Joint Network Coding for Interfering Wireless Multicast Networks

Joint Netw ork Coding for Interfering W ireless Multicast Networks Jalaluddin Qureshi, Chuan Hen g Foh and Jianfei Cai School of Compu ter Engineering Nanyang T e chnologica l Univ ersity , Singapore jala0001@e.n tu.edu.sg Abstract —Interference in wi reless networks is one of the key-capacity limiting factor . The multicast capacity of an ad- hoc wireless network decreases wit h an increasing nu mber of transmitting and /or receiving nodes withi n a fixed area. Digital Network Coding (DNC) has been shown to improv e the multicast capacity of non-interfering wireless network. Ho wev er r ecently proposed Physical-laye r Network Coding (PNC) and Analog Network Coding (A NC) has shown that it is possibl e to decode an un known packet fr om the collision of two packet, when one of the colliding packet is k nown a priori. T aking advantage of such collision decoding scheme, in thi s paper we propose a Joint Network Coding based Cooperative Retransmission (JNC- CR) scheme, where we sho w that ANC along with DNC can offer a much higher retransmission gain than that attain able through either ANC, DNC or A utomatic Repeat reQuest (ARQ) based retransmission. This scheme can b e applied fo r two wireless multicast groups i nterfering with each other . Because of th e broadcast nature of th e wireless transmission, rece iver s of different mu lticast group can opportunistically listen and cache packets from the in terfering transmitter . These cached packets, along with the packets the recei ver receiv es from i ts transmitter can th en be used for decoding the JNC packet. W e validate the higher retransmission gain performance of JNC with an optimal DNC sch eme, usi ng simulation. I . I N T RO D U C T I O N W ireless multicasting is seen as a bandwidth ef ficient me an of dissemin ating commo n information to multiple receivers. V arious emerging applications such as wireless multi-p layer gaming [1] and multim edia broad cast (currently being stan - dardised b y the IEEE 80 2.11aa working g roup) are based on wireless multicasting . While a previous em pirical stu dy [2] o n the deployment of wireless Access Points (AP) in metropolitan areas has sho wn th at APs are often deployed in a chaotic manner, with several of these APs there fore often competin g with each other for access to the same transmission ch annel. Therefo re with an increa se in wireless mu tlicast data traffic, and an increasing d ensity of wireless nod es within a fixed area competin g for the same chan nel, an efficient solution is needed which ad dresses both the increasing wireless m ulticast bandwidth dem and and th e constra int of wireless interference. Digital n etwork coding (DNC) has b een shown to be one such techniqu e which im prove the capa city of multicast wireless network [3], and its re liability gain [ 4] [5] fo r a non-in terfering network. In DNC, multiple pac kets a re coded together ov er Galois Field GF ( q ) , where q is the field size. If the coding vector is random ly selected f rom the Galois Field, then such DNC sche me is known as Rando m Linear Network Coding (RLNC) [1] scheme. If th is co ding vector is selected deterministically then such DNC scheme is k nown as deterministic network coding, the most comm only used form o f the determin istic network coding is known as XOR- coding [4] [ 5], i.e. de terministic network coding over GF (2) . Recent works h av e sh own thats network co ding can also be per formed at the physical layer . Such network co ding perfor med at p hysical lay er , known as Physical-laye r Network Coding (PNC) [6] and Analog Network Coding (ANC) [7] can improve th e throug hput order for multi-pair unica st tran s- mission in ad-hoc wireless network [8]. I n PNC/ANC, a node can deco de the unknown packet c 2 from th e collided packet c 1 ⊙ c 2 1 , pr ovided that the node has packet c 1 a pr iori. The key difference b etween PNC and ANC is that, PNC req uires the colliding packets to collide in a perfectly synchronised manner , whereas in ANC, the collid ing packet need n ot necessarily collide perfectly synch ronised, which therefore makes ANC a more practical cod ing scheme for imp lementation . The refore in our implemen tation we use the ANC scheme. While a significant amo unt of work has b een done to characterise the throug hput benefits of DNC [3] [ 4] and ANC [ 8] [9] in isolation , to the be st o f our kn owledge there has been no work do ne so far which character ises the joint benefits o f DNC and ANC. Further, so far , ANC application s has only been limited for simp le relay networks. T herefor e our cu rrent work is also the first work o f its kind extending the application of ANC beyon d relay networks. In this paper w e d emonstrate the throug hput gain by jointly using ANC and DNC (deterministic XOR-coding ) to transmit packets to rec ei vers in a single-hop setting wh ere two wir eless multicast grou p interfere with each other, which w e call Joint Network Coding using Coo perative Retransmission (JNC-CR). The rest of the paper is organ sied as follow . W e presen t an overview o f related works in Section II. In Section III, we characterise the system model of the network. W e then present the JNC-CR proto col design, alo ng with an illu strating example in Sectio n IV, followed by simulation results in Section V and summar y of ou r work in Sectio n VI. I I . R E L A T E D W O R K Our cu rrent work is pr imarily an extension of our p revious work, Cooperative Retransmission (CR) throu gh collission [9]. 1 W e use the ⊙ notation to denote the collisi on operation, and ⊕ to denote XOR-coding operation. Fig. 1. T wo interfe ring multic ast netw ork, with N=3 and M=1. While in our previous work we had shown the retra nsmission gains of utilising ANC over IE EE 802 .11 ARQ (Au tomatic Repeat Request) for 2 un icast transmissions interfe ring with each oth er , in our curren t work, we demonstra te the retrans- mission gains of JNC-CR over an o ptimal DNC scheme for 2 multicast transmissions interf ering with eac h other . A. DNC Retransmission scheme A bulk of previous work s [1] [4] [5] [10] [14] on net- work cod ing based retransmission sch emes have been limited tow ards using DNC, comparin g th e perfo rmance g ain of DNC over ARQ retr ansmission sche mes. Advantages in such coding g ains co me f rom the in depende nt Bernoulli packet loss model in wir eless networks, as experimen tally shown [11]. In [ 11] the authors showed that wh ile the average p acket loss probab ility of 2 co-located id entical receivers are similar, the receivers’ packet loss burstiness may h owe ver differ und er similar cond itions. Hence, instantan eous packet loss for 2 such receivers r eceiving transmission from the same transmitter show no correlatio n pattern . The refore f or a tran smitter AP 1 multicasting packet c 1 and c 2 to receivers R 1 and R 2 , c 1 may be receiv ed by R 1 only while c 2 may b e r eceiv ed by R 2 only , howe ver unlike ARQ retransmission sch eme where both the packets are retransmitted separ ately in 2 different time slots, in a DNC ba sed retransmission schem e the packets c 1 and c 2 are XOR-coded as c 1 ⊕ c 2 and retran smitted in 1 time slot. Upon reception of this coded packet both R 1 and R 2 can decod e the coded packet using the packet th ey had received earlier . Therefo re DNC reduces the tim e slots n eeded to retr ansmit the lost p ackets from 2 time slots to 1 time slots fo r this exam ple. Our pr evious work, CR [9] was the first w ork of its kind to improve retransmission g ain u sing ANC rather th an DNC. CR is implem ented by two interfe ring APs using the co mmon superimpo sed acknowledgement inf ormation , tr ansmitted by the receivers in the interfer ence regio n. B. Sup erimposed Acknowledgement Superimp osed acknowledgemen t [12] [13] is an A CK- thinning schem e fo r multicast transmission. In a superimp osed acknowledgement each receiver in the multicast network trans- mits a uniq ue A CK packet, which is embed ded with a uniqu e predefined bitstream patterns, such that the simultaneous col- lision of these packets will resu lt in a different co llided p acket for dif ferent perm utation of A CK packets colliding to gether . Therefo re all receiv ers which ha ve received the packet transmit their A CK packet in the same time slot. This collided A CK packet can th en be used to de termine which set of r eceiv ers have receiv ed the da ta p acket. Because of the b roadcast n ature of th ese co llided ACK packet by r eceiv ers in the interf erence region, b oth the APs have the pac ket recep tion status of these receivers. C. Cooperative Retransmission In a CR [9] scheme, 2 interf ering APs retransmit selected lost packets simultan eously , resulting in a collided pa cket, which is then decod ed by the recei vers using ANC and packets oppor tunistically overhear d fro m the interfering AP . Such cooper ati ve retransmission scheme is implem ented without any comp lex handshak ing or scheduling p rocedu re. Consider , for example unicast transmissions AP 1 ∼ R 1 and AP 2 ∼ R 2 , interferrin g with each other and R 1 and R 2 located such that both th e recei vers can hear transmission f rom AP 1 and AP 2 . Because of the broadcast nature of wire less transmission, it is therefor e p ossible that R 1 may overhear (also k nown as op portun istic lis tening) packet destined fo r R 2 and v ice- versa. W e use supe rimposed ackn owledgement in such a CR scheme, whe rein both R 1 and R 2 simultaneou sly transmit A CK packet for transmission received b y both AP 1 and AP 2 . Therefo re b oth the APs are aware of p acket reception statu s of R 1 and R 2 . I n such a network p acket c 1 transmitted b y AP 1 destined f or R 1 can be overheard by R 2 but no t by R 1 , whereas packet c 2 transmitted b y AP 2 for R 2 can be overheard by R 1 but n ot by R 2 . Because of the sup erimposed acknowledgement scheme, R 2 will transmit A CK pa cket for c 1 , and R 1 will transmit A CK pa cket for c 2 . AP 1 and AP 2 can then simultaneously retransmit c 1 and c 2 in the same time slot which re sults in the collided packet c 1 ⊙ c 2 . Each of the receiver can then use th e pr eviously , opportunistically receiv ed packet to decod e c 1 ⊙ c 2 using ANC. Th is th erefore red uces the total nu mber of retr ansmissions needed from 2 to 1 for this example. In th is work we f urther exp and on the benefits of b oth ANC an d DNC, and show that using JNC-CR offers a much higher retransmission gain . I I I . S Y S T E M M O D E L Consider two APs, AP 1 and AP 2 multicasting packets to re- ceiv ers in their network. Let d AP denote the distance between the two APs, an d r t denote th e transmission range of each AP , characterized as an omnid irectional radio p ropag ation, with both the APs following the un iform power assignmen t scheme, i.e. transmitting at an equal transmission power , and at the same transmission rate. Conside r that the interferin g APs are overlapped such that d AP < 2 r t . Each AP associates with N clien t stations, which are unifor mly distributed within the transmission ran ge of the AP . A verag e packet loss prob ability p ij for transmissions from AP i to receiver R j follows an in - depend ent Berno ulli packet loss mo del [11], wher e 1 ≤ i ≤ 2 and 1 ≤ j ≤ 2 N . Recei vers 1 ≤ j ≤ N are connected to AP 1 and receiv ers N < j ≤ 2 N are con nected to AP 2 . The total number of nodes in the overlap region is g iv en as 2 M , where 1 ≤ M ≤ N . W e assume uniform packet loss p for both th e network, such that p ij = p, ∀ i, j . The p robability that a receiver in the non -interfer ence re gion corre ctly receiv es a packet is giv en as (1 − p ) , whe reas the probability that a receiver in the in terference region cor rectly receives a collide d packet is g i ven as (1 − p ) 2 [9], as both the colliding packet need to reach correctly at the receiver . Packet batch size f or transmissions by AP i is deno ted as B i , for simplicity we assume that B 1 = B 2 = B . F or multimed ia applications such as video streaming and file sharing, B is usually a large value. W e assume a reliable feedback mechanism, this is consistent with the previous assumption s u sed in similar w orks [ 4] [5] [1 0]. Further we also assum e a reliable su perimpo sed acknowledge- ment feedba ck m echanism in ou r protoco l design , consistent with our previous work [9]. A. P erformance overview In ou r perfo rmance e valuation, we com pare JNC-CR w ith an op timal DNC scheme. Howev er since it is a NP-hard problem to dec ide whether an o ptimal num ber of tra nsmission can be achieved for a given field GF ( q ) [1 4], we therefore assume an infinitely large value of q for DNC. W ithout loss of ambiguity we ignore the large co ding overhead of B l og 2 ( q ) bits for DNC cor respond ing to an infinitely large value o f q . The expected nu mber of transmission s (and h ence retransmissions) n eeded to transmit B packets to N receivers using DNC has b een calculated in Equation 13 o f [15]. W e therefor e use resu lt from [15], with q = ∞ as a lower b ound for DNC, for specified values o f B and N . Packet overhead of a XOR co ded p acket is given as N l og 2 ( q ) , where q = 2 . I mplemen ting ANC has a total packet overhead of 1 28 bits [7]. Ther efore the total packet overhead of a JNC packet is given as (128 + 2 N ) bits. I V . J N C C R P ROT O C O L D E S I G N In JNC, pa ckets are encoded a t two level. In the first instance, each AP XOR selected d ata packets bit-by-b it, and then both the APs simu ltaneously transmit the XO R coded packet, which results in ANC of the XOR co ded pa ckets. When a receiver r eceiv es a JNC packet, it first perfo rms ANC d ecoding on th e JNC packet to retrieve the XOR-cod ed packets. On ce a receiver decodes the collided packet it then retrieves the XOR-coded packet, on wh ich it then perfo rms XOR decodin g to retrieve the data p ackets. The APs make XOR coding decision usin g BENEFIT coding algorithm [5], and ANC co ding decision using a simple ANC-CR coding decision as shown in T able II. BENE FIT is a memory based h euristic codin g algorithm which makes coding decision such th at every receiver receives an innovate p acket on the reception of the coded packet. An innovati ve p acket, is a packet which the r eceiv er can no t generate using the set of packets it a lready has. A. Illustrating e xample T ABLE I T R A N S M I S S I O N M A T R I X E X A M P L E c 1 c 2 c 3 c 4 R 1 1 0 0 0 R 2 0 1 - - R 3 0 0 0 1 R 4 - - 1 0 Consider for illustratio n a simp le examp le where AP 1 is multicasting p ackets c 1 and c 2 to R 1 and R 2 , wh ile AP 2 is multicasting packets c 3 and c 4 to R 3 and R 4 . R 1 and R 3 are located in th e inte rference region , whereas R 2 and R 4 are lo cated in the no n-interf erence region . The recep tion status of each packet is given in T ab le I, wh ere ‘1’ represen ts that the packet has not b een received by the correspond ing receiver , ‘0’ represents that t he packet has been recei ved, wh ile ‘-’ deno tes that the receiver is not within th e tra nsmission range of the AP tran smitting that packet. In an ARQ based retransmission scheme, AP 1 and AP 2 will retransmit these lost packets in different time slots, therefore requirin g a to tal of 4 tim e slots to retransmit all the 4 pac kets. In a DNC b ased scheme, AP 1 and AP 2 transmit the en coded p acket c 1 ⊕ c 2 and c 3 ⊕ c 4 respectively which the rec eiv ers can decod e using the packet each receiver alre ady h as. Therefore a DNC based retransmission scheme r equires a to tal of 2 time slots. JNC further im proves on the retransmission gain by allowing both the APs to simultaneou sly retransmit c 1 ⊕ c 2 and c 3 ⊕ c 4 , which results in the 2-lay er encode d packet ( c 1 ⊕ c 2 ) ⊙ ( c 3 ⊕ c 4 ) received at R 1 and R 3 , while receiver R 2 and R 4 receive the XOR-coded packet c 1 ⊕ c 2 and c 3 ⊕ c 4 respectively , as these receivers do not fall in the interference region . Sin ce R 1 has packet c 3 and c 4 , it can use these packets to generate c 3 ⊕ c 4 and d ecode ( c 1 ⊕ c 2 ) ⊙ ( c 3 ⊕ c 4 ) using ANC decoding , it then perfor ms XOR decoding to retrieve p acket c 1 from c 1 ⊕ c 2 . Therefo re in a JNC based retransmission scheme, a total of 1 time slots ar e need ed to retransm it the lost p acket. Theref ore for this simple examp le JNC provides a re transmission gain of 4 over ARQ, and 2 over DNC. B. Non-Coo perative Collision Coding Each AP is on ly aw are of the p acket reception status of th e receivers located within its transmission rang e. In o ur model, both the APs start the retransmission phase after transmitting B pa ckets u sing IEEE 802.1 1 b ased Carrier Sense Multiple Access Collision A voidance ( CSMA/CA). The retransmission process take place in 2 stages, the first stage is non-coo perative packet tran smission, whereas the second stage is coope rativ e packet transmission . In the first stage, since the interferin g AP is not aware o f the packet r eception status of r eceiv ers not within its tr ansmission range, both th e AP make indep endent T ABLE II A N C - C R C O D I N G A L G O R I T H M , P S E U D O C O D E c ni ← − Coded packet generated by AP i n i ← − Number of recei vers for which c ni is an innov ati ve packe t f or (m=1; m ≤ 2M; m++) if (node m can perform collision decoding of c n 1 ⊙ c n 2 ) colli sion decodi ng++ JNC benefit = coll ision decoding · (1 − p ) 2 AP i benefit = n i · (1 − p ) , ∀ i XOR benefit = max( AP 1 benefit, AP 2 benefit) if (JNC benefit > XOR benefit) Simultane ously transmit code d packet, collision-codi ng else AP with higher XOR benefit transmits XOR-coded packet, colli sion-free DNC cod ing decisions. Receivers in the n on-inter ference r e- gion receive a n XOR coded packet, whereas receiv ers in the interferen ce region r eceiv e a collided XOR code d packet. Howe ver since each of the AP make such co ding algo rithm decisions independ ently , receivers in th e interference r egion may not n ecessarily benefit from such transmissions. This is because, rece i vers in the n on-inter ference region on ly need to perfor m XOR deco ding, whereas receivers in th e interf erence region need to perfor m b oth ANC an d XOR decod ing. So while each AP can make co ding decision such that the co ded packet can be XOR d ecoded by every receiver in th e multicast group of th at AP , recei vers in the interfe rence region m ay not necessarily b e able to p erform A NC decoding of the collided packet from th e interfer ing AP . In the non-co operative collision retransmission ph ase re- ceiv ers in th e interference r egion can therefo re pe rform co lli- sion decoding opportun istically . Let k represen t the car dinality of the XOR-cod ed packet, BENEFIT c oding algo rithm [5] is designed such that 1 ≤ k ≤ N . The prob ability that a receiver can o pportun istically perf orm collision dec oding is giv en as the pr oduct of the prob ability it receives a co rrect collided packet, and th e pr obability that it h as alread y op - portun istically overhear d the k packets from the interfering AP p reviously , (1 − p ) 2+ k . Ther efore given th e high er packet reception prob ability for r eceiv ers in the non-interf erence region, re ceiv ers in the n on-interf erence region recover the lost p ackets much ear lier than the receiv ers in the interf erence region. Once a ll the recei vers in the non-in terferenc e region have corr ectly r eceived the lost packets, the APs can then perfor m Cooperative Collision Coding . C. Coop erative Collision Coding In the Cooperative Collision p hase, o nly th e receivers in the interferen ce region need to recover the lost packets. Because of the br oadcast nature of superimp osed ack nowledgement, both the APs are aware of all the packet reception statu s of all the receivers in th e interferenc e region, and sinc e both the APs run th e sam e ANC-CR coding algorithm , both th e APs are also aware of the coding decision the in terfering AP makes. A pseud ocode of the ANC-CR algo rithm is g i ven in T able II . 0 0.05 0.1 0.15 0.2 0.25 0 2 4 6 8 10 12 14 16 18 20 Packet loss probability, p Number of retransmissions DNC, lower bound JNC−CR, M=2 JNC−CR, M=5 Fig. 2. A verage number of retransmission under dif ferent p va lues, for N=5 and B=20. 1 2 3 4 5 6 7 8 9 10 6 6.5 7 7.5 8 8.5 9 9.5 10 Number of nodes in the overlap region, M Number of retransmissions DNC, lower bound JNC−CR Fig. 3. A verage number of retran smission under dif feren t M v alues, for N=10, p=0.1 and B=20. Both the APs simultan eously run the sam e coding algorith m, and weig h in the ben efit o f simu ltaneously tran smitting the coded pa cket. If the benefit of simultan eously transmittin g the coded packet is greater than the ben efit of transmitting either of the coded packet withou t collision , then both th e APs tran smit their coded packet simultaneously , which result in the c ollision of the co ded packet. If howev er the benefit of transmitting an XOR from either AP is higher th an JNC-CR, the n the AP with higher tr ansmission benefit tr ansmit the p acket. As we had shown in [9] such coo perative re transmission can be implemented without any complex handsh aking or scheduling proced ures. V . S I M U LT A T I O N Packet decod ing u sing ANC has been successfully demon - strated on a test bed in [7]. Th erefore we can assume that 2 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 Network size, N Number of retransmissions DNC, lower bound JNC−CR, M:N=1:2 JNC−CR, M:N=1:1 Fig. 4. A verage number of retransmission under differen t N val ues, for p=0.1 and B=20. ANC is a practically app licable techn ique. For th e pr oposed collision based cooperative retran smission, we construct a C++ discrete-time simulato r with the system m odel described in Section III. Fig. 2 shows the average number o f retransmission for different p . As p increases th e number of retransmis- sion a lso increases for both DNC and JNC-CR, co nsistent with [4] [10] [15]. JNC-CR shows retransmission gain ov er DNC. The hig her gain for d ecreasing M in Fig. 2 an d 3 co mes from the coope rativ e collision co ding stage. The probability that the receiver in th e interfer ence region will be a ble to perfor m ANC-decoding is given as (1 − p ) 2+ k , for co operative collision co ding, 1 ≤ k ≤ M . Therefore for M = 2 m ore packets get ANC-coded compare d to M = 5 , which improves the retran smission gain. For Fig. 3, a su dden dip in the num ber of r etransmission occurs fo r M = 1 0 , bec ause all the packets are th en retransmitted in a cooperative collision coding, and results in a more efficient AN C coding decision. Fig. 4 sho ws th at the average nu mber of retran smission increases logarith mically as the n etwork size increases. Fig. 5 shows th at the av erage number of retransmissions decreases logaritmically for increasing packet b atch size. Howe ver using a large packet batch size will incre ase transmission latency . The r esults o f Fig. 4 and 5 are con sistent with [4] [10] [15]. For both these figures, JNC-CR sho ws better retransmission bandwidth than DNC. V I . C O N C L U S I O N In this work we ha ve demonstrated the retr ansmission bandwidth g ain of JNC-CR over DNC. 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