Network coding on cooperative relay networks

Viet Nam National University, Ha Noi University of Engineering and Technology Lam Sinh Cong Network Coding On Cooperative Relay Networks Branch: Electronics and Telecommunications Technology Major: Electronics Engineering Code: 60 52 70 Master Thesis Summary Ha Noi-2012 Contents Abstract 1 Introduction 1.1 1.2 1.3 Introduction to cooperative relay networks 1.1.1 The relay protocols 1.1.2 Advantages of Cooperative Diversity Relaying Networks Introduction to Network Coding 1.2.1 Non-Binary and Binary Network Coding 1.2.2 Advantages of Network Coding 1.2.3 Weaknesses of Network Coding Cooperative Diversity Relaying Networks using network coding System models 2.1 Traditional Relay Multiple-Wireless Networks 2.2 Single Relay Networks using Network Coding 2.3 Multiple-Relay Networks using Network Coding Outage Probability Calculations 3.1 Mutual Information 3.2 Outage Probability Definition 3.3 Outage Probability of Multiple-Relay Networks 11 3.3.1 Traditional Decode-and-Forward relaying 11 3.3.2 Selection Decode-and-Forward relaying 12 3.4 Outage Probability of Single Relay Networks using Network coding 12 3.5 Outage Probability of Multiple-Relay Networks using Network Coding 16 Conclusions and Future Works 19 i Bibliography 19 ii List of Figures 2.1 A traditional single relay network 2.2 A traditional multiple-relay network 2.3 Network coding in single relay network 2.4 Multiple-relay network using network coding 3.1 The direct link between the input and the output 10 3.2 Outage probability of a direct link 11 3.3 Outage Probability of fixed and selection DF relay 13 3.4 The degraded system model of a single relay network based on NC 13 3.5 The degraded system model of a single relay network based on NC 14 3.6 Outage probability of the single relay network with and without network coding 15 3.7 Link s1 r1 is in outage 17 3.8 Outage probability of relay networks with different scenarios 18 iii Abstract In communication, Cooperative Diversity Relaying refers to devices communicating with one another with the help of relays in order to increase the performance of the network However, in one timeslot, the relay only transmits the signal of one source Therefore, Network Coding is introduced to improve the throughput of the network Combining Cooperative Relay Network and Network Coding should be studied to achieve significant benefits and overcome some weakness In this thesis, we consider the effect of Network Coding on Cooperative Relay Network We propose to use Selection Decode-and-Forward instead of Traditional Decode-and-Forward protocol at the relay We also use the instantaneous channel gains to calculate the outage probability of the proposal system model The rest of the thesis is organized as follows In Chapter II, the system model of a multiple-relay network is described The outage probability is calculated in Chapter III Finally, the conclusions and the future works are drawn in Section IV Chapter Introduction 1.1 Introduction to cooperative relay networks In recent years, MIMO (multi-input multi-output) technology based on spatial diversity and spatial diversity has attracted attention in wireless communication because it greatly improves the reliability, the throughput and the transmission rate without additional bandwidth nor requiring higher transmitter power However, this technique requires both the transmitter and the receiver to have multi-antennas, and all channels must be independent In practice, users not often achieve full-rank MIMO because they either not have multiple-antennas installed on a small-size devices, or the propagation environment cannot support MIMO, for example, there is not enough scattering Even if the users have enough antennas, full-rank MIMO is not guaranteed because the links between several antenna elements are often correlated To overcome the limitations in diversity gain MIMO, a new communication paradigm which uses an intermediate node to generate independent channel between the user and the base station was introduced The intermediate node often called relay node receives the signal transmitted from the user and forward it to the base station And this paradigm is called Cooperative Diversity Relaying Network 1.1.1 The relay protocols A key aspect of the cooperative communication process is the processing of the signal received from the source node carried out by the relay These different processing schemes depend on the protocols of the relays which can be generally categorized into fixed relaying schemes, selection relaying protocol (adaptive relaying schemes) and incremental relaying protocol 1.1.2 Advantages of Cooperative Diversity Relaying Networks Cooperative Diversity Relaying refers to devices communicating with one another with the help of relays in order to increase the performance of the network [3] Thereby, the relay channel can be considered as an auxiliary channel to the direct channel between the source and destination In Cooperative Diversity Relaying, the user can guarantee the maximum diversity which is equal the number of the relays plus the direct link, i.e being the minimum cut at each source It means that the limitation of MIMO technique has been overcome However, in cooperative relay network, we are able to use one or more relays, but in one timeslot, the relay only transmits the signal of one source 1.2 Introduction to Network Coding As discussed in the previous section, in a typical network, information is transmitted from the source node to each destination node through a chain of intermediate nodes by a method known as store-and-forward In this method, the intermediate node only processes and transmits a unique signal at one time without overlapping, thus slow down the through In order to increase the throughput of the network, network coding technique was introduced in [5] and then further developed in [6], as a new paradigm which exploits the characteristics of the broadcast communication channel to combine several input signals into one output signal at the intermediate node 1.2.1 Non-Binary and Binary Network Coding In binary network coding, the intermediate node uses XOR operator to consolidate the received messages transmitted form sources In non-binary network coding, each intermediate node uses a linear equation to combine the inputs and the destination uses the system of linear equation to decode the received messages 1.2.2 Advantages of Network Coding Increasing throughput achieved by increasing the efficiency of packet transmission is the most well-know benefit of network coding 1.2.3 Weaknesses of Network Coding The main issue of using network coding is that if a transmission error occurs, it could affect the detecting and coding at the intermediate node, and the destination node could receive useless information Besides, synchronization and transmission delay among the incoming data streams at the input of the intermediate node or destination node are also significant issues that need to be considered when network coding is applied The transmitted data can not be recovered until all the necessary information is received These are not big problems for non-real time services (e.g data and voice transmission), but they are should be considered carefully for real time services (e.g video transmission, ) 1.3 Cooperative Diversity Relaying Networks using network coding The most common example of NC-based network model is two-source one-relay topology, as shown in Figure 2.3 In this topology, two sources transmit their signals to the relay and the destination using broadcast technique Then, the relay combines its received signals into a unique signal and sends it to destination The traditional Decode-and-Forward (DF) protocol is often used at the relay which decodes the messages from its input nodes before sending them to its output nodes Often, the links between the sources and relay are assumed to be error-free so that the relay decodes the received messages successfully [3, 11–13] In [14], taking into account of link errors, the relay is assumed to perform DF without error checking and the network codes are designed for error correction In this thesis, instead of using DF relaying as in [14], we propose to use selection DF relaying at the relay The selection DF relaying protocol is designed to overcome the shortcomings of DF relaying when the measured SNR at the relay falls below a threshold such that the relay becomes unable to decode the messages, the source simply continues its direct transmission to the destination using repetition coding [15] In addition, we use Maximum Ratio Combining (MRC) at the destination Finally, we analyze the performance of the proposed scheme in terms of outage probability by using the instantaneous channel gains The analysis is based on a newly developed method for exact calculation of the outage probability [16] Chapter System models 2.1 Traditional Relay Multiple-Wireless Networks In this section, we will discuss about end-to-end signal of the selection Decode-and-Forward relay Relaying is assumed to operate in the time division mode having two phases (two time slots): the relay-receive phase and the relay-transmit phase The total received signal at the destination is given by equation (2.1) and (2.2) or        √  xsi  nsi d  ysi d   Ps hsi d =   +    √ yri d Ps hri d xri nri d (2.1)        √ ysi d   Ps hsi d  xsi  nsi d  =     +  √ ysi d x si nsi d Ps hsi d (2.2) Equatio Now, we consider a wireless network system model using two sources-and-one relay, as show in Figure 2.1 In this system model, the relay shares timeslot for both source S1 and S2 Therefore, it require timeslots to complete a transmission process In order to increase the network’s throughput by reducing the number of timeslots, we increase the number of relay Figure 2.2 shows a relay network using two relays (R1 , R2 ) with selection-DF protocol relaying information for two sources (S1 , S2 ) to the destination [18] It is clear that it requires at least time slots in order to complete a transmission process Because of using less time slot than system model depicted in Figure 2.1, it indicate that system model can improve the throughput of the networks Comparing with the system model depicted in figure 2.2, it cannot save any time slot, but we can save one relay 2.3 Multiple-Relay Networks using Network Coding Figure 2.4 shows a multiple-relay network using coding in the cooperative relays, it is considered as a technique to improve the robustness The system model under analysis is given by the multipleaccess relay channel, where two source nodes, S1 and S2 , communicate with destination with the help of two relays R1 and R2 The notation used for this system and their operation are the same S1 h s1d x1 R1 R2 x2 hs2r2 S2 h r1 d x1  x2 MRC x1  x2 D h r2 d hs2d Figure 2.4: Multiple-relay network using network coding in Session 2.2 for relay R1 and R2 At destination, we use MRC to combine the signals from R1 and R2 in to a better signal of higher SNR I hope that this may improve the robustness of the network Note that, if both relays R1 and R2 are not able to decode the messages of source Si , Si repeats its transmission to the destination by using repetition code In chapter 3, we will show that by using MRC, the performance of the network is increased Chapter Outage Probability Calculations 3.1 Mutual Information The instantaneous capacity of the system is given by the instantaneous mutual information contained in the input-output vectors Xs and Yd for fixed channel realization matrix A, and it is I(Xs ; Yd |A) = h(Yd ) − h(Yd |Xs ) = h(Yd ) − h(AXs |Xs ) − h(N ) (3.1) ARXs A∗ log2 det(Im + ) M +1 RN (3.2) Therefore [21] I(Xs ; Yd |A) = where M is the number of relays; and the covariance matrices of the input signal and the noise are, respectively RXs = E{Xs Xs∗ } = Ps I and RN = E{N N ∗ } = N0 I 3.2 Outage Probability Definition In this section, we define the outage probability of direct transmission between two nodes The received signal at the destination is given by y[n] = x[n]h[n] + w[n] Figure 3.1: The direct link between the input and the output Where x[n], h[n] and w[n] are transmitted signal, channel gain, and Addition White Gaussian Noise (AWGN), respectively We assume that h is independent and identically distributed Thus, the maximum average information between the input and the output is given by using (3.2) with M = 0, A = h, SN R = P/No : I = log(1 + SN R|h|2 ) in which SN R is the received signal-noise ratio at the destination The outage event of the information rate for a given threshold Rth is defined as: I ≤ Rth and equivalently [15] |h|2 < 2Rth − = µth SN R (3.3) µth is called the channel power threshold Then the outage probability is expressed as: Phout (µth ) = P (|hij |2 < µth ) ij (3.4) For Rayleigh fading, |hij |2 is exponentially distributed, with the probability density function (pdf) and cumulative density function (cdf) being respectively given by: fhij (µ) = µ exp − µij µij and Fhij (µ) = − exp −µ µij (3.5) Then, the outage probability is written as follow by combing (3.4) and (3.5) Phout (µth ) = Fhij (µth ) = − exp − ij 10 µth µij (3.6) Outage probability of one direct link Outage Probability 10 −1 10 µij=1 µij=2 −2 10 µ =3 ij −3 10 0.05 0.1 0.15 0.2 µth 0.25 0.3 0.35 0.4 Figure 3.2: Outage probability of a direct link 3.3 3.3.1 Outage Probability of Multiple-Relay Networks Traditional Decode-and-Forward relaying The maximum average mutual information between the input and the two outputs is expressed as below IDF = 1 log(1 + γsd ), log(1 + γsd + γrd ) 2 (3.7) Then the instantaneous channel gain is |hDF |2 = |hsd |2 , |hsd |2 + |hrd |2 (3.8) Then the outage probability of this model is given by [16] out PDF (µth ) = − P (|hDF |2 > µth ) = − P (|hsr |2 > µth )P (|hsd |2 + |hrd |2 > µth ) = − (1 − Fsr (µth )) − (µsd Fsd (µth ) − µrd Frd (µth )) µsd − µrd where µth is calculate by using equation (3.3) 11 (3.9) 3.3.2 Selection Decode-and-Forward relaying The information rate of a selection DF relay network in this case can be expressed as below [22]: ISDF i =      log(1 + 2γ si d ), γsi ri < γth (3.10)     21 log(1 + γs1 d + γr1 d ), γsi ri ≥ γth Because there is no correlation between the signals transmitted from source to the relays and from the relays to destination; and equal power from the sources and the relays, the instantaneous channel gain between the source and the destination is |hSDF i | =     2|hsi d |2 , |hsi ri |2 < µth (3.11)    |hs1 d |2 + |hr1 d |2 , |hsi ri |2 ≥ µth The probability of the event that the instantaneous channel gain falls below the threshold |hSDF i |2 < µth is out PSDF (µth ) = P (|hSDF |2 ≤ µth ) = P (2|hsi d |2 < µth )P (|hsi ri |2 < µth ) + P (|hsi ri |2 > µth )P (|hsi d |2 + |hri d |2 < µth ) (3.12) So, its outage probability under Rayleigh fading condition is [16] out PSDF = Fsd ( − Fsr (µth ) µth )Fsr (µth ) + {µsd Fsd (µth ) − µrd Frd (µth )} µsd − µrd (3.13) in which µth is defined as in equation (3.3) 3.4 Outage Probability of Single Relay Networks using Network coding We analyze all events which cause system outage 12 −1 10 −2 10 −3 Outage Probability 10 −4 10 Fixed Decode−and−Forward Relay Selection Decode−and−Forward Relay −5 10 −6 10 −7 10 0.005 0.01 0.015 0.02 0.025 µth 0.03 0.035 0.04 0.045 0.05 Figure 3.3: Outage Probability of fixed and selection DF relay • Link s1 r is in outage, then the source s1 repeats transmitting its signal to D The system model in Figure 2.3 is degraded to the one which is depicted in Figure 3.4 S1 x1 hs1d hrd R x2 hs2 r S2 D hs2d x2 Figure 3.4: The degraded system model of a single relay network based on NC 13 Therefore, the outage probability of this degraded model is given by: p1 (µth ) =P (|hs1 r |2 < µth )P (2|hs1 d |2 < µth ) (3.14) • Link s1 r and s2 r are free of errors It means that the relay decodes fully the sources’ messages, and then combine them into a unique signal before sending it to the destination The system is in outage if both link s1 d and s2 d are in failure The outage probability in this case is expressed as follows: p2 (µth ) =P (|hs1 r |2 > µth )P (|hs1 d |2 < µth ) P (|hs2 r |2 > µth ) P (|hs2 d |2 < µth ) + P (|hs2 d |2 > µth )P (|hrd |2 < µth ) (3.15) • Link s1 r is free of error, link s2 r is in outage, then the source s2 repeats transmitting its signal to D In this case, the relay only sends the signal of the source s1 The system model in this case is as shown in 3.5 S1 x1 hs1r hs1d hrd R x1 D hs2d x2 S2 Figure 3.5: The degraded system model of a single relay network based on NC Therefore, the outage probability in this case is given by: p3 (µth ) =P (|hs1 r |2 > µth )P (|hrd |2 + |Ps1 d |2 < µth )P (|hs2 r |2 < µth ) 14 (3.16) out (µ ) is calculated as follow: Finally, the outage probability of the system is PSDF th out PSDF (µth ) = p1 (µth ) + p2 (µth ) + p3 (µth ) (3.17) In which µth is the threshold which can be calculated from equation (3.3) In a Rayleigh fading environment, by using 3.6, we have:     p1 (µth ) = Fs1 r (µth )Fs1 d ( µ2th )         p2 (µth ) = (1 − Fs1 r (µth ))Fs1 d (µth ) (3.18)     (1 − Fs2 r (µth ))(Fs2 d (µth ) + (1 − Fs2 d (µth ))Frd (µth ))        p3 (µth ) = 1−Fs1 r (µrd Frd (µth ) − µs d Fs d (µth ))Fs r (µth ) 1 µsr −µs d −1 10 −2 Outage Probability 10 −3 10 Traditional Multiple−Relay Wireless Network Only direct link Single Relay Network using Network Coding −4 10 −5 10 0.01 0.02 0.03 0.04 0.05 µth 0.06 0.07 0.08 0.09 0.1 Figure 3.6: Outage probability of the single relay network with and without network coding 15 3.5 Outage Probability of Multiple-Relay Networks using Network Coding Because |hr1 d |2 and |hr2 d |2 are exponentially distributed, the probability density function and cumulative distribution function of |hrd |2 respectively are: fRD (µ) = µr1 d − µr2d −µ −µ e µr1 d − e µr2 d and FRD (µ) = µr1 d − µr2 d −µ −µ µr1 d (1 − e µr1 d ) − µr2 d (1 − e µr2 d ) then FRD (µ) = {µr1 d Fr1 d (µ) − µr2 d Fr2 d (µ)} µr1 d − µr2 d Therefore FRD (µth ) = 0.5Fr1 d (µth )Fr2 d (µth ) (3.19) The outage probability of the source S1 is obtain by calculating the probability of all events in the source-to-relay links which make the destination unable to decode the x1 messages from S1 • All source-relay links are free of error The probability of this event is given by: P1co = Ps1 d (PRD + (1 − PRD )Ps2 d ) (3.20) P1co (µth ) = Fs1 d (µth )(FRD (µth ) + (1 − FRD (µth ))Fs2 d (µth )) (3.21) Then, In which, FRD is calculated by using equation 3.19 • Link s1 r1 is in outage and others are free of errors The relay R1 only decode fully the message of S2 16 S1 h s1d x1 R1 h r1 d x2 x1  x2 R2 S2 x2 hs2r2 D h r2 d hs2d Figure 3.7: Link s1 r1 is in outage The probability of this event is expressed as below P2co = ps1 r1 ps1 d {(1 − pr2 d )ps2 r1 s + pr2 d } (3.22) Then, P2co (µth ) = Fs1 r1 (µth )Fs1 d (µth ){(1 − Fr2 d (µth ))Fs2 r1 s (µth ) + Fr2 d (àth )} (3.23) Link s1 r2 is in outage and others are in good It is easy to show that the outage probability in this case is express as below P3co (µth ) = Fs1 r2 (µth )Fs1 d (µth ){(1 − Fr1 d (µth ))Fs2 r2 s (àth ) + Fr1 d (àth )} (3.24) Both s1 r1 and s1 r2 are in outage In this case, x2 is only carried on link s1 d, therefore probability of x1 not being recovered is: P4co (µth ) = Fs1 r1 (µth )Fs1 r2 (µth )Fs1 d ( µth ) (3.25) It is not difficult to see that in cases in which there are more than source-relay links or source 17 s2 − ri (i = 1, 2) links are in errors, the outage probabilities are infinitesimal numbers (in the order of P or P ), so we can ignore these cases Thus, the outage probability of the source S1 of this model under a Rayleigh Fading environment is obtained by: P co (µth ) = P1co (µth ) + P2co (µth ) + P3co (µth ) + P4co (µth ) (3.26) −1 10 Traditional Multiple−Relay Wireless Network Single Relay Network using Network Coding Multiple−Relay Network using Network Coding −2 Outage Probability 10 −3 10 −4 10 −5 10 0.01 0.02 0.03 0.04 0.05 µth 0.06 0.07 0.08 0.09 0.1 Figure 3.8: Outage probability of relay networks with different scenarios Fig 3.8 indicates that the performance of the system model based on network coding with multiple-relay is better than others This can be explained as follows: • Using MRC at the destination to combine the signals from R1 and R2 into a better channel makes the transmission between the relays and destination become more reliability Thus, this system model will be more stable than an other which only uses one relay • In multiple-relay networks, there is no interaction between source i and relay j (i, j = 1, and i j) and between the relay R1 and the relay R2 It means that x1 is only transmitted by the source S1 on s1 d and R1 on r1 d link While, in multiple-relay networks using network coding, x1 is carried on link s1 d, r1 d and r2 d 18 Conclusions and Future Works In this thesis, we consider the effects of network coding on cooperative relay networks Instead of using traditional DF relaying, propose to use selection DF relaying which is designed to overcome the weaknesses of DF relaying By using the instantaneous channel gains, we calculate exactly the outage probabilities of systems models, i.e relaying networks with and without network coding, under a Rayleigh fading environment Comparing between the system models that only use one relay, we see that the robustness of the networks will be reduced when network coding is applied However, when we increase the number of the relays (using relays), the performance of network may be increase strongly, even it is better than the case in which network coding is not used Therefore, it may be said that in some cases, network coding also improves the robustness of the network Our proposed system model may be sub-optimal, but it has achieved what we expected 19 Bibliography [1] [Online] Available: http://en.wikipedia.org/wiki/Diversity scheme [2] K J RAYLIU, A K SADEK, W SU, and A KWASINSKI, Cooperative Communications and Networking, ninth dover printing, tenth gpo printing ed New York: Dover, 1964 [3] G Liu and Y Meng, “Completely opportunistic approach to network coding using in wireless network,” in Proc 4th Int Conf Wireless Communications, Networking and Mobile Computing (WiCOM 2008), 2008, pp 1–3 [4] D Tse and P Viswanath, Fundamentals ofWireless Communication CambridgeUni- versity Press, 2005 [5] Y R W and Z Z, “Distributed source coding for satel-lite communications,” IEEE Transactions on Information Theory, vol 45, p 11111120, 1999 [6] R Ahlswede, N Cai, S.-Y R Li, and R W Yeung, “Network information flow,” IEEE transactions on information theory, vol 46, pp 1204–1216, 2000 [7] M Xiao and M Skoglund, “Design of network codes for multiple-user multiple-relay wireless networks,” in ISIT 2009, June, 2009 [8] L Li, K Fan, and D Long, “Nonlinear network coding: A case study,” in IMECS 2008, March 2008 [9] R W Yeung, Information Theory and Network Coding Springer, May 31, 2008 [10] T Noguchi, T Matsuda, and MikiYamamoto, “Performance evaluation of new multicast architecture with network coding,” IEICE Trans Comm, vol E86-B, pp 1788–1795, 2003 20 [11] S Katti, H Rahul, W Hu, D Katabi, M Medard, and J Crowcroft, “Xors in the air: Practical wireless network coding,” IEEE/ACM Transactions on Networking, vol 16, no 3, pp 497–510, 2008 [12] Y Wu, P A Chou, and S.-Y Kung, “Information exchange inwireless networks with network coding and physical-layer broadcast,” Microsoft Research, Tech Rep MSR-TR2004-78, 2004 [13] S Fu, K Lu, Y Qian, and M Varanasi, “Cooperative network coding for wireless ad-hoc networks,” in IEEE GLOBECOM, vol 3, 2007, pp 812–816 [14] M Iezzi, M Di Renzo, and F Graziosi, “Network code design from unequal error protection coding: Channel-aware receiver design and diversity analysis,” in Communications (ICC), 2011 IEEE International Conference on, june 2011, pp –6 [15] J N Laneman and D Tse., “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans Inform, vol 50, no 3, pp 3062–3080, 2004 [16] D T Nguyen, Q T Nguyen, and T C Chung, “Outage probability analysis of cooperative diversity df relaying under rayleigh fading,” in Proc Int Conf Advanced Technologies for Communications (ATC 2011), Danang, Vietnam, 2011, pp 116–120 [17] A Hst-Madsen and J Zhang, “Capacity bounds and power allocation for the wireless relay channel,” IEEE Trans Inform Theory, vol 51, no 3, pp 2020–2040, 2005 [18] Y Wang, C Hu, H Liu, M Peng, and W Wang, “Network coding in cooperative relay networks,” in Proc IEEE 19th Int Symp Personal, Indoor and Mobile Radio Communications (PIMRC 2008), 2008, pp 1–5 [19] C L Sinh, T Q Nguyen, and P Duhamel, “Performance of network coding enabled diversity relay networks,” in The Proceedings of ATC 2012, Ha Noi, Viet Nam, 213-217 [20] X.-T Vu, M D Renzo, and P Duhamel, “Optimal and low-complexity iterative joint network/channel decoding for the multiple-access relay channel,” in ICASSP, 2011 [21] J Proakis, Digital Communications, F Edition, Ed McGraw Hill, 2000 [22] Y Chen, S Kishore, and J Li, “Wireless diversity through network coding,” in Proc IEEE Wireless Communications and Networking Conf (WCNC 2006), vol 3, 2006, pp 1681–1686 21 [23] A Nosratinia, T E Hunter, and A Hedayat, “Cooperative communication in wireless networks,” IEEE Communications Magazine, vol 42, no 10, pp 74–80, Oct 2004 [24] a M S Ming Xiao, “Multiple-user cooperativecommunications based on linear network coding,” IEEE TRANSACTIONS ON COMMUNICATIONS, vol 58, pp 3345–3351, DECEMBER 2010 22 ... multiple -relay networks using network coding, x1 is carried on link s1 d, r1 d and r2 d 18 Conclusions and Future Works In this thesis, we consider the effects of network coding on cooperative relay networks. .. 2.2 Single Relay Networks using Network Coding 2.3 Multiple -Relay Networks using Network Coding Outage Probability Calculations 3.1 Mutual Information ... Decode-and-Forward relaying 12 3.4 Outage Probability of Single Relay Networks using Network coding 12 3.5 Outage Probability of Multiple -Relay Networks using Network Coding 16 Conclusions