Network-coded Cooperation for Multi-unicast with Non-Ideal Source-Relay Channels

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1 This full text pper ws peer reviewed t the direction of IEEE Communictions Society suject mtter experts for puliction in the IEEE ICC 2010 proceedings Network-coded Coopertion for Multi-unicst with Non-Idel Source-Rely Chnnels Yong Liu*, Wen Chen*, Jino Ji*, nd Jieto Zhng *Deprtment of Electronic Engineering, Shnghi Jiotong University, Shnghi, P. R. Chin, SKL for Moile Communictions, Southest University, P. R. Chin, Communiction Technologies Deprtment, Huwei Technologies, CO., Ltd., P. R. Chin Emil:{yongliu1982,wenchen}@sjtu.edu.cn Astrct Network coding is considered s promising technique to improve diversity gin nd network throughput in multi-source rely systems. This pper presents n opportunistic network coded coopertion scheme in wireless multi-unicst system with non-idel source-rely chnnels. In the conventionl network-coding-sed coopertion schemes, the rely merges the messges received from multiple sources nd lwys forwrds them to the destintions without checking their reception sttus. The destintions recover the sources messges either from the direct trnsmissions or from the rely forwrding. Such mode is esy to implement, ut my led to error propgtion in the event of decoding filures t rely. In contrst to these works, the proposed scheme is opportunistic, where the rely forwrding is determined y the qulity of S R chnnels, tht is, the rely does not ssist trnsmission unless it hs correctly decoded the received sources messges. Systemtic performnce nlysis in the form of outge proility nd spectrl efficiency is performed in this pper. Comprisons with the conventionl network coded multi-unicst nd Incrementl Relying protocol re mde under fixed system energy constrint. The outge results show tht the proposed scheme performs etter thn the conventionl network-coded schemes when source-rely links hs poor qulity. Compring with Incrementl Relying protocol, the opportunistic scheme chieves reduced system outge proility s well s higher spectrl efficiency. This scenrio cn e extended to generl multi-user environment without much cost. Index Terms Network coding, spectrl efficiency, multiunicst, opportunistic trnsmission, outge proility. I. INTRODUCTION With the potentil for remrkle enefits in terms of system cpcity nd diversity gin, coopertive relying, who hs een extensively investigted in [1]-[4], is proposed s n effective mens to improve system performnce for future genertions of wireless networks. In typicl rely system setup, the source rodcsts messge to the destintion s well s rely in the first phse; the rely, who is lwys locted etween the source nd destintion, forwrds the received signl to the destintion in the second phse. The destintion recover the sources messge sed on the two phses trnsmission. Depending on the chnnel stte of the network, vrious forwrding strtegies cn e employed to exploit the potentil enefits provided y node coopertion, mong which Amplify-nd-Forwrd AF nd Decode-nd- Forwrd DF were introduced nd crefully exmined in [3]. In rely coopertion system using AF technology, the rely node, who cts s virtul ntenn, overhers the signl, mplifies nd forwrds it to the destintion, wheres in DF scheme, the rely node first decodes the received messge, re-encodes nd forwrds it to the destintion. Trnsmission diversity is thus chieved vi the two methods, which enles the network to comt chnnel fding. Similr to the single source-destintion pir, multiple source-destintion pir cn lso derive enefit from one rely node if ll the terminls lies in the coverge of the rely [5], [6], mong which Multiple Access Rely Chnnel MARC is typicl setup. Network coding, where the pckets of mny seprte messges flows cn e mixed vi lgeric opertions [7], [8], hs drwn significnt ttention for its potentil in chieving splendid throughput increses. The core of network coding technology is to llow nd encourge dt merging in the intermedite nodes to sve the system resources such s ndwidth, power, nd time slots. Although network coding is first introduced for wired network, mny works hve proved tht it is lso eneficil in wireless networks [9]-[11]. Network coding is used to increse the efficiency of informtion exchnge in wireless environments ws erly proposed in [9]. The uthors in [11] showed tht network coding leds to etter diversity performnce in distriuted ntenn system DAS. Actully, how to leverge network coding in wireless physicl lyer networks for system cpcity improvement is still under intensive study recently. As mentioned ove, multi-source systems cn derive significnt enefits from network coding in terms of throughput nd roustness. Therefore, there hve een severl proposls for pplying network coding to multi-sources relying systems [12]-[16]. In [12] nd [14], n XOR-sed network coding scheme is employed to fcilitte the i-directionl informtion exchnge etween pir of nodes over two hops. In [13], in order to improve oth the reliility nd throughput for two-stge DF network with multiple source-destintion pirs, network coding is comined with Best-Select coopertion which is performed y exploiting the instntneous chnnel stte informtion CSI. In [15]nd[16], networkcoding-sed MARC is proved mintining the diversity gin, ecuse the rodcst nture of wireless networks is fully exploited to provide flexile trnsmission in the schemes. The forementioned works were minly imed t improving the performnce of multi-source network with sttionry trffic flows. However, fding nture is stochstic in wireless /10/$ IEEE

2 This full text pper ws peer reviewed t the direction of IEEE Communictions Society suject mtter experts for puliction in the IEEE ICC 2010 proceedings networks. Sometimes chnnels condition etween the sources nd rely my not so good to gurntee relile decoding. In such cse, network-coded coopertion performed y the rely would led to error propgtion. Bsed on this fct, we propose n Opportunistic Network-Coded ONC multi-unicst scheme in this pper, where the rely node decides whether or not to trnsmit the network-coded informtion sed upon the qulity of S R chnnels. In other words, the rely will do nothing unless it hs correctly decoded the trnsmitted messges. The concept here is similr to the Incrementl Relying mentioned in [3], ut network coding technology is not dopted in tht scheme. The dvntges of our work over the existing coopertion protocols re shown in two spects. On one hnd, the proposed scheme utilizes opportunistic relying scheme, where the rely does not cooperte unless it hs correctly decoded some messges form the sources. Due to exploittion of opportunistic relying, the new scheme improves spectrl efficiency like incrementl relying y voiding unnecessry relying. This property relizes more efficient use of the degrees of freedom of the chnnel thn the existing protocols where the rely lwys perform coopertion. On the other hnd, network coding technology is dopted, which overll reduces time slots compred with those not exploiting network coding. As consequence, with the sme system energy constrint, ech trnsmit node will e llocted with much more trnsmit power. In this pper, we perform outge nd spectrl efficiency nlysis of the network-coding-sed multi-unicst system. To mke fir comprison, we ssume tht the sme ndwidth nd trnsmit power re llocted in ll setups, which however were missing in the previous works. Compred with Incrementl Relying scheme tht does not exploit network coding, the new scheme provides higher spectrl efficiency while mintining slightly reduced system outge proility. We especilly compre the stic nd opportunistic networkcoding-sed schemes. The rest of this pper is orgnized s follows. Section II descries the ONC system model. In Section III, outge proility, nd spectrl efficiency for the proposed scheme re nlyzed. In Section IV, performnce evlution re presented to verify the performnce improvement of the new scheme. Section VI concludes the pper. A. Chnnel Model II. SYSTEM MODEL The multi-unicst system considered in this pper is depicted in Fig. 1, which consists of five nodes, where two sources S nd S communicte with two destintion nodes D p nd D q ssisted y one hlf duplex rely R. The chnnels re ssumed to e flt-fding, mutully sptilly independent, with dditive white Gussin noise AWGN nd modeled s y i,j = h i,j x i,j + n i,j, 1 where h i,j represents the fding gin of the corresponding chnnel, in which i {,, r} nd j {r, p, q}, x i,j nd y i,j re the inputs nd outputs of the chnnel, n i,j is the Fig. 1. S S X S D q R X = X X r X Multi-unicst model with two sources-destintion pirs. trnsmits X trnsmits R trnsmits X X X trnsmits trnsmits R trnsmits R trnsmits X T/2 S S X X X X D p S X ONC- Multi-unicst Conventionl Multi-unicst Time Fig. 2. Timing chnnel lloction of the conventionl nd the proposed network-coding-sed multi-unicst system. dditive Gussin white noise with vrince N 0. Chnnels re modeled s zero-men, circulrly symmetric complex Gussin rndom vriles with vrinces 1/α i,j. Hence h i,j is Ryleigh distriuted nd h i,j 2 is exponentilly distriuted with exponent α i,j respectively. In ddition, ll the trnsmit terminls re ssumed to hve common trnsmit power denoted s P. Then the instntneous SNR of the chnnel cn e denoted s γ i,j = h i,j 2 P N 0. As ll nodes work in the hlf-duplex mode, trnsmission orthogonlity should e stisfied. In the conventionl multi-unicst coopertion schemes, source trnsmits signl x i in the first hlf time slot. Then the rely forwrds the sme informtion in the second hlf time slot employing AF or DF scheme in TDMA mode. The proposed network coding sed trnsmission scheme, however, relize network coding nd spectrl efficiency simultneously. In the new scheme, the source trnsmits two different symols x nd x in the first two hlf time slots respectively. Then the rely my forwrd the XOR x x to the destintions in third hlf time slot, s shown in Fig. 2. This scheme my sve 1/4 time slot compred with the conventionl scheme, nd improve the spectrl efficiency s well s power efficiency. B. Description of ONC-Multi-Unicst Scheme In this susection, the opertion of ONC-multi-unicst Scheme will e descried in detils. Due to the exploittion of opportunistic relying, the proposed scheme improves spectrl efficiency s incrementl relying scheme in [3], since the rely is only employed when helpful. During the first two hlf time slots, S nd S trnsmit their own dt towrds the distinct destintion nodes s well s the rely t spectrl efficiency R it/s/hz respectively. Bsed on decoding result, the rely chooses to work either in sttic or opportunistic mode [3]. In the sttic mode, the rely decodes the messges nd performs the network coding without checking the decoding sttus. Apprently, if t lest one of the two messges is incorrectly decoded, the network-coded messge does not help in recovering the sources messges t the destintion. Such mode is simple to implement, ut my

3 This full text pper ws peer reviewed t the direction of IEEE Communictions Society suject mtter experts for puliction in the IEEE ICC 2010 proceedings led to error propgtion; While in the opportunistic mode, the rely does not perform network coding unless oth sources trnsmissions re correctly decoded. If the received SNR t R from S i is not high enough to gurntee successful decoding, the rely will not perform network coding. It either forwrds the correctly decoded one of the two messges if ny, or keeps idle. For clrity, we rodly ctegorize the opportunistic protocols into three disjoint cses s follows. 1 The rely correctly decodes oth of the two sources messges. Then the rely performs the network coding nd forwrds the network-coded messge to destintions in the third hlf time slot. 2 The rely filed to decode ny of X nd X. Then the rely keeps idle in the third hlf time slot. 3 The rely succeeds in decoding only one of the two sources messges. Then it merely forwrds the correctly decoded messge in the third hlf time slot. III. PERFORMANCE ANALYSIS AND IMPROVEMENTS Outge proility is n nlyticl mesurement for lock fding environment, which denotes the proility of event tht the instntneous mutul informtion I is smller thn the dt rte R. Consider the point-to-point trnsmission of S to the destintion D p for exmple. When the instntneous SNR of the chnnel γ,p = h,p 2 Pt N 0 is less thn some threshold, the destintion D p will wrongly decode X. Then n outge is sid to occur, nd the outge proility is P X =Pγ,p < 2 R 1 = 1 exp 2R 1 Γ,p, 2 where X represents X in outge, the chnnel coefficient h,p 2 is exponentilly distriuted, nd Γ,p is the verge SNR of the chnnel h,p. According to the decoding sttus t the rely, there re severl possiilities of trnsmission. We will nlyze the outge proility of the network-coding-sed multi-unicst system for ech cse in the following.without loss of generlity, we only consider the outge event of the signl X t destintion D p, which cn e esily modified to other events. Let X j,k i e the correctly decoded messge of source i trnsmitted from node j to node k; while X j,k i denotes the corresponding outge. A. Rely operting in sttic mode In this mode, rely try to decode the messges nd lwys performs network coding without checking the decoding sttus. Depending on the qulity of S i R chnnels, the outge computtion cn e clssified into two cses. CASE 1 : The rely succeed in decoding oth sources messges, nd forwrds the network coded symol X = X X to the destintions. Then the outge event of source S is X,1 = X,r X,r X,p X,p + X r,p, 3 where + nd represent the logicl or nd nd opertors respectively, nd the suscript 1 denotes the cse 1. Becuse the rodcst nture of wireless communiction, D p cn overher X t the first hlf time slot, nd D q cn overher X t the second hlf time slot. So even if X sometimes fils to e received from the direct trnsmission, the destintion D p is lso le to recover the messge y comining X nd X, provided tht oth X nd X re correctly received. Therefore, we cn write the system outge event X s s X s,1 = X,r X,r X,p X,p + X r,p + X,r X,r X,q X,q + X r,q. 4 CASE 2 : At lest one signl is wrongly decoded t the rely. In this cse, the trnsmission y the rely node does not help in messge recovery t the destintions, nd the outge events t the destintion merely depend on direct trnsmission. Then the outge of X is X,2 = X,r + X,r X,p. 5 Therefore the system outge in cse 2 is X s,2 = X,r + X,r X,p + X,q. 6 Becuse of the independence of outge events, the system outge proility is P X s =PX,r P X,r P X,p P X,p + X r,p + P X,r P X,r P X,q P X,q + X r,q + P X,r + X,r P X,p + X,q, where ll individul proilities in 7 cn e computed y 2. B. Rely operting in opportunistic mode Similrly, there re severl possiilities of forwrding ctions depending on the decoding results t the rely node. In the following, we will nlyze the outge proility for ech cse. CASE 1 : Both sources messges re lost t the rely. Then the rely keeps idle. Hence the outge events t the destintion D p is decided y the direct trnsmissions only, tht is X p,1 = X,r Then the system outge event is X s,1 = X,r X,r X,r 7 X,p, 8 X,p + X,q. 9 CASE 2 : The rely only correctly decodes one messge from the two sources. Without loss of generlity, we only

4 This full text pper ws peer reviewed t the direction of IEEE Communictions Society suject mtter experts for puliction in the IEEE ICC 2010 proceedings consider the rely correctly decodes messge from S,ut fils to X. In this cse, the rely just forwrd X insted of performing network coding. Then the outge event ecomes where X C X,2 = X,r X,r X C, 10 = MRC X,p,X r,p represents the comined messge t the destintion. The outge event of D q cn e otined similrly, nd the system outge event in cse 2 is X s,2 =X,r + X,r X,r X,r X C + X,q X C + X,p. 11 System Outge Proility without sttic NC with sttic NC without sttic NC with sttic NC Γ,r =Γ,p +5dB Γ,r =Γ,p 5dB SNRdB CASE 3 : Both of the messges re correctly decoded t rely. This is the sme s the first cse of the sttic mode, nd eqution 3 nd 4 cn e pplied here. Therefore, the system outge proility in the opportunistic mode cn e expressed s P X s =PX,r P X,r P X,p P X,p + X r,p + P X,r P X,r P X,q P X,q + X r,q + P X,r P X,r P + P X,r + P X,r P X,r P P X,r P X,p X C + X,q + X,q X C + X,p 12 where P X C nd P X C re the CDFs of the sum of two exponentilly distriuted rndom vriles, which is given y eqution 14. In eqution 14, λ u = 1 Γ,p, λ v = 1 Γ r,p, nd ω =2 2R 1 is the threshold [3]. Then we cn use eqution 2 nd 14 to evlute the individul proilities ccordingly. IV. NUMERICAL RESULTS In this section, we present some numericl results to evlute the proposed scheme. We use monte-crlo simultion in Mtl for 10 6 runs to estimte the outge proility for the new scheme. Besides, the conventionl multi-unicst nd the Incrementl Relying schemes in [3] re lso presented for comprison. An informtion rte of R =1is ssumed. Moreover, results re sed on symmetric source-destintion nd source-rely chnnels, tht is, Γ,p =Γ,q, Γ,r =Γ,r. Apprently, the selection of opertion modes minly depends on the qulity of the source-rely links Γ i,r. In order to illuminte the superiority of the opportunistic network coding, we first exhiit the outge proility curves of sttic protocol with nd without network coding, which is, Fig. 3. Outge proility vs SNR of sttic protocol with nd without network coding. NC is short for Network coding, nd results re sed on 2 different vlues of Γ i,r System Outge Proility IDF scheme The ONC schme No coopertion IDF scheme The ONC schme Γ,r =Γ,p +5dB Γ,r =Γ,p 5dB SNRdB Fig. 4. Outge proilities of IDF nd opportunistic network-coding-sed protocols. IDF stnds for Incrementl Decode-nd-Forwrd, ONC is short for Opportunistic Network-Coding shown in Fig. 3. We cn find n interesting phenomenon tht the protocol without network coding lwys performs etter compred to tht in sttic mode. So it is not necessry to employ network coding in sttic modes in terms of outge proility even though the protocols re reltively simple to implement. Fig. 4 shows the outge proilities of IDF nd the opportunistic network-coding-sed protocols. It is esy to find tht the opportunistic network-coding scheme mintins lower system outge proility thn IDF. Actully stle SNR gin of 0.5dB is chieved y the new scheme compred with IDF. Next, we study the spectrl efficiencies of IDF nd the opportunistic network-coding-sed protocols. Apprently, oth of the two schemes re rteless, ecuse they do not lwys perform messge forwrding. Bsed on the nlysis in Section III, expected spectrl efficiency of ONC-sed protocol

5 This full text pper ws peer reviewed t the direction of IEEE Communictions Society suject mtter experts for puliction in the IEEE ICC 2010 proceedings P X C =Pγ,p + γ r,p < 2 R 1= [ 1 λ u λ u λ v e λvω + λ v λ v λ u e ], λuω λ u λ v, λ u ω e λuω, λ u λ v, 14 Spectrl Efficiency it/s/hz IDE scheme The ONC scheme SNRdB Fig. 5. Spectrl Efficiency comprison of IDF nd opportunistic networkcoding-sed protocols. R =1/s/Hz. is S ONC =R P {γ,p < 2 R 1} + 2R 3 P {γ,r < 2 R 1}P {γ,r < 2 R 1} + R 2 P {γ,r > 2 R 1}P {γ,r < 2 R 1}; while tht of IDF protocol elorted in [3] is, S IDF i =R exp α ij 2 R 1P/4N 0 + R 2 1 exp α ij2 R 1P/4N 0, where i {, } nd j {p, q}. We cn see tht the opportunistic network-coding-sed protocol exceeds the IDF protocol in terms of spectrl efficiency. Moreover, oth IDF nd the proposed scheme provide n expected spectrl efficiency pproching R = 1it/s/Hz s SNR si,d j pproches to, which cn e understood intuitively. Bsed on these results, one cn oserve tht compred with the schemes without network coding nd IDF, the opportunistic network-coding-sed protocol provides reduced system outge proility while mintining n incresed expected spectrl efficiency, which comes from the employment of the network coding technology nd the opportunistic forwrding. V. CONCLUSION In this pper, we propose n opportunistic network-codingsed multi-unicst protocol, nd present the outge proility nd spectrl efficiency nlysis of vrious coopertive trnsmission schemes including the conventionl multi-unicst nd the IDF scheme. By employing network coding technology, the time slots re reduced in the trnsmission, which cn e trnslted into the higher spectrl efficiency nd incresed trnsmit power. On the other hnd, y employing opportunistic scheme in the protocol, unnecessry forwrding y rely is voided, which results in efficient use of the degrees of freedom of the chnnel. We proved tht our scheme outperforms IDF in terms of system outge ehvior nd spectrl efficiency vi theoreticl nlysis nd numericl results. Moreover, we oserved tht the sttic protocols do not enefit from network coding in terms of outge proility. ACKNOWLEDGEMENT This work is supported y NSF Chin # , y SEU SKL project #W200907, y Huwei Funding #YJCB WL nd #YJCB WL, nd y Ntionl 973 project #2009CB REFERENCES [1] G. Krmer, M. Gstpr, nd P. Gupt, Coopertive Strtegies nd Cpcity Theorems for Rely Networks, IEEE Trns. Inf. Theory, vol. 51, no. 9, pp , Sept., [2] P. Herhold, Coopertive relying protocols nd performnces, PhD thesis t the Technicl University of Dresden, July, [3] J. L. Lnemn, D. N. C. Tse, nd G. W. Wornell, Coopertive diversity in wireless networks: efficient protocols nd outge ehvior, IEEE Trns. Inf. Theory, Vol. 50, No. 12, pp , Dec., [4] Y. Ling, nd G. Krmer, Rte regions for rely rodcst chnnels, IEEE Trns. Inf. Theory, vol. 53, no. 10, pp , Oct., [5] L. Snkr, Y. Ling, H. V. Poor, N. Mndym, Opportunistic Communictions in n othogonl Multiccess Rely Chnnel, IEEE Interntionl Symposium on Informtion Theory, Nice, Frnce, June 24-29, [6] O. Shin, E. Erkip, Dynmic resource lloction for multi sourcedestintion rely networks, CISS 07, pp , Mrch, [7] R. Ahlswede, N. Ci, R. Li, nd R. Yeung, Network informtion flow, IEEE Trns. Inf. Theory, vol. 46, no. 4, pp , July, [8] R. Li, R. Yeung, nd N. Ci, Liner network coding, IEEE Trns. Inf. Theory, vol. 49, no. 2, pp , Fe., [9] Y. Wu, P. A. Chou, nd S.-Y. Kung, Informtion exchnge in wireless networks with network coding nd physicl-lyer rodcst, Microsoft Reserch Technicl Report MSR-TR , Aug., [10] J. Zhng, P. Fn, nd K. B. Letief, Network Coding for Efficient Multicst Routing in Wireless Ad-hoc Networks, IEEE Trns. Com., no.4, vol. 56, pp , Apr., [11] Yingd, S. Kishore, nd J. T. Li, Wireless Diversity through Network Coding, Proc.IEEE WCNC., vol. 3, pp , April, [12] Y. Wu, P. Chou, nd S. Kung, Informtion exchnge in wireless networks with network coding nd physicl-lyer rodcst, in Proc. of CISS 2005, Mrch 16-18, [13] C. Peng, Q. Zhng, M. Zho, nd Y. Yo, SNCC: A selective networkcoded coopertion scheme in wireless networks, in Proc. of ICC 2007, pp , June, [14] W. Chen, K. Letief, nd Z. Cho, Opportunistic network coding for wireless networks, in Proc. of ICC 2007, pp , June, 24-28, [15] C. Husl, nd P. Duprz, Joint network-chnnel coding for the multiple ccess rely chnnel, in Proc. Intern. Workshop on Wireless Ad Hoc nd Sensor Networks, New York, USA, vol. 3, pp , June, [16] D. H. Woldegerel, nd H. Krl, multiple-ccess rely chnnel with network coding nd Non-idel source-rely chnnels, in Proc. IEEE ISWCS, pp , Oct., 2007.