Random Network Coding in Wireless Sensor Networks: Energy Efficiency via Cross-Layer Approach

Transcription

1 Radom Network Codig i Wireless Sesor Networks: Eergy Efficiecy via Cross-Layer Approach Daiel Platz, Dereje H. Woldegebreal, ad Holger Karl Uiversity of Paderbor, Paderbor, Germay {platz, dereje.hmr, holger.karl}@upb.de Abstract The applicatio of Network Codig (NC) i Wireless Sesor Networks (WSNs), where each ode broadcasts its iformatio to all other odes, is cosidered. Traditioally, this all-to-all broadcast is implemeted by lettig each ode store ad forward received packets. I the NC-based approach, each ode overhears packets trasmitted from eighbourig odes, combies the received packets, ad forwards the resultig packet to its eighbours. The hope is to eed fewer trasmissios, which helps to save eergy. I this paper, we study the NC-based all-to-all broadcast assumig all iter-user chaels are slow fadig ad receptio eergy is comparable to trasmissio eergy. A cross-layer approach, that realizes the NC at the etwork layer ad uses the MAC layer s forwardig ad schedulig decisios to determie whether ad how a packet has bee etwork coded, is cosidered. Theoretical ad simulatio results show that the NC-based system cosumes less eergy tha traditioal store ad forward (SaF) approach. However, cosideratio of o-zero receive eergy reduces the eergy gai of NC over SaF sigificatly; this is because more packets should be received to effectively utilize the etwork codig. Additioally, the performace of etwork codig over various field sizes is studied; results show that, for a fadig chael, eve smaller field sizes (e.g. F or F 4) perform well as compared to the traditioal SaF approach. Idex Terms Wireless sesor etwork, radom etwork codig, protocol, eergy efficiecy, cross layer. I. INTRODUCTION I a Wireless Sesor Network (WSN), a all-to-all broadcast, where each ode i the etwork broadcasts its packet to all other odes, ca be required (e.g. to update routig iformatio, durig iitializatio ad calibratio phases, or i applicatios where trackig ad predictig of several objects movig patters is required). All-to-all broadcasts cause heavy traffic, callig for eergy-efficiet trasmissio schemes. Store-ad-forward is oe geeral approach to implemet a all-to-all broadcast (e.g. via floodig or probabilistic forwardig); i this approach, odes forward the same packet they received from previous trasmissios. I floodig, each ode simply retrasmits every ewly received packet; however, this scheme suffers from redudat trasmissios. More efficiet floodig schemes establish a broadcast structure based o some form of topology cotrol, e.g. trees or clusters [1], []. Geerally, these approaches allow a reliable ad efficiet broadcast by artificially reducig the complexity of the topology ad assigig each ode a clear role, e.g. a ode i the tree is resposible to forward packets to/from all its childre odes. However, costructio ad maiteace of such a structure icurs sigificat overhead ad is thus useful oly if the broadcast service is eeded repeatedly ad ode mobility is low. I a highly dyamic eviromet, a radomized approach such as probabilistic forwardig is ofte used [3], [4]. I this approach, odes retrasmit ewly received packets oly with a certai probability; however, the retrasmitted packets are beeficial oly for a fractio of odes i the eighborhood. Recetly, Network Codig (NC) has emerged as a efficiet alterative to the simple store-ad-forward all-to-all broadcast. The core idea of NC is that each ode i the etwork combies previously received packets ad forwards the combiatio to eighborig odes, istead of storig ad forwardig idividual packet. This leads to fewer trasmissios ad thus helps to save trasmissio ad receptio eergy. The remaider of the paper is orgaized as follow. Sectio II describes our cotributios ad puts them ito cotext of related work. I Sectio III, a brief itroductio to Radom Liear Network Codig (RLNC) is give, followed by a descriptio of various NC-based protocols i Sectio IV. Sectio V gives the system model ad derives theoretical bouds. Results are preseted i Sectio VI ad coclusios are draw i Sectio VII. II. CONTRIBUTIONS AND RELATED WORK Referece [5] presets, usig aalysis ad simulatio, that i a oe-to-all broadcast the umber of trasmissios ca be reduced usig NC over a probabilistic chael. All-toall broadcast protocols, based o the cocept of RLNC ad probabilistic forwardig, are preseted i [6]. Via theoretical aalysis ad simulatios, it is show that NC requires fewer trasmissios compared to probabilistic forwardig for codig over sufficietly large field sizes. I a related paper [7], various RLNC-based protocols have bee implemeted usig the stadard IEEE Medium Access Cotrol Layer (MAC) ad their performace is aalyzed; the results show that the cosidered MAC has oly margial ifluece o the performace. A proactive approach, where each ode periodically seds out ew radom packet combiatios istead of oly trasmittig upo receptio of a iovative packet, is

2 proposed by Fasolo et al. [8]. I [9], the maximum broadcast rate of this proactive approach is aalyzed. The above metioed related work is based o the followig critical assumptios: first, reliable iter-user chaels exist such that odes ca always perform the NC. Secod, the eergy spet for receivig packets is isigificat compared to the trasmissio eergy. The reliable chael assumptio may ot hold if mobility of odes or the eviromet is cosidered where iter-user chaels will be fadig. Also, i WSN the receptio eergy is comparable to trasmissio eergy. I this work, we propose NC-based, cetralized ad distributed allto-all broadcast schemes takig mobility ad receptio eergy ito accout. Lower bouds are show via theoretical aalysis ad simulatios results are also preseted. Our cotributios are summarized as follows: A cross-layer approach, that itegrates RLNC-based allto-all broadcasts with the MAC protocol ad suitable for slow fadig iter-user chaels, is studied. For ideal sleep schedulig, the eergy efficiecy of RLNC is aalyzed, takig both trasmissio ad receptio eergy ito accout. The RLNC-based protocols are studied for various field sizes. Cosiderig trasmissios from two-hop eighbors, the performace of small field sizes is show to improve. The results show that RLNC ca achieve performace improvemets over the traditioal forwardig approach eve for smaller fields sizes (e.g. F ad F 4 ); the cross-layer optimizatio helps to leverage the gais of RLNC more efficietly. III. RANDOM LINEAR NETWORK CODING This sectio recaps some of the saliet poits i RLNC. I RLNC, each ode liearly combies previously received packets ad trasmits the resultig packet; radomly geerated coefficiets are used i the combiig. To explai the operatio further, suppose i a etwork of odes, packet x i origiates at ode i, 1 i. I a symbol-level NC, s cosecutive bits of x i are treated as a symbol over the Galois field F q with q = s ; hece a packet of legth l bits cosists of l s symbols. Assume a ode receives m packets (g k,y k ), where 1 k m. g k = (g k,1,...,g k, ) is the global ecodig vector ad y k is the etwork-coded payload. The relatio to the source packets x i is give by y k = i=1 g k,ix i, i.e. g k describes the liear combiatio of source packets that produced y k. A ew packet (g,y) ca be obtaied by choosig a local ecodig vector l = (l 1,...,l m ) ad computig (g,y) = m i=1 l i (g i,y i ). I RLNC, l is chose radomly. If ode j does ot have ay packets received yet, e.g. at iitial stage, the the packet (e j,x j ) is trasmitted, where e j is the j-th uit vector. With the global ecodig vectors icluded i the etworkcoded packet, the source packets x i ca be decoded by solvig the system of liear equatios {y k = i=1 g k,ix i } k for received packets (g k,y k ), 1 k m. I case m ad of the vectors g i are liearly idepedet, the decodig matrix formed by these vectors G has rak ad the source packets x i ca be recovered. To guaratee all the received packets to be iovative (which is what packets with liearly idepedet vectors g i are called) with high probability i RLNC, a sufficietly large field F q has to be chose [10]. A dowside of a large field size is the cosiderable overhead i processig, memory cosumptio, ad trasmitted meta data. Operatio over smaller field sizes (e.g. F ) thus seems appealig i a WSN, but the tradeoff betwee smaller probability of iovativeess ad easier processig is ot clear. IV. ALL-TO-ALL BROADCAST PROTOCOLS The protocols cosidered i this work ca be categorized as follow: Coordiatio: Cetralized: A global coordiator is required to coordiate trasmissios, i.e. the coordiator iforms each ode whe to trasmit, receive, re-trasmit (if a eighborig ode fails to receive this odes s trasmissio), or go to sleep mode. These protocols oly serve as compariso cases. Distributed: Each ode makes local decisios wether to trasmit, receive, or go to sleep. Choice of codig coefficiets: Determiistic: The codig coefficiets are precalculated based o a codig scheme with a miimal umber of trasmissios for a give etwork graph. Because we cosider this codig scheme o a wireless topology, erroeous trasmissio have to be take ito accout. If a packet trasmitted by a ode is ot correctly received at the iteded receivers, the seder re-trasmits the same packet util correct receptio. Radom: I cotrast to the determiistic approach, odes radomly chose the coefficiets to be used i the liear combiatios. Quality of service: Reliable: A protocol is cosidered reliable if it assures that the full all-to-all broadcast is carried out. Typically, retrasmissios will be ecessary. Ureliable: If a broadcast is ot guarateed to reach all odes, the protocol is ureliable. As a example, probabilistic forwardig is ureliable as packets are oly retrasmitted with a certai probability; thus, broadcast might die out. We see that by combig the three degrees of freedom give above, i.e. coordiatio, codig coefficiets, ad quality of service, oe ca desig various protocols, tradig-off betwee complexity of a protocol ad its performace. I this work, the followig three combiatios are cosidered. Cetralized, determiistic, ad reliable, hereafter called Determiistic NC. Cetralized, radom, ad reliable, called Radom NC. Distributed, radom, ad ureliable, called Probabilistic NC.

3 As a baselie for compariso, we also cosidered store-adforwardig-based protocols with cetralized ad distributed coordiatios. The Determiistic ad Radom NC protocols are cosidered reliable, which is achieved via the cetral coordiator ad a roud-based trasmissio, i.e. we cotiue the trasmissios util the all-to-all broadcast is completed. As the etwork codig used i the two protocols is differet, i.e. determiistic ad radom, this helps to study the effect of the various codigs, especially the performace of RLNC over differet field sizes. For the Probabilistic NC protocol, we use ideas from probabilistic forwardig, where a ode trasmits a radomly coded packet with probability f. This probability f, also called the forwardig factor, is chose depedig o etwork topology ad required level of reliability of the broadcast. A smaller value of f meas fewer trasmissios which reduces collisios ad saves eergy; however, this may ot assure a full broadcast. As the distributed protocol is easy to implemet i a WSN but suffers from its ureliability, we would like to study the improvemet i reliability of the all-to-all broadcast whe the MAC desig is cosidered. For this, two MAC-related variatios are cosidered. Ackowledgmet (ACK)-based retrasmissio: Here, a stadard ACK-based re-trasmissios is used to assure correct receptio of a trasmitted packet by at least oe ode. For this, a radom eighbor is selected to sed a ACK upo successful receptio, ad this iformatio is icluded i the packet from the seder. If a trasmissio fails, the same packet is thus retrasmitted. MAC Packet-Pull: Suppose the etwork-coded packet is received by some of the eighborig odes. If the same packet is re-trasmitted, the those eighborig odes that correctly received the packet will ot beefit from the re-trasmissio. We propose to use a ewly geerated, radom (ad hopefully iovative) packet for the retrasmissio. The two variatios clearly show the eed for a joit cosideratio of NC ad MAC, i.e. if the MAC is ot aware of the RLNC approach, the iovativeess of the retrasmissios decreases ad thus the potetial of RLNC will ot be fully leveraged. V. THEORETICAL BOUNDS I this sectio, we describe the system, chael, ad eergy cosumptio models; the lower bouds o the eergy cosumptio for traditioal forwardig ad NC are derived ext. A. System Model The circular etwork depicted i Fig. 1 is cosidered i this work. Nodes are placed at equidistat poits o the periphery of a circle. Ulike previous work that cosiders the same topology with a Boolea coectivity model [6], [7], we use a chael model that icludes pathloss, fadig, ad oise. Fig. 1: The circular topology cosistig of = 8. We model the eergy cosumptio i a wireless sesor ode as cosistig of the eergy for trasmissio ad receptio, where receptio also icludes idle listeig. As this is commo for a large class of Wireless Sesor Networks (WSNs), we assume that power draw i trasmissio ad receptio mode is essetially equivalet, i.e. P tx = P rx = P elec. The overall eergy cosumptio per ode for the all-to-all broadcast trasmissio is the defied as E = P elec (T tx + T rx ), (1) where T tx is the overall time spet i trasmit mode ad T rx is the time spet i receptio mode, respectively. B. Trasmissio Bouds To derive lower bouds o the eergy cosumptio for the cetralized protocols preseted i Sectio IV, bouds o the umber of trasmissios per ode are required. I [6], this has already bee doe for a ode commuicatig oly with their two oe-hop eighbors (odes directly adjacet o the circle). It was show that a optimal forwardig scheme i terms of umber of trasmissios requires trasmissios ad a optimal NC scheme requires trasmissios to complete the broadcast i error-free chaels. As we are cosiderig a wireless topology, we do ot have this restrictio o the coectivity. This meas that odes ca receive packets from odes that are further away, eve though a larger distace reduces the probability of correct receptio. Thus, we are iterested i the performace of a optimal NC scheme if packets eve from more distat eighbors are used, e.g. from two-hop eighbors. Eve though we are ot goig to costruct the NC scheme explicitly, the followig theorem states that there must exists such a scheme. Theorem 5.1: There exists a NC-based trasmissio scheme for a two-hop circular etwork with odes, such that a all-to-all broadcast ca be performed i 4 rouds. Proof: To proof the existece of a NC-based scheme that operates i 4 rouds, we eed to show that each trasmissio icreases the rak of the decodig matrix for the four receivig eighbors. This leads to the fact that after 4 rouds each ode has a decodig matrix G of full rak. The exact proof is similar to the oe give i [6, Theorem 4] for the square grid topology. I fact, the proofs oly differ i oe lemma. Lemma 5. is a reformulatio of that statemet

4 Fig. : Argumet of the proof of Lemma 5.. Nodes of A are draw i black ad odes of C are draw white. The four distict eighbors of A are coected via solid lies to A. for the two-hop circular topology; with the correctess of it, this theorem is prove. Lemma 5.: Let G(V,E) be a circular etwork of V = odes where each ode is coected to its oe- ad two-hop eighbors. The, for every set A V with A 4 there exists at least B 4 distict eighbors B V \ A. Proof: Let C be the set V \ A. By assumptio, C 4. Suppose there exists b B which is ot a eighbor of A. The there must be at least four other odes i B, because these are the eighbors of b. For the case of C = 4, this caot be true. I case C > 4, oe has to go alog the mai cycle from ode b to the left ad to the right util odes a left,a right A are reached. Let the path for the right-had walk be (b,b 1,...,b i,a left ). Because C > 4, it must hold that i. So, A has two distict eighbors b i 1 ad b i o this path. For the left-had walk path, the same argumetat holds ad thus there are overall at least four distict eighbors for A. Figure illustrates the argumet of the proof. As the umber of rouds is equivalet to the umber of trasmissios per ode, the umber of trasmissios ca be reduced from to 4 by listeig to the trasmissio of the two-hop eighbors. For a fair compariso, it must be oted that there also exists a more efficiet forwardig scheme for this two-hop topology. This scheme ca be easily described as follows. Basically, each ode trasmits its packet to its four eighbors i the first roud (four iovative receptios for oe trasmissio) ad i subsequet phases oly the right two-hop eighbor forwards the ewly received packet (two iovative receptios for oe trasmissio) to his right oe- ad two-hop eighbor. This leads to overall phases ad thus = 3 trasmissios. TABLE I: Lower boud o the umber of trasmissio per ode for forwardig ad NC o the circular topology. oe-hop listeig Forwardig NC two-hop listeig 3 4 The bouds o the trasmissios per ode for the oe- ad Fig. 3: Lower bouds o the eergy cosumptio of a ode per broadcast for forwardig ad NC over differet topology sizes. two-hop topologies are give i Table I. The receptio phases per ode are ot show i the table as they are the same for all schemes, i.e. a ode is required to receive at least 1 iformatio uits, o matter if forwardig or NC is cosidered. C. Eergy Cosumptio Bouds With the bouds o the umber of trasmissio ad receptios per ode, a lower boud o the eergy cosumptio per ode ca be easily derived. We assume, like for the cetralized protocols of Sectio IV, that odes are oly awake while trasmittig or while receivig a packet of iterest. Equatio (1) requires us to calculate the time spet i trasmit ad receive mode, i.e. T tx ad T rx, respectively. As these values deped o the bitrate R with which packets are trasmitted ad o the packet size p() for odes, we obtai the eergy cosumptio as E = P elec p() (#trasmissios + #receptios). R The packet legth p() cosists of the payload legth l plus additioal meta iformatio to idetify the packet. For the store-ad-forward protocol, we ca store this meta-iformatio i log () bits, i.e. the idetifier of the packet source; for NC this meta iformatio cosists of the global ecodig vector, which requires a overhead of log (q) bits, with q the field-size. Figure 3 shows the eergy cosumptio per ode for the differet optimal schemes ad icreasig topology size. It is assumed that NC is performed over F ad all other parameters are chose i accordace with the simulatio parameters that are listed i Table II. The results show that, for ideal chaels, it is beeficial to liste to the trasmissios of twohop eighbors i terms of eergy cosumptio. Both twohop schemes perform better tha the oe-hop schemes for sufficietly large topology sizes. For the oe-hop scheme ad = 0 odes, the eergy savig by usig NC istead of

5 (a) Oe-hop listeig (b) Two-hop listeig Fig. 4: Average umber of trasmissios per ode to complete the all-to-all broadcast for the store-ad-forward, Determiistic NC, ad Radom NC protocols. SaF is approximately 5 mj; however i the two-hop case this savig reduces to.5 mj. This obviously stems from the fact that oly the umber of trasmissios ca be reduced with a exteded listeig ad the umber of receptios stays the same i a optimal sceario, i.e. still 1 packets have to be received. It has to be oted though that the bouds for two-hop listeig are hardly practical as this would require for oe- ad two-hop eighbors to have practically error-free coectios. I the simulatio results we will see that this boud is ot approached. TABLE II: Simulatio Parameters Parameter Value Topology size 0 Packet payload legth l 51 bits Physical Layer (PHY) bitrate R 0 kbps Power cosumptio P elec 5 mw Thermal oise power N 0 10 dbm Pathloss coefficiet α 3.5 RMS delay spread σ 10 6 s Carrier frequecy f c 900 MHz Doppler shift f d 15 Hz VI. SIMULATION RESULTS Simulatio of the various broadcast protocols is performed usig the OMNet++ discrete evet simulator [11] i combiatio with Chsim, a fadig chael simulator [1]. The simulatio parameters are listed i Table II. The payload (i bits) of trasmitted packets ad the PHY bitrate are chose to be small; this is commo for large classes of sesor etworks ad their applicatios. A static topology is assumed; however, to accout for evirometal movemet, which cotributes to the fadig ature of the chael, a doppler shift of 15 Hz is assumed ad used to simulate the chael s fadig characteristics. To improve readability, cofidece itervals are ot show i the preseted figures, yet they are always withi 5 % of the plotted average value at a cofidece level of 95 %. A. Determiistic ad Radom NC Protocols I this sectio, simulatio results for the cetralized protocols described i Sectio IV are preseted. The metrics of iterest are average umber of trasmissios per ode ad eergy cosumptio, also per ode, util the all-to-all broadcast is completed. Figures 4a ad 4b show the average umber of trasmissios per ode to complete the broadcast for store-ad-forward, Determiistic NC, ad Radom NC protocols over differet field sizes F q. The two figures show the rage of Sigal-to- Noise Ratio (SNR) values i which the theoretical lower boud is achieved. Figure 4a shows the results for oe-hop listeig, i.e. odes oly liste to the trasmissios of directly eighborig odes. We see, for all schemes, that a higher umber of trasmissios is required i the lower SNR regio as trasmissios are more likely to fail; at high SNR values, all schemes approach their theoretical limits, i.e. = 18 for store-ad-forward ad = 10 for the NC-based schemes, respectively. Over the etire SNR rage, Determiistic NC ad Radom NC with F perform best ad worst, respectively. Radom NC with field sizes F 4 ad F 56 perform better tha store-ad-forward, ad this is oticeable whe the SNR is relatively high, i.e. greater tha 15 db. With Radom NC, the performace improves whe a large field size, e.g. F 56, is used; at this field size the performace approaches Determiistic NC for high SNR values. A small field size like F performs worst. Now let us focus o Radom NC oly. Figure 4b compares Radom NC for oe- ad two-hop eighborhood listeig ad over three field sizes. Whe icreasig the eighborhoods to which a ode listes, fewer trasmissios to fiish the all-to-all

6 (a) Oe-hop listeig (b) Two-hop listeig Fig. 5: Eergy cosumptio per ode to complete the all-to-all broadcast for the store-ad-forwardig, Determiistic NC, ad Radom NC. broadcast are required. This improvemet is so sigificat at a smaller field size like F. Furthermore, we see that Radom NC with two-hop listeig coverges to the lower boud of 4 = 5 trasmissios for larger field sizes. Next, let us cosider the average, overall eergy cosumptio per ode to complete the all-to-all broadcast. Figure 5a shows the eergy cosumptio results for oe-hop listeig. Here we otice a differece whe receptio eergy is cosidered. Store-ad-forward performs comparable to Determiistic NC ad eve better tha Radom NC at F 56, which is cotrary to the cojecture that the former is always iferior to the later two. If we compare the eergy cosumptio with Fig. 3 for = 0 odes, we see that the theoretical boud of 4 mj for store-ad-forward is achieved at high SNR values, but 18 mj for NC is ot approached completely. This is best explaied by the fact that for a store-ad-forward trasmissio oly oe ode is listeig, whereas for NC two odes have to receive the same trasmitted packet, makig the first trial more probable to fail ad a secod receptio phase for this ode more likely. The worse performace of Radom NC ad, more specifically, the almost equivalet performace for fields F 4 ad F 56 ca be explaied as follows. For a small field size, the geerally poor performace of RLNC cotributes to the high eergy cosumptio; for large field sizes, the meta data trasmitted i each packet produces a overhead that is ot amortized by the improved performace i umber of trasmissios. For a field F 56 the global ecodig vector, which has to be trasmitted with the payload, has a size of 0 log (56) = 160 bits, compared to oly 0 log () = 0 bits for F. We thus see that at least i terms of eergy efficiecy, the performace of RLNC does ot ecessarily improve with a icreasig field size. This is especially true for applicatios where the payload of a trasmitted packet is relatively small (a commo case i WSNs). I Figure 5b, we see the eergy cosumptio of Radom NC for oe- ad two-hop listeig. I cotrast to cosiderig the trasmissios oly, the gai from a icreased eighborhood is cosiderably reduced due to more receptios. As a cosequece, it ca be difficult to amortize the costs of the higher receptio eergy per trasmittig ode depedig o the chael quality. This ca be see best from the two SNR regimes that are give for all field sizes. E.g. for Radom NC over F it is ot beeficial to cosider two-hop listeig util a SNR of more tha 1 db is available for eighborig odes. For larger field sizes ad realistic SNR regimes, the gai from usig two-hop listeig ca eve be eglected. B. Probabilistic NC Protocol I this sectio, we preset results of the Probabilistic NC protocol. The traditioal probabilistic forwardig, i.e. without NC, is cosidered as a baselie for compariso. Sice i these protocols, the broadcast might die out, our performace metric here is the Packet Delivery Ratio (PDR). It is defied as # successfully decoded source packets PDR =. # source packets Ulike the cetralized-coordiator-based protocols where optimal sleep-schedulig ca be performed, here we assume that odes are awake all the time, which is also a commo assumptio for the traditioal probabilistic forwardig protocol. Moreover, for all preseted results, a mea receive SNR of 0 db betwee eighborig odes is assumed (this traslates ito assumptios about power cotrol or distace). Figure 6a shows the PDR results for differet field sizes. Regardig the MAC-variatios, packet-pull ad ACK are used for the protocols with NC ad probabilistic forwardig, respectively. The results show that the traditioal probabilistic forwardig performs worse tha Probabilistic NC, ad this is true over the etire forwardig factor rage. Withi probabilistic NC, a larger field size of F 56 outperforms the field

7 (a) Differet Field size (b) Protocol extesio Fig. 6: PDR of Probabilistic NC i compariso to Probabilistic Floodig for a mea SNR of 0 db betwee eighborig odes. sizes F ad F 4. Whereas the traditioal forwardig does ot achieve a PDR of oe at a forwardig factor less tha oe, the etwork-codig-based protocols achieve PDR of almost oe for forwardig factors greater tha 0.7. Note that a lower forwardig factor meas fewer trasmissios ad receptios ad hece lower eergy cosumptio. Show i Fig. 6b are the PDR results for probabilistic forwardig (without ad with ACK) ad Probabilistic NC for a field F (without ACK, with ACK, ad with packetpull). The performace for a give forwardig factor, i both probabilistic forwardig ad probabilistic NC protocols, improves whe re-trasmissio is itroduced (as expected). The packet-pull variatio performs best. However, it has to be oted that the improvemet i both variatios comes with a icrease i cotrol overhead, amely trasmittig ACK packets ad performig retrasmissios. VII. CONCLUSION Throughout this paper, we studied the etwork-codig-based all-to-all broadcast, takig the total trasmissios ad overall eergy efficiecy as well as PDR as performace metrics. Traditioal approaches are used as baselie for compariso, ad eergy cosumptio whe a ode trasmits ad receives a packet is cosidered. Theoretical ad simulatio results, usig a circular topology ad slow fadig chaels, were preseted. The results show that Determiistic NC cosumes less eergy as compared to store-ad-forward ad Radom NC. However, store-ad-forward is better tha Radom NC. The performace of NC over various field sizes is studied; results show that eve smaller field sizes (e.g. F or F 4 ) perform well whe two-hop listeig is cosidered. The performace of F 4 is comparable to F 56 ; this is of particular iterest i WSN, where a large field size requires NC operatios that are processig ad memory itesive, which icrease the eergy cosumptio of the wireless odes. Additioally, the protocol variatios at the MAC, amely retrasmissios ad packet-pull, allow iterestig performace gais at a icreased overhead i trasmitted cotrol packets. REFERENCES [1] J. Wieselthier, G. Nguye, ad A. Ephremides, O the costructio of eergy-efficiet broadcast ad multicast trees i wireless etworks, i Nieteeth Aual Joit Coferece of the IEEE Computer ad Commuicatios Societies (INFOCOM), vol., pp , 000. [] J. Wu ad F. Dai, A geeric distributed broadcast scheme i ad hoc wireless etworks, IEEE Trasactios o Computers, vol. 53, pp , October 004. [3] Y. Sasso ad D. C. A. Schiper, Probabilistic broadcast for floodig i wireless mobile ad hoc etworks, tech. rep., Swiss Federal Istitute of Techology (EPFL), 00. [4] P. Kyasaur, R. R. Choudhury, ad I. Gupta, Smart gossip: A adaptive gossip-based broadcastig service for sesor etworks, i IEEE Iteratioal Coferece o Mobile Adhoc ad Sesor Systems (MASS), (Vacouver, BC), pp , 006. [5] D. Nguye, T. Nguye, ad B. Bose, Wireless broadcastig usig etwork codig, Third Workshop o Network Codig, Theory, ad Applicatios, Jauary 007. [6] C. Fragouli, J. Widmer, ad J.-Y. L. Boudec, Efficiet broadcastig usig etwork codig, IEEE/ACM Trasactios o Networkig, 007. [7] E. Fasolo, M. Rossi, J. Widmer, ad M. Zorzi, O mac schedulig ad packet combiatio strategies for practical radom etwork codig, i IEEE Iteratioal Coferece o Commuicatios, pp , Jue 007. [8] E. Fasolo, M. Rossi, J. Widmer, ad M. Zorzi, A proactive etwork codig strategy for pervasive wireless etworkig, i IEEE Global Telecommuicatios Coferecec (GLOBECOM), (Washigto, DC, USA), pp , IEEE, 007. [9] C. Adjih, S. Cho, ad P. Jacquet, Near optimal broadcast with etwork codig i large sesor etworks, i 1st Itl. Workshop o Iformatio Theory for Sesor Networks (WITS), Jue 007. [10] T. Ho, R. Koetter, M. Medard, D. Karger, ad M. Effros, The beefits of codig over routig i a radomized settig, 003. [11] A. V. et al., OMNeT++, discrete evet simulatio system, 006. [1] S. Valeti, ChSim A wireless chael simulator for OMNeT++, 006.