ARQ Scheme

Throughput Evaluation of ARQ Scheme

for Multi-route Coding in Wireless Multi-hop Networks

Hiraku Okada*, Tadahiro Wadat, Kouji Ohuchit, Masato

Saito§,

Takaya Yamazato1, Masaaki Katayama~

*Centerfor Transdisciplinary Research, Niigata University, 8050, Ikarashi 2-no-cho, Niigata, 950-2181, Japan, [email protected]

tDepartment

of Electrical and Electronic Engineering, Shizuoka University,

tGraduate School of Electronic Science and Engineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, 432-8561, Japan, {tetwada, dkoouti}@ipc.shizuoka.ac.jp

§Graduate

School of Information Science, Nara Institute of Science andTechnology, 8916-5, Takayama-cho, Ikoma, 630-0192, Japan, [email protected]

¶EcoTopia Science Institute, Nagoya University,

Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan, {yamazato, katayama}@nuee.nagoya-u.ac.jp

Abstract- For reduction in bit errors on wireless channels, we proposed the multi-route coding scheme on multiple routes for wireless multi-hop networks. In this paper, we introduce ARQ to the multi-route coding. In the multi-route coding, the destination node combines and decodes sub packets which are encoded anddivided by the source node. The intermediate node relays a sub packet, thatis, only a part of a packet. Therefore, the intermediate node cannot detect packet errors, and only the destination node can do after combining and decoding sub packets. We propose theARQ scheme between the source node and thedestination node. We analyze the proposedARQ scheme and evaluate thethroughputperformance.

\ Intermediate

nodes/

Mi

hops/

/ \ MNhops Destination -_ Routes from source node to destination node

Other wireless links

Fig. 1. Wirelessmulti-hop network model.

I. INTRODUCTION

On of the most important candidates for the future ^gen- eration mobile communication systems is a wireless multi- hop network[l], [2]. In wireless multi-hop networks, apacket is transmitted from a source node to a destination node via intermediate nodes. Wireless multi-hop networks can be constructed flexibly by various ^ways to select intermediate nodes. So, multipleroutes froma sourcenodetoadestination node canbe established by using the multi-path routing[3].

For reduction in bit errors on wireless channels, ^{we pro-} posed the multi-route coding scheme on multiple routes for wireless multi-hop networks[4]. In the proposed scheme, ^a transmitter at a source node encodes a packet, divides it into sub packets, and transmits them to the next nodes on

multiple routes. Intermediate nodesrelay the sub packets toa

destination node.A receiverat the destination node combines and decodes the received sub packets to get the coding and diversity gain. The concept of this scheme is similar to that ofmultiple description coding for ^source coding[5].

Inthis paper, we introduce ARQtothe multi-route coding.

Inthe multi-route coding, the destination node combines and decodes sub packets which ^are encoded and divided by the

source node. The intermediate node relays ^a sub packet, that is, only a part of a packet. Therefore, the intermediate node cannotdetectpacket^errors, andonly the destination node^can do aftercombining and decoding sub packets.

Then,weproposetheARQ scheme between thesourcenode and the destination node for the multi-route codinginwireless multi-hop networks. In this scheme, the error detection is performed at the destination node. Iferrors are detected, the destination nodereturns aNACKmessagetothe sourcenode.

The source node retransmits sub packets after receiving the NACK message. In contrast to the single hop transmission, the sub packet propagation time ^on each route is random variable in the multi-hop networks[6]. The arrival time of ^a sub packet on each route is different. The destination node decodes and error-detects subpackets everytime asubpacket arrives. However, ifaNACKmessage is returned everytime,

unnecessary sub packets ^are retransmitted, and they result in the trafficjam. To avoid it, ^we introduceto adjust the timing to return the NACK message at the destination node. The proposed ARQ scheme is analyzed and evaluated interms of the throughput performance.

II. MULTI-ROUTE CODING

In this section, ^we explain the multi-route coding in the wireless multi-hop networks[4].

A. Network Model

The wireless multi-hop network model is shown in Fig.l.

A packet is transmitted from a source node to a destination 0-7803-9392-9/06/$20.00 (c)2006IEEE

668

Lnode

Nsubpackets

Fig. 2. Transmitter structure of a source node.

ACK/NACK Nsubpackets

(to source node)

Recovered B er

packet Err i~ai u rChannel [-De

Combiner _ t

detector decoder odeinterleaverL modulator

Fig. 3. Receiver structure of a destination node.

node via this network. Intermediate nodesrelay the transmitted packet. By using a certain routing algorithm, N routes from the source node to the destination node are established. The number of hops from the source nodeto the destination node on the nth route is denoted by Mn. In each hop, the packet transmission is according to a certain access control protocol.

B. Transmitter Structure of the Source Node

Figure 2 shows the transmitter structureof the sourcenode.

A bit sequence of a packet is encoded to an encoded bit sequence by the turbo code. The encoded bit sequence is divided into N sub packets for multiple routes. The sub packets are stored at the buffers. Against the influence of time-variant fading, a channel interleaver for sub packets is employed. Each stored sub packet is interleaved, and after modulation, it is transmittedtothenextnodeonthe nthroute.

This operation isrepeated until all sub packets aretransmitted to the nextnodes onN routes.

C. RegenerativeRelay of the Intermediate Node

The intermediate nodesperform only the regenerative relay.

At the intermediatenodes, the received signal is demodulated to the hard-valued binary sequence, remodulated, and trans- mitted to the next node. Note that error correcting or error detecting are not performed at the intermediate nodes.

D. ReceiverStructure of the DestinationNode

After Mn hops, the sub packet arrives at the destination node. The receiver structure of the destination node is shown inFig.3. The receivedsignalvia the nthrouteisdemodulated, hard-decided and deinterleaved to the estimated bit sequence of the sub packet. It is stored at the buffer. Every time a sub packet arrives at the destination node, the sub packets storedatthe bufferare combined, reorderedbythe combiner, and decoded to the bit sequence of the recovered packet by the iterative decoder. Note that the estimated bit sequence of the sub packet is assumed to be all-zero sequence ifthe sub packetonthe nthroutedoesnotarriveatthe destination node.

The recovered packet is error-detected, and an ACK/NACK messageis returnedtothe sourcenode. The detail of theARQ procedure is described in the following section.

-ircroute NACK NACK ACK Source node

~~~ubpack~~sbpet

1st route *

~~~~transmissions

Destinationnode

failure failure success time

Fig. 4. An example of unnecessarysub packet transmissions (N 3).

III. SOURCE-DESTINATION ARQ

As mentioned in Section I, the arrival time of a sub packet on each route is different. Of course, it is possible todecode sub packets after receiving all N subpackets. But, toreduce thedelay which is defined asthe elapsed time from the occurrence of the transmission request to its successful transmission, the destination node decodes the sub packets arriving before and error-detects themeverytimeasubpacket arrives. Note that an ACK/NACK message does nothave to be returned every errordetection. Ifit is returned every time, unnecessary sub packets are retransmitted since sub packet retransmissions cannotbe cancelled before an ACK message arrives at the source node (Fig.4).

Then, we introduce the threshold a to adjust the timing to return a NACK message. When k sub packets among N transmitted subpackets arriveatthe destinationnode,aNACK message is returned as the following:

1) k < a; ANACK message is not returned.

2) k⁼a; The destination node returns aNACK message, which contains the information of theroutes ofa arrival sub packets. The source node retransmits the a sub packets on the a routes when it receives the NACK message.

3) a < k <N; ANACKmessage is returned, and the sub packet onthe route is retransmitted.

Ifall N sub packets arrive but errors aredetected, the above procedure is repeated until thepacket transmission succeeds.

IV. ANALYSIS A. Assumptions andModeling

First, weexplain assumptions andaqueuing network model used inthe analysis. The detail of them is described in [6].

Anideal mediumaccess controlprotocol is assumed, where each node can transmit and receive a packet independently, each node is allowed totransmit and receive only onepacket simultaneously, every packet sent from nodes is received without collisions. When packet transmissions are controlled as described above, a transmission request arrival process at any wireless node is modeled as a queue. Generations of transmission requests correspond ^to arrivals ofpackets at the queue. The time between thebeginning ofatransmission and the end of itcorresponds tothe service time of the queue.

For each wireless node, the generation process of trans- mission requests from all its neighbors is assumed to be modeled as an independent Poisson process withmean

A-'.

669

The packet length is assumed to be exponential with mean

Tp.

Then, the sub packet length is also exponential with mean Ts ⁼

TpIRN,

where R is the coding rate. According to the assumptions described above, each wireless link is modeled as an M/M/1 queue with the birth rate A and the death rate ,t⁼

lTs.

The time between thegeneration ofatransmission requestand the end of its transmission equals the waiting time of the queue plus the service time of that.

As described in Section II-A, any two routes which exist between different source-destination pairs mayhave common nodes or wireless links. This means that each intermediate node on a route may also be anintermediate node onanother route. Therefore, each intermediate node on a route has multiple inputs and multiple outputs. In this case, we can use the independence assumption[7]. With the assumption, the packet delay of a route which consists of Mn wireless links is represented by the sum of the waiting times of Mn M/M/1 queues. For simplification of the analysis, we assume the number ofhops Mn is identical among N routes, andwe define Mn ⁼M.

B. State Transitionfor ArrivalProcess of Sub Packets We introduce a trellis diagram T⁼ (V, 5) to show the arrivalprocess of subpackets atthe destination node. Let

w,

indicate the nth route and S be the set of all N routes, that

iS,

S = {71,r72, * * ^N (1)

Then, the trellis 7 has thefollowing characters.

1) The node setV is the power setofS, that is, V ⁼ 2S.

Each node means the set of the routes on which sub packets arrive at the destination node.

2) The node set V is divided into N + 1 disjoint subsets

Vj

(O <j < N), thatis,

V⁼ VOUVIU * VN.

The subset

Vj

is defined as,

Vj

={XlXl ⁼j,XCV(= 2S)}, (2) wherejisequaltothe number of subpackets arrivingat the destination node. Clearly, Vo {X} andVN {S}.

The number of their elements is

Vo VN

1.

3) Theedge set S is obtainedas,

SF

{e(A,13)A

C

Vj-j,

13 ^C

Vj,

^{A c} B, 1^< j< N}.

The label Lfj of the edge

e(A,

t3) is defined as the(3) element which satisfies the conditions L.A f A and L.A C 13. From (2) and (3), 13 -A ⁼ 1. Therefore, The label L.A is uniquely decided. The label L.A means the route on which a sub packet newly arrives at the destination node.

Furthermore, we introduce the node set

2(1)

and F(A) definedas,

P(13)

⁼ {A1AC

V3-t,

3C

Vj ,e(A>,5)

^C

-F)J,

(4)

F(A)

⁼{13> C

VI-l,

3C

Vj, e(A, 1)

^C

-F)j.

⁽⁵⁾

The node set P(13) means the previous node set of the node 13, and the nodeset F(A) is the forward nodesetof the node A.We derive the state transition probability -z(A, 13) from the node A to the node 13, where B C F(A). From the assumptions describedin SectionIV-A, the arrivalprobability of a sub packet is independent identically distributed (iid).

Therefore, the state transition probability'y(A, 13) is identical amongthe node set F(A), that is, y(A,3) ⁼

I/SF(A)

^.

Let Pe(X) be the packet error rate when sub packets on the routes X arrive at the destination node. For example, if X ⁼ {171,172}, Pe(X) is the packet error rate when sub packetsonthe1stand 2ndroutesarrive. The cumulativepacket success ratePCS(X) is defined asthe packet success ratesfor allpossibleroutesubsets of X.Forthe aboveexample,PCS(X) is the packet success rate when asub packet onthe 1stroute arrives, a sub packeton the 2ndroute arrives, or subpackets on the 1st and 2nd routes arrive. Due to a mutual exclusive event, Pc5(X) ⁼1-Pe(X).

The termination probability Il(X) is defined as the proba- bility that the arrival process of sub packets is finishedatthe node X since the packet transmission succeeds. Obviously, P1(q) ⁼0. Furthermore,

Ex

vrl(X) ⁼PCs(S)

WhenC C

Vj

(1 <j < N), the cumulative packet success rate PCS(C) has to be larger than Ps(13) (13 C T'(C)) since a sub packet on the route Lc newly arrives at the destination node. Then, the packet success rate when a sub packet on the route Lc newly arrives is derived as PCs(C) -PCS(13) Pe(13)-e(C). Considering the possible statetransitions, the termination probability H(C) maybe expressed as,

PI(C)

⁼

E !3(13)'y(1C){Pe(1) -Pe(C)},

BE3P(C)

where

13(13)

is defined as,

I1 (if=3=)

$13

)

j

E j3(A)y(A 13) (otherwise)*

AG-P(B)

(6)

(7) C. Total Number of Sub Packet Transmissions and Traffic

Intensity

In this section, the total number of sub packet transmis- sions is derived by using the termination probability.Let

Kijj

be the total sub packet transmissions of the case that the packet transmission succeeds when j sub packets of the ith (re)transmission arrive. To consider unnecessary sub packet transmissions, it maybe derived as,

i. N (j <a)

N',

iXi

^N+

(j-1-I) ('>a) ⁽⁸⁾

Then, theaveragenumber of total sub packet transmissions may be expressed as,

(9)

00 N if

=

E E E

i{i,jPI(X)Pe(S)t 1

1='j=lxGvJ

670

We assume the traffic intensity p ⁼

A/,

of each wireless link increases inproportion to the average number of total sub packet transmissions. The base traffic intensity po is defined as the traffic intensity which does not include retransmitted sub packets. Then, the traffic intensity may be expressed as P= K Po.

D. Delay andThroughput Analysis

According to the queueing model described in Section IV- A, each wireless link is modeled as an

MIMI1

^{queue. The}

probability density function

fwnm(t)

for the packet delay Wn,m ofthe mth wireless link on the nth route is exponential andgiven by

fWn,. (t)

⁼

P>(1

^-

p)e [t(1-p)t.

(10) Since wireless links on a route are statistically independent and have the same service time distribution, the probability density function fw(t) for thepacket delay w of the routeis derivedby M-fold convolution of(10) andmaybe expressed as,

fw(t)

=

/-(Ai _{(Al- 1)!}

^A

⁾ tM-1C-1/l(1-p)t.(1

The cumulative distribution function

Fw(t)

for the packet delay w ofa route is also obtainedby,

Fw(t)

(M)- F(M,M(l -p)t)

⁽¹²⁾

where F7(z) is the gamma function and F(a, z) is the incom- plete gamma function.

Let W(n,j) be defined as the elapsed time ofj sub packet arrivals at the destination node when n sub packets are sent by the sourcenode. Then, the probability density function of W(n,j) is derived by

fW^{(n j)}(t)

(j 1)!(n

!

-~

*Fwj-l (t{-w(t)jn-jfw(t).

(13) Therefore, the average delay time ofW(n,j) is obtainedby

d(n,j) tfW(nj)dt. (14)

Whenn j 1, d(n,j) ^can be simply expressed as,

d(1,1)

p(l p)

M. (15)(5

Byusingd(n,j), theaveragedelay time whenj sub packets of the ith transmission arrive is derived asthe following:

1) Forj < a,

fd(N,j) (i=1)

~D

^{d(N,a)+d(1, 1) +}

^d(a,j)

^(16-a)

+{d(1, 1)

⁺

d(a, a)}(i -2)

^{(i >}

2)

2) Forj > a,

Dij

⁼d(N,j)+2d(1, 1)(i -1). (16-b)

Then, the whole average delay time may be expressed as, (17)

oo N

D ⁼ Z

E DijUl(X)Pe(S)-

1=lj=lxGvJ

The throughput is defined as the time ratio of a packet trans- mission to the elapsed time until its successful transmission ineach wireless link. The throughput is obtained by

DIM

T ⁽¹⁸⁾

E. Case of Iid Wireless Link Model

Ifthe statistical character of each wireless linkisassumedas iid process, the derived equations can be simplified. In the iid wirelesslinkmodel, the packeterror rateof the nodes X C Vj is identical. Ifthis packet error rate is denoted as Pe

(Vj),

(6), (9) and (17) maybe rewroteby,

r,(vj)

^=Pe(vj-1) ^-Pe(vj)

(19)

00 N

-

E E

ZZ ,ji

j(Vj)Pe(S)

1

i=lj=l

and 00 N

D ⁼ZDi

ij(Vj)Pe(S)i

1

i=lj=l

V. NUMERICAL RESULTS

(20)

(21)

We evaluate the throughput performance inthe iid wireless link model.

The packet error rate

Pe(Vj)

is obtained by Monte Carlo simulation. The operating parameters are shown in Table I.

The Rayleigh fading environment is assumed on each wire- less link. The fading loss is constant during a sub packet transmission, and independently varies at each wireless link.

Forcomparison, the performance of the hopby hop ARQ on single route (N = 1) is also shown. In this case, the rate compatible punctured turbo (RCPT) ARQ with the puncturing period P ⁼2 [8] is performed hop by hop.

Theaveragenumber of total subpacket transmissionsversus

EbINO

^{is shown in} Fig.5, where Eb is bit energy and

N012

istwo sidepower spectral density. The minimum value of the average number comes close to 1 for the case of the hop by hop ARQ withN ⁼1. Forthe case of the source-destination ARQ withN ⁼3, the minimum value converges at 3 except fora = 1.However,it becomes4fora =1. Itis because2 or more sub packets arerequired for successful decoding. Then, anunnecessary sub packet transmissionoccurs for ^a= 1.

Figure 6 shows the throughput normalized by the packet length versus Eb NO for po ⁼ 0.1. Large average number of total sub packet transmissions brings about an increase in the traffic anddegradation of the throughput. When

EbINO

^is

below10dB, theaveragenumber of total subpacket transmis- sions becomes very large. So the throughput is unacceptably low. The throughput of the source-destination ARQ is better than that of the hop by hop ARQ when

EbINO

becomes larger. But for much larger

EbINO,

^{the best} throughput is 671

9

Qn 0

C.)

~zct

C.)

ct Qn C

TABLE I SIMULATION PARAMETERS.

averagedata length 1,000 bits turbo code coding rate 1/3, (37,21) RSC

5 iteration decoding

modulation scheme BPSK

wireless link model Rayleigh fading

number of routes N 3

number of hops Mn 3

15

10

Fig. 5. A

0.8

,0.7- oc=j oc-2 ~

0.67

-

0.6I ,..

source-destinationARC

04

Z 05^{0.4 ..} hopbyhopARQ(N=1)

00.1

5 10 15 20 25 3

Eb/No

Fig. 6. Normalized throughputversusEbINo.

06

0.5

o5 .,10 15 _Lb/NO~20,,25 30 = ^0.4-

~~ ~~~~~~~~~b

0

cveragenumber of total subpackettransmissions versusEbINO. 0.3

E ^0.2

obtained by the hop by hop ARQ. It is because the packet 7.

error rate is pretty good and to reduce the number of sub packet transmissions is the dominant factor to increase the throughput.

Figure 7 shows the normalized throughput versus base traffic intensity for

EbINO

^{= 12} dB. For the low base traffic intensity, the throughput of the source-destination ARQ is better than that of the hop by hop ARQ because the hop by hop ARQ increases the delay and it results in the throughput degradation. However, the source-destination ARQ increases the traffic due to multiple sub packet transmissions. So the throughput is degraded for the high base traffic intensity.

Furthermore, the throughput for^{a= 1} is the bestperformance for the low base traffic intensity because of the reduction ofdelay. On the other hand, the highest throughput ^can be obtained for ^{a =} 3 for the high base traffic intensity since

unnecessary sub packet transmissions ^areprevented.

VI. CONCLUSIONS

In this paper, we have proposed the source-destination ARQ scheme for the multi-route coding in wireless multi- hop networks. To reduce the delay, the destination node decodes and error-detects sub packets^everytime asubpacket arrives. Furthermore, ^we have introduced the threshold to adjust the timing to return a NACK ^message. By analyzing the proposed scheme, ^we have clarified that it can achieve the good throughput performance, specially for the low traffic intensity.

ACKNOWLEDGMENT

This work was supported in part by The Strategic Information and Communications R&DPromotionProgrammeof theMinistry of

0.1

0.05 0.1 0.15

Base trafficintensity po ^0.2 Fig. 7. Normalized throughput^versusbase traffic intensity po.

Public Management, HomeAffairs, Postsand Telecommunications.

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