montorsi, A search for good convolutional codes to be used in the construction of turbo codes, IEEE Transactions on Communications, vol.46, issue.9, pp.1101-1105, 1998.
DOI : 10.1109/26.718548

S. L. Nguyen, A. Ghrayeb, G. Al-habian, and M. Hasna, Mitigating Error Propagation in Two-Way Relay Channels with Network Coding, IEEE Transactions on Wireless Communications, vol.9, issue.11, pp.3380-3390, 2010.
DOI : 10.1109/TWC.2010.090210.091464

M. Uysal, Diversity analysis of space-time coding in cascaded Rayleigh fading channels, IEEE Communications Letters, vol.10, issue.3, pp.165-167, 2006.
DOI : 10.1109/LCOMM.2006.1603372

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

T. Duong and V. N. Bao, Performance analysis of selection decode-and-forward relay networks, Electronics Letters, vol.44, issue.20, pp.1206-1207, 2008.
DOI : 10.1049/el:20081952

P. Frenger, P. Orten, and T. Ottosson, Convolutional codes with optimum distance spectrum, IEEE Communications Letters, vol.3, issue.11, pp.317-319, 1999.
DOI : 10.1109/4234.803468