Bi-Directional Relay for Coded Cooperation

8/6/2019 Bi-Directional Relay for Coded Cooperation

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Bi-Directional Relay for Coded Cooperation

Chan T.D. Thai and J.-K. Kevin Rhee Jinoo Joung SungBo Yang

Info. and Comms. University

119 Munjiro, Yuseonggu

Daejeon, South Korea

{chanttd|rhee.jk}@icu.ac.kr,

Sangmyung University

7 Hongji, Jongro

Seoul, South Korea

[email protected]

Hyundai-Kia Motor Corp.

231 Yangjae-dong, Seocho-gu

Seoul, South Korea

[email protected]

Abstract - Coded cooperation (CC) allowing a pair of users to

help each other with relaying part of partners data is inves-

tigated to extend wireless channel reach by cooperative diver-

sity. Taking advantage of a bidirectional property of data

flows, instead of transmitting the each packet from each user

in the second phase of CC, we propose to broadcast a joint

packet with XOR-gated information of the two second pack-

ets from both users. The throughput is increased and the

quality is also improved based on mathematical analysis and

simulation.

Keywords - coded cooperation, network coding, cooperative

networking, diversity, bidirectional relay

I. INTRODUCTION

Cooperative networking diversity [1] has been proposedas an effective method to combat fading impairment whichis a challenge in wireless communications. Openness ofwireless channel, which provides channel diversity, is ex-ploited and possibly considered as an advantage rather thana disadvantage as before. In spatial diversity, replicas oforiginal data are transmitted in different paths so that thedestination can combine them to retrieve original data.Cooperative networking in which the users help each otherby relaying their partners data is based on that principle.Some typical cooperative networking algorithms are store-and-forward, amplify-and-forward, decode-and-forward

[2], compress-and-forward [3], coded cooperation (CC) [4],and space-time coded-cooperation [5]. In multi-hop scenar-ios, an intelligent coding scheme has been proposed to gen-erate codewords delivered over multiple paths as a diversitymethod [6].

Diversity makes transmission more reliable when net-work coding [7] is carried out at a higher layer and thushelps increasing throughput by reducing the bandwidthusage. Bi-directional relaying [8] is itself a special case ofthis method. In the coded bi-directional relay (CBR), therelay node combines the two packets from two users into asingle joint-packet by XOR-gating the information andmulticasts it to both users. Amplify-and-forward CBR [9]utilizing the inherent packet combining that emerges from

simultaneous utilization of a multiple access channel canprovide a higher throughput in an errorless channel butseverely degrade the performance in noisy channels com-pared with the former. Investigating in multiple-node co-operation, Ref. [10] assumed that every node can receive allother packets except the packet destined to it, the relaybroadcasts a packet achieved from XOR-gating all trans-mitted packets together. However, the assumed situation isnot always the case, therefore more general situation shouldbe investigated. Adaptive network coded cooperation [11]proposed a coding method that can adapt to the currentnetwork graph.

Coded cooperation and network coding combinationmethod was also proposed. A network coding approach tocooperative diversity [12] can be considered as a typicalalgorithm of this type. An encoding was proposed in whicheach partner transmits the algebraic superposition of itslocal and relayed information. Packet decoding is done byiterating between the codewords from the two partners.

Considering both uplink and downlink stream, we pro-pose a method based on a combination of coded coopera-tion and bi-directional relaying to increase throughput ofthe network. System model and algorithm will be de-scribed in part II. We discuss about throughput enhance-ment in III by a mathematical analysis. Computer simula-tion is presented in IV.

II. SYSTEM MODEL AND PROPOSED METHOD

We consider a wireless network including many stationscommunicating with an AP. A situation where nodes X, Yexchange packets with the AP as shown in Fig. 1. We firstdiscuss how regular CC applies to this scenario, followedby the proposed method.

A. Regular coded cooperationWe first investigate sending XU from X and sending YU

from Y to AP (uplink transmission). In regular coded co-

operation, packet XU after being coded by convolutional

coding to XU is punctured into two packets XU1 and XU2 (i.e.XU = XU1 + XU2) with punctuation ratio Rp i.e.

11 XPXLRL = , (1)

where LxU1 and LxU2 are respectively the packet sizes ofXU1 and XU2.

In the first phase, Stations X and Y broadcast their ownpackets (XU1 and YU1) (Fig. 1a). Depending whether theycan correctly receive the packet from the partner or not inthis phase (by checking CRC), they send their own data orpartners data in the second phase. Station Y composes XU2from XU1 by decoding XU1 to get XU with high enough con-

volution coding rate so that decoding XU1 to get XU ispossible, and then puncturing XU into XU1 and XU2 [8].

Similarly, Station X can get YU2 from YU1. Four cases inthe second phase are shown in Fig. 2b (fully cooperative), c(non-cooperative), and d-e (partly cooperative).

Figure 1. Network model


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Figure 2. Two-phase transmissions in regular coded cooperation: a. for the first phase for transmitting the first parts of coded packets, and b. - e. for the second phases

for transmitting the second parts of coded packets, Transmission Case 1: All channels with retrievable errors (b), Transmission Case 2: Cooperating channels with

bidirectional irretrievable errors (c), and Transmission Cases 3 and 4: Cooperating channels with unidirectional irretrievable errors (d and e), respectively.

When looking at the second phase of CC, we can see thatCases 1 and 2 are symmetric so that the AP receives X U1, YU1,XU2, and YU2, but Cases 3 and 4 are not symmetric, where theAP receives XU1, YU1, and 2YU2 for Case 3 or XU1, YU1, and2XU2 for Case 4. This reduces diversity degree and therefore theperformance.

B. Symmetric Coded CooperationSymmetric CC is similar to CC and the difference is that insymmetric CC there Cases 3 and 4 do not exist, i.e. the secondphase is fully cooperative or non-cooperative: It is never partlycooperative. Because we consider symmetric CC here in orderto easily make a comparison between conventional CC and theproposed bidirectional CC (BiCC), it is not investigated herehow a user in symmetric CC chooses either full cooperation ornon-cooperation mode.

On the other hand, the downlink transmission is not de-scribed in CC. Based on the principle of CC, we propose atransmission scheme for the downlink transmission so that BiCCperformance can be compared with CC.

C. Bi-directional Relay for Coded CooperationInstead of requiring uplink and downlink packets in two dif-

ferent time slots in the second phase, we propose a method toreduce transmission steps by broadcasting a joint packet ofXOR-gated information of these packets. However, the relaymay not be able to decode all packets in a severely degraded

channel condition. The relay checks the packet overheard fromits partner by looking at CRC attached to packet. For easy un-derstanding, we call the process of transmitting and receiving XUand XD is the first transmission set, the process of transmittingand receiving YU and YD is the second transmission set. For thesake of simplicity, we only investigate the first transmission setwhen X and AP exchange XU and XD packets and Y is the relay.The second transmission set is carried out in a similar way andalso shown in Fig. 3 as examples. The principle is as follows:

X encodes and punctures an uplink packet, XU, into XU1and XU2 as in CC. X transmits XU1 only. AP uses thesame processes for transmission of a downlink packet,XD for X.

If Y can overhear and decode both XU1 and XD1, it re-

covers XU2 and XD2 as in CC, and broadcasts a joint

packet XJ (=XU2 XD2); otherwise, it stays in silence.

X recovers XD2 from the joint packet XJ by taking

XU2 XJ. In the same way, AP recovers XU2.

If X and AP do not receive XU2 XD2 after waiting for a

certain time period, they transmit XU2 and XD2, respec-tively.

X and AP respectively combine the received packets toretrieve XD and XU.

Considering four cases for the first transmission phase and fourcases for the second transmission phase, we have 16 cases intotal. Fig. 3a shows the first case when all relays receive theirpartners data correctly. It is fully cooperative in both uplink anddownlink transmissions. In the sequence diagram of data flowthe small boxes indicate the sources of transmissions, the arrowends indicate destinations, and the small circles represent over-

hearing nodes (relays). A solid line indicates connection be-tween a source and a destination while a dashed line indicates anoverheard packet. Considering link health of a source-destinationpacket and overheard packet, the total 16 cases are classified into3 types:

1) Type 1: Full-bidirectional relay:Type 1 is used when Ycan decode XU1 and XD1, and X can decode YU1 and YD1 (Fig

3b). Y transmits the joint packet XJ (=XU2 XD2) in the first

transmission phase. X thereafter transmits YJ (=YU2 YD2) in

the second phase. At X, because XU2 is originated from X, XD2can be retrieved by doing XU2 XJ. In the same manner, XU2YU2, and YD2 are retrieved at corresponding destination nodes

Corresponding combining processes are achieved at the nodes

to get the data. Compared with CC, the number of transmissionsteps is reduced by two in two transmission phases, thus the

throughput increases by a certain ratio . Remember that the

number of steps in regular CC and symmetric CC is the same

The ratio will be evaluated in Sec. III.

2) Type 2: Semi-bidirectional relay: Type 2 is used wheneither X or Y can decode both overheard packets - e.g. in Fig

3c, Y can decode XU1 and XD1; whereas the other cannot decode

both overheard packets - e.g. in Fig. 3c, X can decode YU1 but

not YD1. We also show two other cases when Y can decode

both overheard packets but X cannot. X can decode YD1, not

YU1 (Fig. 3d) and X cannot decode both YD1 and YU1. In Fig. 3d

and 3e, the first transmission phases are not shown. Compared

with CC, the number of transmission steps is reduced by only

one in this case thus the throughput increases by a ratio of/2


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Figure 3. a. Regular coded cooperation, b. Full-bidirectional relaying, c, Semi-bidirectional relaying, d and e. Semi-bidirectional relaying (secondtransmission phase) f. Non-bidirectional relaying. Dashed lines indicate overheard packets.

3)4) Type 3: Non-bidirectional relay: Type 3 is used

when X or Y as a relay cannot decode both overheard

packets in both transmission pairs. An example is shown in

Fig. 3f. Both relays react similarly as Y in the example we

considered in Type 2. We cannot eliminiate any

transmission step and thus the throughput remains the

same as that of CC.For easy understanding, the improvement of throughput

from CC to BiCC is two fold. First, due to symmetry, BERof symmetric CC is lower than that of CC. Second, due tobroadcasting a joint packet, BiCC has a higher throughputeven in the case that BER is the same as in symmetric CCcase.

In BiCC, all transmissions become one of the threetypes discussed above. The full-bidirectional relay gives usthe highest throughput increase, and the semi-bidirectionalrelay can give one half of the increase by the full-bidirectional case. The probability of each type will be es-timated in the next section. Accordingly, the generalthroughput of the system can be defined.

III. THROUGHPUT ANALYSIS

Compared with symmetric CC, Type 1 can save one trans-mission step in one CC procedure (four steps) by broadcast-

ing XU2 XD2 instead of transmitting XU2 and XD2 indi-

vidually. The corresponding transmission time duration ofsymmetric CC is obtained from (1):

XU= XU1+XU2 = (Rp + 1)XU2.

Here we simply use XU instead of LxU for packet size ofXU. The same rule is applied in the following derivation.The transmission time duration in Type 1 is

22

121

2Up

UU XRXX

+=+

.

Factor 1/2 comes from the effective bandwidth occupation

by broadcasting one packet (XU2 XD2). With the same

bandwidth used, the throughput is inversely proportional tothe transmission time. Thus when Type 1 is used instead ofsymmetric CC, the throughput increase is

( )

++=

+

+

12

11

2

1

1

pp

p

RR

R

. (2)

Throughput of Type 3 can be evaluated the same as that ofsymmetric CC, since the number of transmission steps isthe same:

)1(3 eB PTT = ,

where Pe is the packet error rate and TB is the throughput

when the channels are ideally error-free. If Type 1 is used,the throughput is increased by a ratio of (2) thus can bewritten as follows:

++=

12

11)1(1

p

eBR

PTT

.With a similar way, we can get throughput for Type 2 as

++=

)12(2

11)1(2

p

eBR

PTT

.Let Pi the probability that type i is used and will be evalu-ated later. The system throughput can be easily obtained as

3322311

3212211

3

1

)()(

)1(

TTTPTTP

TPPTPTP

PTTi

ii

++=

++=

= =

.

The throughput increase compared with symmetric codedcooperation is

)12(2

)2)(1(

)()(

21

3223113

+

+=

+==

p

eB

R

PPPT

TTPTTPTTT

. (3)

In order to calculate probability Piof type i, we considerone BiCC process as two regular CC processes (uplinktransmission and downlink transmission) as shown in TableI. The cases of CC are defined in Fig. 2.

TABLE I. TYPECLASSIFICATIONBASEDONCCCASES

Uplink

Transmission

Downlink Case

Transmission

Case

1 2 3 4

1 1 2 2 2

2 2 3 3 3

3 2 3 3 3

4 2 3 3 3


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P1 = P11,

=

+=

3

2

112

i

ii PPP, (4)

P3 = 1P1P2,

where Pij is the probability that the first phase is in case iand the second phase is in case j. Because these events are

independent, letpi is the probability of case i in a single CCprocess, we have

Pij =pipj . (5)Probability for case 1 is evaluated in [8] with reciprocalinter-channels

=

0

1212

2

121 )()|()(,1min1 dpdPdap

B

f

N

dd,

where NB is the number of Trellis branches in the codeword, df is the code free distance, a(d) is the number oferror events of Hamming weight d, ij is instantaneous SNRof the channel from node i to nodej, and p(ij) is probabilitydensity function ofij that depends on fading type. Othercases can be similarly evaluated. PER for each case can be

bounded as followsB

f

N

ddie

idpdaP

=

0 0

1010 ),,|()(,1min11

10102010 )()( ddpp .

Consequently, PER for CC can be obtained:

=

=

4

1i

iiCCepPerP

. (6)

It is also the same for BiCC. In conclusion, with (4), (5),and (6), the throughput increase in (3) can be defined.

IV. NUMERICAL RESULTS

We use computer simulations to compare BERs and spec-tral efficiencies of BiCC and CC and to evaluate the prob-ability of each BiCC case. In the BiCC case, we assumethat there are two wireless stations communicating with anAP as in Fig. 1. The four packets are exchanged to followthe scheme in the Fig. 3. In the CC case, becausedownlink transmissions are not supported, only uplinktransmissions are simulated. Accordingly, only XU and YUare sent.

The instantaneous signal-to-noise ratio (SNR) of thewireless channel between node i and j is modeled as fol-lows

2

,,,

0

2

,,, jijijijijiji hdKSN

Ph

==

.

where P is the transmission power and N0 is the additivewhite Gaussian noise power at the receivers, K= 1 is thepath loss for an arbitrary reference distance, Si,j is a log-normal shadowing component with E[10 log Si,j] = 0 dBand Var[10 log Si,j] = 1, di,j = 0.5 is the distance betweennode i and j, = 2 is the path loss component and |hi,j| isfading magnitude. We investigate both quasi-static Rician( = 1, = 1) and Rayleigh ( = 1) fading. The Rician fad-ing magnitude is distributed with pdf

( )

=

+

202

2

2

22

),|(

xv

Iex

vxf

vx

,

whereI0(z) is the modified Bessel function of the first kindwith order zero. When v = 0, the distribution reduces to aRayleigh distribution. Shadowing coefficients {Si,j} areconstant for a given transmitted block, or code word, butare independent and identically-distributed random vari-ables for different blocks. Packet length is 200 bits, 1/2 rateconvolutional code is used with polynomial generator [1517 13 15], 8PSK modulation is used and puncturing rate is50% with puncturing table [1 0 1 0] forN1 and [0 1 0 1] forN

2.BERs of BiCC and CC are shown in Fig. 4 when there

is Rayleigh or Rician fading. Figure 5 shows the through-puts of BiCC and CC. When SNR is higher, the probabilityof full-bidirectional relaying is higher and throughput ishigher. The percentile fraction of finding each BiCC typeis shown in Fig. 6.

Figure 4. BER performance comparisons of BiCC and regular CC forRayleigh (Ray) and Rician (Ric) channels models.

Figure 5. Spectral efficiency comparisons of BiCC and regular CC for

Rayleigh (Ray) and Rician (Ric) channels model.

V. CONCLUSION

Taking advantage of a bi-directional flow property andopenness of radio channels, a novel approach is proposed toincrease the throughput transmission without degradingnetwork performance. Instead of always sending the sec-ond packets of coded cooperation, a joint packet of the sec-ond packets of collaborating nodes is generated and broad-casted to reduce the bandwidth usage. We show thethroughput increase in mathematical analysis and computersimulations.


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Figure 6. BiCC type percentage

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Bi-Directional Relay for Coded Cooperation