Network coding on cooperative relay networks = Mã hóa mạng trong hệ thống mạng hợp tác chuyển tiếp Network Coding on Cooperative Relay Netwoks

11 1.3 Cooperative Diversity Relaying Networks using network coding.. Selection relaying SR protocol is designed to overcome the shortcomings of DF relaying when the measured SNR at the

1.1 Introduction to cooperative relay networks 1

1.1.1 The relay protocols 4

1.1.2 Advantages of Cooperative Diversity Relaying Networks 5

1.2 Introduction to Network Coding 7

1.2.1 Non-Binary and Binary Network Coding 8

1.2.2 Advantages of Network Coding 9

1.2.3 Weaknesses of Network Coding 11

1.3 Cooperative Diversity Relaying Networks using network coding 13

2 System models 15 2.1 Traditional Relay Multiple-Wireless Networks 16

2.2 Single Relay Networks using Network Coding 20

2.3 Multiple-Relay Networks using Network Coding 22

3 Outage Probability Calculations 24 3.1 Mutual Information 24

3.2 Outage Probability Definition 25

3.3 Outage Probability of Multiple-Relay Networks 27

3.3.1 Traditional Decode-and-Forward relaying 27

3.3.2 Selection Decode-and-Forward relaying 29

3.4 Outage Probability of Single Relay Networks using Network coding 32

3.5 Outage Probability of Multiple-Relay Networks using Network Coding 36

Bibliography 43

List of Figures

1.1 Frequency Diversity 2

1.2 Space Diversity 2

1.3 Cooperative relay network 6

1.4 An example of Network Coding 7

1.5 An example of Non-linear Network Coding 8

1.6 An example of linear Network Coding 9

1.7 The butterfly network 10

1.8 The weakness of Network Coding 12

2.1 A traditional single relay network 19

2.2 A traditional multiple-relay network 19

2.3 Network coding in single relay network 20

2.4 Multiple-relay network using network coding 22

3.1 The direct link between the input and the output 25

3.2 Outage probability of a direct link 27

3.3 Outage Probability of fixed and selection DF relay 32

3.4 The degraded system model of a single relay network based on NC 34

3.5 The degraded system model of a single relay network based on NC 35

3.6 Outage probability of the single relay network with and without network coding 36 3.7 Link s 1 r 1 is in outage 39

3.8 Outage probability of relay networks with different scenarios 41

In communication, Cooperative Diversity Relaying refers to devices municating with one another with the help of relays in order to increase theperformance of the network However, in one timeslot, the relay only trans-mits the signal of one source Therefore, Network Coding is introduced toimprove the throughput of the network Combining Cooperative Relay Net-work and Network Coding should be studied to achieve significant benefitsand overcome some weakness In this thesis, we consider the effect of Net-work Coding on Cooperative Relay Network We propose to use SelectionDecode-and-Forward instead of Traditional Decode-and-Forward protocol atthe relay We also use the instantaneous channel gains to calculate the outageprobability of the proposal system model

com-The rest of the thesis is organized as follows In Chapter II, the systemmodel of a multiple-relay network is described The outage probability iscalculated in Chapter III Finally, the conclusions and the future works aredrawn in Section IV

Chapter 1

Introduction

The sharp increase in the number of mobile subscribers which needs largebandwidth for multimedia applications anywhere and anytime requires thenetwork service providers to optimize and develop the current technologies inorder to ensure that the Quality of Services (QoS) is always satisfied Diversityscheme are used to improve the reliability of a message signal by transmittingmultiple version of the same signal over different communication channels.Because of time-varying channel conditions, the diversity plays an importantrole in combating fading and co-channel interference Diversity techniquesare divided into the following types: time diversity, frequency diversity, spacediversity, polarization diversity, muiltiuser diversity! [1]

• Time diversity: The transmitter sends the same data at different timeinstants or a redundant error correcting code is added into the messagesbefore transmitting Repetition coding is one of the most popular types

of time diversity

• Frequency diversity: The signal transmitted by using different frequencychannels on a single antenna At the destination, it requires the number

of receivers as the number of frequencies used at the transmitter Ittherefore requires more spectrum usage

Transmitted signal

Transmitted signal

Transmitter 1

Transmitter 1

Transmitter 2

Transmitter 2

Receiver 1

Receiver 2

Recovered signal

Recovered signal

Figure 1.1: Frequency Diversity

• Spatial diversity The signal is transmitted over different path by usingseveral antennas at the transmitter in order to allow multiusers to share

a spectrum and avoid co-channel interference

Figure 1.2: Space Diversity

• Polarization diversity: The same messages are transmitted and received

by using antennas with different polarization A diversity combining nique designed to combine the multiple received signals at the destination

tech-is used in thtech-is case

• Multiuser diversity: In this technique, the transmitter and receiver rely

on the quality of the link between the transmitter and each receiver inorder to selects the best partner

In recent years, MIMO (multi-input multi-output) technology based onspatial diversity and spatial diversity has attracted attention in wireless com-munication because it greatly improves the reliability, the throughput and thetransmission rate without additional bandwidth nor requiring higher trans-mitter power However, this technique requires both the transmitter and thereceiver to have multi-antennas, and all channels must be independent Inpractice, users do not often achieve full-rank MIMO because they either donot have multiple-antennas installed on a small-size devices, or the propaga-tion environment cannot support MIMO, for example, there is not enoughscattering Even if the users have enough antennas, full-rank MIMO is notguaranteed because the links between several antenna elements are often cor-related

To overcome the limitations in diversity gain MIMO, a new communicationparadigm which uses an intermediate node to generate independent channelbetween the user and the base station was introduced The intermediatenode often called relay node receives the signal transmitted from the userand forward it to the base station And this paradigm is called CooperativeDiversity Relaying Network

1.1.1 The relay protocols

A key aspect of the cooperative communication process is the processing ofthe signal received from the source node carried out by the relay These dif-ferent processing schemes depend on the protocols of the relays which can begenerally categorized into fixed relaying schemes, selection relaying protocol(adaptive relaying schemes) and incremental relaying protocol

In Fixed relaying protocols, the relay either amplifies what it receives, orfully decodes, re-encodes, and re-transmits the source message These fixedrelaying options are called amplify-and-forward (AF) and decode-and-forward(DF), respectively Amplify and Forward is the protocol in which the relayreceives the signal form the source and amplifies it before forwarding to thedestination While, Decode-and-Forward relay decodes and re-encodes thereceived message before sends it to the destination Note that the decodedsignal at the relay may be incorrect If an incorrect signal is forwarded tothe destination, the decoding at the destination is meaningless [2] Therefore,sometimes the relay must be silent because it can not detect the presence ofthe signal or the signal quality is not good enough for the relay to decodefully the messages

Selection relaying (SR) protocol is designed to overcome the shortcomings of

DF relaying when the measured SNR at the relay falls below a threshold thatthe relay becomes unable to decode the message, the source simply continuesits direct transmission to the destination using repetition coding or other morepowerful codes

In incremental relaying (IR) protocol, the relay only transmits upon a

neg-ative feedback from the destination Fixed relaying makes inefficient use ofrelay channel resources when operating at high rates because the relays repeatall the time, and under good transmission conditions this is un-necessarily.

In IR networks, the destination sends a one-bit ACK to the source and therelay if it can successfully decode message from the source, otherwise it sends

a NACK to signal it fails to decode the message Only when the relay ceives a NACK and if it is able to decode the source message, it will forwardthe message to the destination by employing AF relaying The destinationreceiver then uses maximum ratio combining (MRC) of the signal from thesource and the relay to build up its receive SNR until it can successfullydecode the message This is equivalent to using the well known repetitioncoding technique to combat deep fading situations

re-1.1.2 Advantages of Cooperative Diversity Relaying NetworksCooperative Diversity Relaying refers to devices communicating with oneanother with the help of relays in order to increase the performance of thenetwork [3] Thereby, the relay channel can be considered as an auxiliarychannel to the direct channel between the source and destination

Figure 1.3 shows a network model using M relays The operation of thismodel can be divided into M + 1 time slots In the first time slot, the sourcesends its messages to the relays and the destination using the broadcastmethod The relay i relies on the defined protocol to receive and processthe source message before retransmitting it to the destination in timeslot i.The presence of the signal is decided at the destination by comparing the

measured SNR with a threshold.

Broadcast mode Direct link

Figure 1.3: Cooperative relay network

The operation of each relay is independent of the others, so that there is nocorrelation among all channels We will show that the diversity gain and therobustness of this system model is increased significantly It is clear that thedestination can not decode a source’s messages if and only if all links connect-ing the M relays and that source to the destination are in outage Assumingthat the outage probabilities of these links are the same, and denoted by p.Then the probability of system outage event is pout = pM +1

In [4], the diversity gain is defined as

has been overcome.

However, in cooperative relay network shown in figure 1.3, we are able touse one or more relays, but in one timeslot, the relay only transmits the signal

of one source

As discussed in the previous section, in a typical network, information istransmitted from the source node to each destination node through a chain ofintermediate nodes by a method known as store-and-forward In this method,the intermediate node only processes and transmits a unique signal at onetime without overlapping, thus slow down the through In order to increasethe throughput of the network, network coding technique was introduced

in [5] and then further developed in [6], as a new paradigm which exploits thecharacteristics of the broadcast communication channel to combine severalinput signals into one output signal at the intermediate node

Figure 1.4: An example of Network Coding

In figure 1.4, both N1 and N2 want to send their signal to node N4 using

broadcast mode When network coding is applied, the intermediate node willcombine these signals into an output before retransmitting to the destina-tion The question are how the intermediate node combine them and howthe destination node detect the received messages When we study on theprotocol of the intermediate node, we can divide network coding into binaryand non-binary network coding.

In binary network coding showed in figure 1.5, the intermediate node usesXOR operator to consolidate the received messages transmitted form sources.Because XOR operator is only used to add two binary bits, the input data

Figure 1.5: An example of Non-linear Network Coding

must be in binary form It means that the data must be decoded over GF (2)and it only supports two sources The main benefit of non-linear networkcoding is simple and can be easily implemented by a hardware However, it issub-optimal [7] It means that, the diversity order of system does not change

when we increase the number of relays.

In non-binary network coding, each intermediate node uses a linear tion to combine the inputs and the destination uses the system of linearequation to decode the received messages Figure 1.6 is an example of linearnetwork coding with two sources and one relay a1 and a2 are elements of

equa-GF (2q); x1 and x2 are decoded over GF (2q) One drawback of using network

Figure 1.6: An example of linear Network Coding

coding over non-binary fields may be higher complexity, since computations

in large finite fields are more complex than over the binary field Therefore, italso causes worse transmission delay and more bandwidth consumption [8]

So that, in general case, we cannot conclude which better linear or non-linearnetwork coding In this thesis, we only concentrate on binary network coding

Increasing throughput achieved by increasing the efficiency of packet mission is the most well-know benefit of network coding To prove this point,

trans-we consider a typical model of network coding which is called the butterflynetwork (see Figure 1.7) [9].

Figure 1.7: The butterfly network

In this network, the source node S wants to send its signal in the form bits

b1 and b2 to two destination nodes D1 and D2 over different output channels

by using multi-cast mode Figure 1.7a indicate that b1 is sent on channel(s, 1) and b2 is sent on channel (s, 2) The received signal at the intermediatenodes 1 and 2 are b1 and b2, respectively In turn, node 1 (or 2) broadcasttheir signal to destination D1 and node 3 ( or D2 and node 3) by using twochannels (1, D1) and (1, 3) (or (2, D2) and (2, 3)) Now, we consider the inputand output of the node 3 There are two input channels but only one outputchannel (3,4) Normally, node 3 has to choose either b1 or b2 to send tothe node 4 Suppose the b1 is sent to the node 4 by using link (3, 4) as in

Figure 1.7a To complete the transmission, the node 4 broadcast b1 to thedestination D1 and D2 Finally, at the node D2, both b1 and b2 are received.While, at node D1, two copies of b1 are received, therefore the problem is that

b2 cannot be recovered

(b1 ⊕ b2) ⊕ b1 = (b1 ⊕ b1) ⊕ b2 = b2

However, if network coding is applied at node 3 as shown in 1.7b, thisproblem may be solved In Figure 1.7b, node 3 receives both b1 and b2 thencombines them into a unique signal by using modulo 2 addition before re-transmitting it to node 4 Then, the signal at the destination D1 are b1 ⊕ b2and b1 In order to recover b2, we add b1 ⊕ b2 and b1 by using module 2operator It is similar to recover b1 at the destination D2

This network model illustrates an important point: If network coding is notapplied at node 3, in order to send both b1 and b2 to D1 and D2, we must usemore capacity at channel (3, 4) or more timeslot So that, we may concludethat network coding can increase throughput for broadcast network

The main issue of using network coding is that if a transmission erroroccurs, it could affect the detecting and coding at the intermediate node,and the destination node could receive useless information [10] Consideringthe scenario shown in Figure 1.7, the channel between the source S and theintermediate node 2 is faded It mean that node 2 is unable to decode thereceived messages successfully Then, it could send incorrect messages to

node 3 and the destination D2 Therefore, combing and encoding the signalstransmitted from node 1 and node 2 at node 3 is incorrect even when thechannels s − 1 and 1 − 3 are perfect After several transmission phases, thereare two messages at the destination D1: b1 (correct or incorrect) and b1 ⊕ b2(incorrect) It means that b1 is detected by using incorrect messages.

1b  b

 

2 2 1

Figure 1.8: The weakness of Network Coding

Besides, synchronization and transmission delay among the incoming datastreams at the input of the intermediate node or destination node are alsosignificant 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 dataand voice transmission), but they are should be considered carefully for real

time services (e.g video transmission, ).

using network coding

As discussion above, both cooperative diversity relaying and network ing have advantages and weaknesses thus combining cooperative relaying withchannel coding should be studied to achieve significant benefits and overcomesome drawbacks In an NC-based network, a source node sends messages to adestination node via a number of relay nodes whereby an intermediate nodefirst encodes the messages received from its input nodes into a new messageand then sends this message to its output nodes By decoding its inputs, thedestination node can recover the original messages sent by the source node.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 transmittheir signals to the relay and the destination using broadcast technique Then,the relay combines its received signals into a unique signal and sends it todestination The traditional Decode-and-Forward (DF) protocol is often used

cod-at the relay which decodes the messages from its input nodes before sendingthem to its output nodes Often, the links between the sources and relayare assumed to be error-free so that the relay decodes the received messagessuccessfully [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 aredesigned 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 isdesigned to overcome the shortcomings of DF relaying when the measuredSNR at the relay falls below a threshold such that the relay becomes unable todecode the messages, the source simply continues its direct transmission to thedestination using repetition coding [15] In addition, we use Maximum RatioCombining (MRC) at the destination Finally, we analyze the performance ofthe proposed scheme in terms of outage probability by using the instantaneouschannel gains The analysis is based on a newly developed method for exactcalculation of the outage probability [16].

Chapter 2

System models

In theory, the relay node can operate in both time-division (TD) andfrequency-division (FD) If the frequency-mode method is applied, the band-width W is divided into a bandwidth of αW where the relay node listens and(1 − α)W where the relay transmits The destination node pays attention thewhole bandwidth W Similarly, if the time-division mode is applied, then for

a given time window D, in the relay-receive phase, the relay uses a fraction oftime αD to received the messages from its source and uses the remaining time(1 − α)D of the window to send the received messages to its destination It

is clear that from an information-theoretic point of view, there is no differentbetween TD mode and FD mode for the fixed channel gain case In fadingchannels, however, the TD mode has more benefit than the FD mode becausecan be adjusted to the instantaneous channel conditions, whereas α is oftenfixed in the FD mode [17] So, in this thesis, we only deal with the relaysoperating in the TD mode

In fixed DF relaying, the relay decodes the received message from the sourceand sends it to the destination The decoded message at the relay can be

correct or incorrect If an incorrect signal is transmitted to the destination,the decoding at the destination is meaningless It is clear that the diversityorder of this scheme is only one, because the performance of the system islimited by the worst of the source−relay and source−destination links.

Selection relaying (SR) protocol is designed to overcome the shortcomings of

DF relaying when the measured SNR at the relay falls below a threshold thatthe relay becomes unable to decode the message, the source simply continuesits direct transmission to the destination using repetition coding or other morepowerful codes

In this thesis, we only consider the relay using selection Decode-and-Forwardprotocol in Time-Division mode

Net-works

In this section, we will discuss about end-to-end signal of the selectionDecode-and-Forward relay Relaying is assumed to operate in the time divi-sion mode having two phases (two time slots): the relay-receive phase andthe relay-transmit phase

In phase 1 called the relay-receive phase, the sources S1, S2 transmit the

N -symbol message to both the destination D and the relays R1,R2, i.e, thebroadcast mode is applied We assume that the transmitted power of eachrelay is constant, then the received signals at the relay R1,R2 and destination

D are respectively given by:

ysiri[n] =pPshsirixsi[n] + nsiri[n], (2.1)

ysid[n] =pPshsidxsi[n] + nsid[n] (2.2)

Where

• i = 1, 2; n = 1, , N

• xsi[n] is the transmitted signal from source Si

• hsiri and hsid are the instantaneous channel gains between source Si and

Ri, between source Si and destination D, respectively

• Ps is the transmitted power of each source; nsiri[n] and nsid[n] are theadditive white Gaussian noise (AWGN)

If the relays are assumed to decode successfully the messages they receivesfrom the sources in relay-receive phase, then they send these messages tothe destination during phase 2 called the relay-transmit phase The receivedsignal from the destination yrid[n] is

yrid[n] = pPshridxri[n] + nrid[n] (2.3)

in which hrid is the channel gain between source Ri and destination D; nrid[n]

is the additive white Gaussian noise (AWGN)

On other hand, if the relay is unable to decode the message, i.e the measuredSNR at the relay falls below a threshold, the source simply continues its directtransmission to the destination using repetition coding

Finally, the total received signal at the destination is given by equation (2.4)

sources-and-• In T S1, S1 sends its signal to the relay and the destination.

• In T S3, S2 broadcasts its signal to the relay and the destination.

• In T S4, the relay transmits the received signal to the destination

( x

2

) 3

( x

2

) 4

( x

Figure 2.1: A traditional single relay network

In order to increase the network’s throughput by reducing the number oftimeslots, we increase the number of relay Figure 2.2 shows a relay networkusing two relays (R1, R2) with selection-DF protocol relaying information fortwo sources (S1, S2) to the destination [18] It is clear that it requires at least

Figure 2.2: A traditional multiple-relay network

3 time slots in order to complete a transmission process

• T S1: The source S1 transmits its data in broadcast mode to both thedestination and the relays.

• T S2: The source S2 transmits its data in broadcast mode to both thedestination and the relays

• T S3: Both relays send their information to the destination

In this thesis, we review the calculation of the cumulative distributionfunction (cdf) of instantaneous channel gains of various wireless links in adiversity relay network, which was published by the author of this thesis andhis co-author in [16, 19]

– S1 sends its signal x1 to both relay and destination by using broadcastmode.

– The relay can or cannot decode x1

• In timeslot 2

– If R can not decode x1, S1 repeats sending x1 to D, thus D receives

x1 on 2hs1d

– If R can decode x1, S1 will do nothing in timeslot 2 and R store x1 in

it and waits for x2

In the meantime

– S2 transmits its signal x2 to relay and destination using broadcastmode

– R can or cannot decode x2

– If R cannot decode x2, S2 repeats sending x2 to D, thus D receives x2