BROADBAND and wireless networks are currently the

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1 64 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005 A Nw Hybrid ARQ-FEC Schm for Wirlss ATM Ntworks J. M. C. Brito and I. S. Bonatti Abstract - Wird ATM (Asynchronous Transfr Mod) ntworks ar dsignd taking into account an optical link in th physical layr. Th main problm to implmnt a wirlss ATM ntwork is th fact that its radio link bit rror rat is high and variabl, dmanding th us of an additional rror control mchanism. Th usual tchniqus for rror control ar ARQ (Automatic Rpat Rqust) and FEC (Forward Error Corrction). ARQ works bttr than FEC if th channl bit rror rat is low, and is wors if it is high, thus indicating that hybrid ARQ-FEC tchniqus can improv th radio link prformanc. A nw hybrid ARQ-FEC schm with multipl FEC stats is proposd in this papr. Th prformanc of th proposd schm is compard with non-adaptiv ARQ and FEC schms, which hav similar complxitis, and with an idal adaptiv FEC schm. It is shown that th proposd schm works bttr than th nonadaptiv schms, and that th hybrid and th idal adaptiv FEC schms hav similar prformancs. Morovr, th hybrid schm dos not rquir an stimat of th bit rror rat in th channl, lading to a lss complx implmntation. Indx Trms: Wirlss ATM Ntworks, Error Control, Hybrid ARQ-FEC Schms. I. INTRODUCTION BROADBAND and wirlss ntworks ar currntly th two major drivrs in th tlcommunication industry. Asynchronous Transfr Mod (ATM) is th intrnationally accptd mod for broadband ntworks and has bn usd by svral tlcommunications oprators to implmnt th backbon of thir ntworks. Wirlss ATM combins th advantags of th traditional wirlss ntworks with th flxibl bandwidth allocation and guarantd quality of srvic providd by th wird ATM ntworks. Morovr, using ATM in th accss ntworks yilds th intgration of ths ntworks to th backbon of th oprators. Raychaudhuri and Wilson [] wr th first to propos th wirlss ATM concpt, in 992. Th potntial scnarios to us wirlss ATM ntworks ar local ara ntworks, rsidntial ntworks and accss ntworks (with fixd or mobil trminals). J. M. C. Brito is with National Institut of Tlcommunications,.O. Box 05, S. Rita do Sapucaí, MG, Brazil mail: brito@inatl.br I. S. Bonatti is with School of Elctrical & Computr Enginring, Univrsity of Campinas, DT FEEC UNICAM C , Campinas, S, Brazil mail: ivanil@dt.f.unicamp.br Svral rsarch projcts hav bn proposd in th last fw yars, such as: th WATMnt projct, dvlopd by NEC for prsonal multimdia ntworks in a micro-cllular nvironmnt with fixd and mobil trminals [28]; th Magic Wand (Wirlss ATM Ntwork Dmonstrator) projct, proposd by Europan Union ACTS (Advancd Communications Tchnologis and Srvics), for indoor nvironmnt with mobil trminals [2]; th BAHAMA projct proposd by Bll Laboratoris, for ad hoc local ara ntworks with mobil trminals [3]; th SWAN (Samlss Wirlss ATM Ntworks) dvlopd by Bll Laboratoris for indoor ntworks with picocllular nvironmnt and mobil trminals [4]; th ATMmobil projct, proposd by a pool of univrsitis and ntrpriss in Grmany, considring four diffrnt scnarios: local ara ntworks, mobil broadband cllular ntworks, rsidntial ntworks, and fixd accss ntworks [5]. In gnral, th goal of wirlss ATM ntworks is to provid th sam charactristics of th wird ATM ntworks, in a transparnt way, through a wirlss link, for fixd or mobil trminals. Thus, wirlss ATM ntworks must intgrat svral kinds of traffic with guarantd quality of srvic. Th main problms to mak th wirlss ATM ntworks fasibl ar rlatd to th following rsarch aras [3][6][7]: mobility managmnt, multipl accss protocol and rror control in th wirlss link. Th noisy and tim-varying nvironmnt of radio links is a problm for wirlss ATM ntworks bcaus wird ATM ntworks wr dsignd for an optical mdium, which has a vry low bit rror rat. A high bit rror rat lads to unaccptabl valus for th paramtrs Cll Error Ratio (CER) and Cll Loss Ratio (CLR), rquiring additional mchanisms for rror control in th radio link. Th traditional schms for rror control ar Forward Error Corrction (FEC) and Automatic Rpat Rqust (ARQ). FEC or ARQ in th wirlss link dcrass th rsidual bit rror rat (i.., th bit rror rat considring th rror control mchanism), howvr th dlay in transmitting a cll is incrasd. Th throughput, du to ovrhad of th rror control mchanisms, is also dcrasd. Thrfor, th paramtrs CTD (Cll Transfr Dlay) and CDV (Cll Dlay Variation) ar affctd by th rror control mchanism. Thr ar two diffrnt approachs to implmnt th rror control mchanism: a non-adaptiv approach, which is simplr and lss fficint, and an adaptiv approach, which is mor complx but can maximiz th prformanc. In non-adaptiv schms, th numbr of parity bits in th cods usd in th FEC or ARQ ar calculatd for th highst bit rror rat in th radio link in ordr to satisfy th targt QoS (Quality of Srvic) paramtrs. In adaptiv schms, th numbr of ISSN /$20.00 c 2005 SBrT/IEEE

2 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, parity bits in th ARQ and FEC cods is function of th bit rror rat in th channl, rquiring a good stimat of th bit rror rat in th wirlss link. Morovr, th ncodr and dcodr must b abl to implmnt cods with diffrnt rats. Svral solutions to rror control in wirlss ATM ntworks hav bn proposd in th litratur. Th tchniqus usd in ths solutions includ using ARQ limiting th numbr of rtransmissions for dlay snsitiv applications [2], FEC (with or without concatnatd cods) or a hybrid typ ARQ-FEC schm [][4][5][8]-[2], FEC cod to protct th hadr and anothr on to protct th payload [3][4], adaptiv FEC cods with or without ARQ [3][5]-[8] and FEC cod (mor powrful than th cod spcifid to th Hadr Error Control), adaptiv or not, to protct th hadr [9]. Th most usd ARQ protocols ar th Go-Back-N (GBN- ARQ) [2][8] and th Slctiv Rpat (SR-ARQ) [][4][8] (or som variant). Th most usd FEC cods ar th BCH (Bos, Chaudhuri and Hocqunghm) [][8][0][3][4][5][9] and th Rd-Solomon [5][8][]-[3][7]. In th solutions using concatnatd cods, th most common combination is a Rd- Solomon or BCH cod with a convolutional cod [0]-[2]. A nw hybrid ARQ-FEC schm that has multipl FEC stats is proposd in this papr. Th prformanc of th proposd schm is compard with non-adaptiv FEC and ARQ schms (all having similar complxity). It is also compard with an idal adaptiv schm, usd as rfrnc. Th proposd schm is provd to work bttr than th nonadaptiv schms and it has similar prformanc whn compard with th idal adaptiv FEC schm. Th rmindr of this papr is organizd as follow: th rfrnc scnario usd in th analysis is prsntd in Sction 2; in Sction 3, th critrion to dfin th cods is prsntd; in Sction 4, th non-adaptiv ARQ and FEC schms and an idal FEC schm ar analyzd; in Sction 5, th schm proposd is prsntd and its prformanc is computd; conclusions ar prsntd in Sction 6; a summary of th notations usd in th txt is prsntd in th Appndix. II. REFERENCE SCENARIO Th rfrnc scnario is composd of on wirlss and L optical links. In th wirlss link, svral trminals shar a radio-bas station using a multipl accss protocol. Th rror control mchanism and th multipl accss protocol ar implmntd in a Data Link Layr (usually comprising a Data Link Control Layr and Multipl Accss Control Sub-Layrs) locatd btwn th ATM and hysical Layrs. Th main multipl accss tchniqu usd in th wirlss ATM ntworks rportd in th litratur is a TDMA/TDD (Tim Division Multipl Accss / Tim Division Duplx) tchniqu [][2][8][5]. A DAMA-TDMA (Dmand Allocation Multipl Accss Tim Division Multipl Accss) multipl accss is considrd in this papr. In this schm, th tim is dividd into frams, ach fram bing dividd in downlink and uplink priods. In th downlink priod, th basstation transmits to trminals using Tim Division Multiplxing (TDM). Th uplink priod is dividd in a contntion priod and a transmission priod. Th trminals snd rqusts in th contntion priod using a random multipl accss (lik Slottd-Aloha) and, whn allowd, transmit data in th transmission priod using TDMA. Th transmission priod is dividd into slots, ach transmitting on ATM cll. An ATM cll consists of a 40-bit hadr and a 384-bit information fild. Th hadr includs an 8-bit hadr rror control (HEC) fild. Th HEC has two opration mods: corrction mod and dtction mod. In th corrction mod th HEC can corrct -bit rrors. Th ATM adaptation layr (AAL) considrd for data transmission is th AAL5 [27]. Intrlaving is usd to randomiz channl burst rrors in such way that a mmorylss channl modl can b considrd. Th frams and thir priods in th wirlss link ar illustratd in Fig.. Downlink priod Fram Uplink priod Contntion priod Slot Transmission priod Fig.. Fram structur in th wirlss link. Downlink and uplink priods ar considrd to hav th sam fixd siz slots. Th siz of th slots in th rsrvation priod can b rprsntd as a fraction of th siz of th slots in th transmission priod. Thus, th fram tim can b computd by Vu τ + Vd τ + α Vu τ V τ Tq = = () Rs Rs whr V u and V d rprsnt th numbr of slots in th uplink and downlink priods, rspctivly; α rprsnts th siz of th slots in th rsrvation priod as a fraction of th slots in th transmission priod; R s is th bit rat in th wirlss link; τ is th total numbr of bits in ach transmission slot in th uplink priod, and V = V u + V d + αv u. Th paramtr τ dpnds on th rror control tchniqu usd in th wirlss link. Th tim dlays that affct all th systms in th sam way hav not bn considrd in th analysis. Thrfor, th tim to mak a rsrvation, th ovrhads of th MAC (Mdium Accss Control) protocol, th wird ntwork dlays (lik quuing and switching tim dlays), and th tim spnt to transmit an acknowldgmnt from th rcivr to th transmittr ar not takn into account. III. DEFINING THE ARQ AND FEC CODES Th critrion usd to dfin th ARQ and FEC cods is to mak th wirlss link work lik an optical link, concrning th bit rror charactristic. This is quivalnt to say that th probability of th wirlss link to dlivr a corrct cll to th optical link is qual or gratr than th probability of on optical link to dlivr a corrct cll to th nxt optical link. This critrion is in agrmnt with th analysis prsntd by Cain and McGrgor in [].

3 66 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005 Considring that th HEC is in th corrction mod, th probability of an optical link to hand a corrct cll to th nxt optical link is th probability of th cll to contain no rrors in th payload fild and to contain at most -bit rrors in th hadr. This probability is givn by = ( p ) 384 ( ) ( ) (2) p p 39 p cco whr p is th bit rror rat. Th valu of th paramtr p was considrd as 0-8 for optical links. A. CHOICE OF ARQ CODES In ARQ tchniqus, th clls ar individually protctd by an (n,k) block cod, bing k th numbr of information bits, n th total numbr of bits and (n-k) th numbr of parity bits. On cll arriving in th bas station can contain no rrors with probability c, it can contain a dtctabl rror with probability, or it can contain an undtctabl rror with probability u. Th probability of a cll to lav th radio link without rror is givn by [25] k c c cca = c + c = = (3) k = c + u Considring that th HEC of th ATM hadr is not usd in th rror control mchanism in th wirlss link, th probability c is computd by = p (4) c n ( ) To satisfy th critrion, th maximum prmittd valu for u is givn by u c ( ) cco Th minimum numbr of parity bits in th ARQ cods can b computd using an itrativ algorithm and th Korzhik s bound, givn by th xprssion [20] u 2 cco [ n ( n k ) ( p) B. CHOICE OF THE FEC CODES In th FEC tchniqu, an (n,k) block cod is usd to corrct rrors in ach cll. Not considring th HEC influnc, th probability of th dcodr to dlivr a corrct cll to th optical link is givn by t n ( p) i n i ccf = p (7) i= 0 i Th paramtr t, which is th rror corrction capacity of th FEC cod, is a function of th n k valu and of th cod usd. To comput th minimum numbr of parity bits in FEC cods, w hav usd an itrativ algorithm and th lotkin s bound, givn by [2] ( d min ) log 2 min n k 2 d whr d min is th minimum distanc of th cod. IV. COMARING ARQ AND FEC ERFORMANCES Th tim dlay to transmit a DU (rotocol Data Unit), composd of Z ATM clls, was adoptd as th paramtr to compar th prformanc of ARQ and FEC schms. Th man tim to transmit a corrct DU in a systm using Stop-and-Wait ARQ (SW-ARQ) protocol in th wirlss link, not considring th tim to transmit th acknowldgmnt from dstination to th sourc trminal, can b calculatd by [22] Z n 424L T swa = Tq + + ξ a + γ (9) c Rs Ro whr T q is th fram tim, computd by (), ξ a is th dcoding dlay of th ARQ cod, R s and R o ar th bit rat in th wirlss and optical links, rspctivly, and γ is th man numbr of transmissions ndd to rciv a corrct DU, considring rtransmission in th AAL layr. Th paramtr γ can b calculatd by i γ = i pc ( pc ) = (0) i= whr pc, th probability to rciv a corrct DU, is givn by ( L+) Z pc = cco () For a FEC systm, in which on cll is transmittd on ach slot, th man tim to transmit a corrct DU is givn by [22] n 424 L T fc = ( Z ) Tq ξ f γ (2) Rs Ro (5) whr ξ f is th dcoding dlay of th FEC cod. As svral paramtrs affct both tchniqus in th sam way, on can simplify th computation dfining a prformanc factor, δ, as th ratio btwn th tim dlay to transmit a DU in th FEC schm and th sam dlay in th ARQ schm. Considring that th bit rat in th wirlss link and optical ] (6) links ar th sam and that th cods ar implmntd in hardwar (th dcoding dlays ar ngligibl), th prformanc factor comparing Stop-and-Wait ARQ and FEC is givn by V Z n + n + 424L (8) ( ) f δ sw = (3) Z V nsw + nsw + 424L c whr th sub-indx f and sw ar includd in som paramtrs to dtrmin if th paramtr is rlatd to th FEC or SW- ARQ tchniqu, rspctivly. Th paramtrs L, V and Z hav ngligibl influnc in th prformanc factor valu. Th total numbr of bits in th FEC and ARQ cods, paramtrs n f and n sw, rspctivly, ar computd to achiv th critrion prsntd in Sction 3. For non-adaptiv implmntation, n f and n sw ar computd considring th highst rror rat in th channl, rsulting in n f = 487 bits and n sw = 449 bits. Fig. 2 shows th prformanc factor δ as a function of th bit rror rat in th wirlss channl for non-adaptiv systm f pc

4 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, considring L = 3, V = 40, and Z = 5 or Z = 000. Th ARQ tchniqu has bttr prformanc than th FEC tchniqu if th bit rror rat is low and wors if th bit rror rat is high. Both tchniqus hav th sam prformanc for p =.8 x rformanc factor 0.5 rformanc factor SW-ARQ GBN-ARQ SR-ARQ Fig. 3. rformanc factor comparing ARQ and FEC schms, considring adaptiv cods Z = 5 Z = 000 Fig. 2. rformanc factor comparing SW-ARQ and FEC schms. Whn comparing th Go-Back-N and Slctiv-Rpat ARQ protocols with th FEC schm, th conclusion is similar to th conclusion obtaind for th Stop-and-Wait protocol. Th ARQ schm prforms bttr than th FEC schm if th bit rror rat is low and wors if th bit rror rat is high. A dtaild comparison among ths tchniqus can b found in [22][23][24]. For an adaptiv implmntation, th paramtrs n f and n sw ar calculatd as a function of th bit rror rat in th channl. Fig. 3 shows th prformanc factor comparing ARQ tchniqus and th FEC tchniqu considring an idal adaptiv implmntation, for which th stimat of th bit rror rat in th channl can b obtaind without additional ovrhad. Th paramtrs L, V and Z wr fixd to th following valus: L = 3, V = 40 and Z = 00. For th Go- Back-N and Slctiv-Rpat protocols, N was st as N = 5 [22]. With idal adaptiv implmntation, th FEC tchniqu works bttr than th ARQ tchniqus in th whol rang of bit rror rat considrd. Basd on th rsults prsntd in this sction, it can b concludd that th FEC adaptiv schm maximizs th prformanc of th ntwork. Howvr, an adaptiv implmntation incrass th complxity and, in ral world, it can rquir additional ovrhad, dcrasing th fficincy of th systm. If, as an attmpt to rduc th ovrhad, th stimat is mad only at th start of th connction, changs in th bhaviour of th wirlss link can rsult in a significant dgradation of th prformanc. If a non-adaptiv schm is considrd, th rsults in Fig. 2 show that a hybrid ARQ-FEC tchniqu can improv th prformanc of th ntwork. In th following sctions, th idal adaptiv FEC schm is usd as a rfrnc to analyz th prformanc of th proposd tchniqus. V. HYBRID ARQ-FEC SCHEME A hybrid adaptiv ARQ-FEC tchniqu, which dos not rquir an stimat of th bit rror in th channl, is prsntd in this sction. In this tchniqu thr ar two cods: on for corrction (FEC cod) and on for dtction (ARQ cod). Th total numbr of bits (424 bits of th ATM cll plus th parity bits) of th FEC cod is dfind as n f and th total numbr of bits of th ARQ cod is dfind as n a. Sinc thr is not an stimat of th bit rror rat in th channl, th numbr of parity bits of th FEC and ARQ cods must b chosn considring th worst bit rror rat, p = 0-2. In this schm, th systm switchs to th FEC mod whn a cll containing rror is rcivd (and th rtransmission is rqustd), and switchs to th ARQ mod whn a corrct cll is rcivd, as shown in Fig. 4 [25]. ARQ N Fig. 4. Transition diagram. FEC N Th probability of th wirlss link to dlivr a corrct cll to th optical link is givn by [25]

5 68 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005 cch ( + ) + ( ) = (4) c ccf whr c is th probability of a cll to contain no rrors in th ARQ stat, is th probability of a cll to contain a dtctabl rror in th ARQ stat, = c u, ccf is th probability of a cll to contain a corrctabl rror in th FEC stat, givn by (7), and is th stady stat probability of th ARQ stat, givn by [25] cf = (5) cf + whr cf is th probability of a cll to contain no rrors in th FEC stat. Th probabilitis c and cf ar calculatd by (4). Th minimum numbr of parity bits for ach cod can b obtaind as follows. First st p as th highst bit rror rat in th channl (for xampl, p = 0-2 ). Thn, stting n a big nough to mak u ngligibl, tnds to zro cch tnds to ccf and th minimum numbr of parity bits of th FEC cod can b computd using th approach prsntd in Sction 3. As shown in Fig. 5, th FEC cod rquirs at last t = 7 and it is not possibl to dcras this bound vn by incrasing indfinitly th numbr of parity bits in th ARQ cod. Also, on can vrify that n a 438 to attain cch cco. Thus, for p = 0-2, th minimum numbr of parity bits of th ARQ and FEC cods ar 4 (n a = 438) and 63 (n f = 487), rspctivly. Whn th bit rror rat dcrass, th probability of th systm bing in th FEC stat also dcrass, and th influnc of th ARQ cod in cch valu incrass. In a first approach, th minimum numbr of parity bits of th ARQ cod can b obtaind stting th minimum valu for n f and computing th valu of n a for ach valu of p, in such way that cch cco. As shown in Fig. 6, th ARQ cod rquirs 6 parity bits (n a = 440 bits) to achiv cch cco in th whol bit rror rat rang considrd. Th probability cch dpnds on th paramtrs n f and n a. Howvr, it is not possibl to rduc th valu of n a by incrasing th valu of n f, as shown in Fig. 7. Thrfor, th final solutions for th cods ar n a = 440 bits and n f = 487 bits. robability cch ccf Total numbr of bits of th ARQ cod t = 6 t = 7 Minimum valu to cch Fig. 5. Minimum capacity of th FEC cod, for p = 0-2. Total numbr of bits of th ARQ cod Fig. 6. Total numbr of bits of th ARQ cod, as a function of p, for n f = 487. Th probability cch dpnds on th paramtrs n f and n a. Howvr, it is not possibl to rduc th valu of n a by incrasing th valu of n f, as shown in Fig. 7. Thrfor, th final solutions for th cods ar n a = 440 bits and n f = 487 bits. Th man tim to transmit th first (Z ) clls of th DU, considring that all slots in th fram ar in th sam stat, can b computd by [25] T [ T ( ) + ( T + T ) ] + T ( ) z = qa qa qf qf (6) whr T qa and T qf ar th fram tim of th ARQ and FEC mods, rspctivly, and can b computd using (), stting th n valu proprly. Th man tim to transmit th last cll of th DU is givn by [25] T z [ T ( ) + ( T + T ) ] + T ( ) = (7) xa qa xf whr T xa and T xf ar th tim to transmit on cll in th ARQ stat and FEC stat, rspctivly, and can b computd dividing th numbr of bits in th transmission slot, in th propr stat, by th bit rat in th wirlss link. Total numbr of bits of th ARQ cod t = 7 t = 30 t = 00 Fig. 7. Influnc of th valu of t in th total numbr of bits of th ARQ cod, as a function of p. xf

6 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, Th man tim to transmit a corrct DU, not considring th tim to transmit th acknowldgmnt from th dstination to th sourc trminal, is givn by [25] 424L Th = ( Z ) Tz + Tz + γ (8) Ro whr γ, th man numbr of transmissions ndd to rciv a corrct DU, is computd by (9) and (0). Th throughput for th hybrid ARQ-FEC tchniqu is computd by k η h= (9) n + n + n + n [ ( ) ( ) ] ( ) a a f To assss th prformanc of th hybrid ARQ-FEC tchniqu, its prformanc has bn compard to that of th non-adaptiv SW-ARQ and FEC tchniqus, which hav similar complxitis. Two prformanc factors hav bn dfind. Th first on is dfind as th ratio btwn th man tim to transmit a corrct DU in th SW-ARQ tchniqu (givn by (9)) and th corrsponding tim in th hybrid tchniqu (givn by (8)). Th scond on is dfind as th ratio btwn th man tim in th FEC tchniqu (givn by (2)) and th corrsponding tim in th hybrid schm. Figurs 8 and 9 show th rsults, as a function of p, considring V = 40, L = 3 and Z = 00. Th hybrid schm prforms bttr than th non-adaptiv SW-ARQ tchniqu in th whol rang of th bit rror rat considrd and th diffrnc btwn th two tchniqus is mor significant for high bit rror rats. Th hybrid schm has bttr prformanc than th non-adaptiv FEC tchniqu only for p , but th dclin in prformanc for highr bit rror rat is not so significant. A prformanc comparison btwn th hybrid schm and th idal adaptiv FEC schm is shown in Fig. 0, basd on th man tim to transmit a corrct DU, and in th Fig., basd on th throughput (th throughput is k/n in th FEC schm). Th prformanc factor, prsntd in Fig. 0, is dfind as th ratio btwn th tim to transmit a corrct DU in th FEC schm and th corrsponding tim in th hybrid schm. Th hybrid and th idal adaptiv FEC schms hav similar prformanc, xcpt for p around 0-3. f rformanc factor Fig 9. rformanc factor comparing th non-adaptiv FEC and th hybrid schms. rformanc factor Fig. 0. rformanc factor comparing th hybrid and th idal adaptiv FEC schms. Fig. 8. rformanc factor comparing th non-adaptiv SW-ARQ and th hybrid schms. Fig.. Comparing th throughput in th hybrid schm and in th idal adaptiv FEC schm.

7 70 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005 Th vally in th hybrid schm s prformanc, around p = 0-3, occurs du to th larg probability of switching btwn ARQ and FEC stats for thos valus of p. Fig. 2 shows th probability of th ARQ and FEC stats as a function of p. Fig. 4 shows th influnc of th y valu in th probabilitis of th ARQ and FEC stats, considring n a = 440 and n f = 487 bits. It can b sn that th valu of p in th crosspoint dcrass whn y incrass. robability 0.5 robability ARQ stat FEC stat Fig. 2. robability of th ARQ and FEC stats. A. HYBRID ARQ-FEC SCHEME WITH MULTILE FEC STATES Sinc th FEC tchniqu has bttr prformanc than th ARQ tchniqu whn th bit rror rat in th channl is high, th prformanc of th hybrid ARQ-FEC schm can b improvd by incrasing th probability of th systm to b in th FEC stat for high bit rror rats. To achiv this bhaviour, an approach with multipl FEC stats, in which th switching from th FEC to th ARQ stat occurs only aftr rciving y conscutiv corrct clls is proposd. Th stat diagram of this nw systm is shown in Fig. 3 [26]. N N ARQ stat, y = FEC stat, y = ARQ stat, y = 3 FEC stat, y = 3 ARQ stat, y = 0 FEC stat, y = 0 Fig. 4. robability of th ARQ and FEC stats, as a function of y. Th ARQ and FEC cods must b dfind such that cch cco, with th cch valu computd by xprssion (4), using givn by xprssion (20). Stting p = 0-2, th largst bit rror rat in th channl, and choosing n a big nough to mak u insignificant, cch tnds to ccf, indpndntly of th y valu, and th minimum capacity of th FEC cod can b found. Th minimum capacity is t = 7, rsulting in n f = 487 bits, as shown in Fig ARQ FEC N FEC N FEC Total numbr of bits - ARQ cod Fig. 3. Stat diagram for th hybrid approach with multipl FEC stats. Th probability of th ARQ stat can b writtn as [26] cf = (20) y cf + y y j= 0 j cf y = y = 5 y = Fig. 5. Minimum total numbr of bits of th ARQ cod.

8 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, If n f is qual to its minimum valu, th numbr of parity bits of th ARQ cod that produc cch cco can b computd. Fig. 5 shows th rsults for y = (n a = 440), y = 5 (n a = 439) y = (n a = 437) [26]. Sinc cch dpnds on n f and n a, it is ncssary to invstigat if it is possibl to rduc th numbr of parity bits in th ARQ cod by incrasing th capacity of th FEC cod byond its minimum valu. Th capacity of th FEC cod has bn varid, starting with t = 7 and, for ach valu of t, th minimum valu of n a has bn computd for ach valu of p such that cch cco. Fig. 6 shows th rsults for t = 7, t = 30 and t = 00, considring y = 5. Although a big valu for t rsults in a small n a for som valus of p, it is still ncssary to hav n a 439, for y = 5, to achiv cch cco for any valus of p. Th conclusions ar th sam for othr valus of y [26]. Th man tim to transmit a corrct DU is calculatd by xprssion (8), with bing givn by xprssion (20). Fig. 7 compars th prformanc btwn th hybrid schm and a non-adaptiv FEC schm, assuming R s = R o, L = 3, V = 40 and Z = 00. Total numbr of bits - ARQ cod t = 7 t = 30 t = 00 Fig. 6. Minimum total numbr of bits of th ARQ cod, as a function of t. Th vally in th prformanc factor tnds to disappar whn y incrass. For y =, th vally practically disappar, without significant loss of prformanc for low bit rror rats. Thus, by proprly choosing y, th nw hybrid ARQ-FEC schm prforms bttr than th oldr on (y = ) in th whol rang of p. Th nw hybrid schm has similar prformanc to th idal adaptiv FEC schm as shown in Fig. 8. Th hybrid schm dos not rquir an stimat of th bit rror rat in th channl, rsulting in a non-complx implmntation. Th throughput in th hybrid schm is givn by xprssion (9), with bing computd by xprssion (20). Th throughput of th hybrid schm can b maximizd by proprly choosing y, as shown in th Fig. 9. Again, for y =, th vally practically disappar, without significant loss of prformanc for low bit rror rats. Morovr, th throughputs in th hybrid and in th idal adaptiv FEC schms ar similar. Throughput Idal adaptiv FEC Hybrid, y = Hybrid, y = 5 Hybrid, y = Fig. 7. rformanc factor comparing th hybrid and th non-adaptiv FEC schms. rformanc factor y = y = 5 y = Fig. 8. rformanc factor comparing th idal adaptiv FEC and th nw hybrid ARQ-FEC schms. VI. CONCLUSIONS A nw hybrid ARQ-FEC schm with multipl FEC stats has bn proposd in this papr. To compar th prformanc of th rror control schms, th man tim to transmit a corrct DU (composd by Z clls) and th throughput in th ntwork wr analytically computd.

9 72 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005 rformanc factor y = y = 2 y = 3 y = Fig. 9. Comparing th throughput in th hybrid ARQ-FEC schm and in th idal adaptiv FEC schm. Th proposd schm and two non-adaptiv ARQ and FEC schms (all of thm having similar complxitis) hav bn compard with an idal adaptiv FEC schm (considrd as a rfrnc). It has bn shown that th proposd schm prforms qual or bttr than th non-adaptiv ARQ and FEC schms providd that th numbr of FEC stats is proprly chosn. Morovr, although th idal adaptiv FEC and th hybrid schms hav similar prformancs, th lattr dos not nd an stimat of th channl bit rror rat, thus having low implmntation complxity. L V AENDIX: SUMMARY OF THE MAIN ARAMETERS R s T q cco p k n-k n c u ccf t Z R o γ numbr of optical links in th ntwork total numbr of slots in a fram bit rat in th wirlss link fram tim probability of an optical link to hand a corrct cll to th nxt optical link bit rror rat numbr of information bits in a block cod numbr of parity bits in a block cod total numbr of bits in a block cod probability of a cll to contain no rrors probability of a cll to contain a dtctabl rror probability of a cll to contain an undtctabl rror probability of th FEC dcodr to dlivr a corrct cll to th optical link rror corrction capacity of th FEC cod numbr of ATM clls in a DU bit rat in th optical links man numbr of transmissions ndd to rciv a δ n f n a cch cf y corrct DU prformanc factor - th ratio btwn th tim dlay to transmit a DU in a FEC schm and th sam dlay in an ARQ schm total numbr of bits in th FEC cod total numbr of bits of th ARQ cod in th hybrid schm probability of th wirlss link to dlivr a corrct cll to th optical link in th hybrid schm stady stat probability of th ARQ stat in th hybrid schm probability of a cll to contain no rrors in th FEC stat in th hybrid schm numbr of conscutiv corrct clls producing a transition from FEC stat to ARQ stat in th hybrid schm ACKNOWLEDGMENT Th authors wish to thank th financial support of th Conslho Nacional d Dsnvolvimnto Cintífico Tcnológico CNq, Brazil. REFERENCES [] D. Raychaudhuri and N. Wilson, Multimdia rsonal Communication Ntworks: Systm Dsign Issus, roc. 3 rd Workshop Third Gnration Wirlss Inform. Ntworks, Rutgrs Univrsity, Nw Brunswick, April 992, pp [2] J. Mikkonn, J. Aldis, G. Awatr, A. Lunn and D. Hutchison, Th Magic WAND Functional Ovrviw, IEEE Journal on Slctd Aras in Communications, Vol. 6, No 6, pp , August, 998. [3] E. Ayanoglu, K. Y. Eng and M. J. Karol, Wirlss ATM: Limits, Challngs, and roposals, IEEE rsonal Communications, pp. 8-33, August, 996. [4]. Agrawal t alii, SWAN: A Mobil Multimdia Wirlss Ntwork, IEEE rsonal Communications, pp. 8-33, April, 996. [5] R. Kllr t alii, Wirlss ATM for Broadband Multimdia Wirlss Accss: Th ATMmobil rojct, IEEE rsonal Communications, pp , Octobr, 999. [6] A. Acampora, Wirlss ATM: A rspctiv on Issus and rospcts, IEEE rsonal Communications, pp. 8-7, August, 996. [7] D. Raychaudhuri, Wirlss ATM Ntworks: Architctur, Systm Dsign and rototyping, IEEE rsonal Communications, pp , August, 996. [8] J. Mikkonn t alli, Emrging Wirlss Broadband Ntworks, IEEE Communications Magazin, pp. 2-7, Fbruary, 998. [9] K. Y. Eng t alii, BAHAMA, A Broadband Ad-Hoc Wirlss ATM Local- Ara Ntwork, roc. IEEE Intrnational Confrnc on Communications (ICC95), pp , Jun, 995. [0] F. C. Chng and J. M. Holtzman, Wirlss Intllignt ATM Ntwork and rotocol Dsign for Futur rsonal Communication Systms, IEEE Journal on Slctd Aras in Communications, Vol. 5, No 7, pp , Sptmbr, 997. [] J. B. Cain and D. N. McGrgor, A Rcommndd Error Control Architctur for ATM Ntworks with Wirlss Links, IEEE Journal on Slctd Aras in Communications, Vol. 5, No, pp. 6-28, January, 997. [2] I. Jo, Error Control for Wirlss ATM Ntworks, hd Thsis, Gorgia Institut of Tchnology, July, 998. [3] C. Schulr, Dsign and Implmntation of an Adaptiv Error Control rotocol, GMD Rsarch Sris, No 2, 999. [4] S. Aikawa, Y. Motoyama and M. Umhira, Error Corrction and Error Dtction Tchniqus for Wirlss ATM Systms, Wirlss Ntworks, Vol. 3, pp , 997. [5] J. H. So, H. T. Oh and S. W. So, A Nw MAC and DLC Schm Considring Channl Conditions in Wirlss ATM, roc. Vhicular Tchnology Confrnc (VTC 2000), pp , Tokyo, Japan, 2000.

10 JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, [6] K. Yamada, H. Okada and T. H. Lai, An Intgratd Dynamic Error Control Schm for Wirlss ATM Ntworks, IEICE Transactions on Fundamntals, Vol. E82-A, No 7, pp , July, 999. [7] I. F. Akyildiz, I. Jo, H. Drivr and Y. L. Ho, An Adaptiv FEC Schm for Data Traffic in Wirlss ATM Ntworks, IEEE Transactions on Ntworking, Vol. 9, No 4, pp , August, 200. [8]. R. Dnz, rformanc of Error Control Coding Tchniqus and th Dvlopmnt of a Dynamic Error Control Coding Mchanism for Wirlss ATM, hd Thsis, Faculty of North Carolina Stat Univrsity, 999. [9] M. M. Al-Khatib, Nw Wirlss ATM Automatic Error Control Systm, hd Thsis, Univrsity of Southwstrn Lousiana, 999. [20] I. S. Rd and X. Chn, Error Control Coding for Data Ntworks, Kluwr Acadmic ublishrs, 999. [2] J. G. roakis, Digital Communications, scond dition, McGraw-Hill, 989. [22] J. M. C. Brito, Error Control in Wirlss ATM Ntworks, hd. Thsis, Stat Univrsity of Campinas Unicamp, Brazil, 2003 (in ortugus). [23] J. M. C. Brito and I. S. Bonatti, A Comparison of End-to-End Dlay in Wirlss ATM Ntworks using FEC and Slctiv Rpat ARQ in th Wirlss Link, 3 rd Intrnational Confrnc on Information, Communications, and Signal rocssing (ICICS 200), 5 pags, Singapor, 5-8 Octobr, 200. [24] J. M. C. Brito and I. S. Bonatti, A Comparison of End-to-End Dlay in Wirlss ATM Ntworks using FEC and Go-Back-N ARQ in th Wirlss Link, 5 th IEEE Malaysia Intrnational Confrnc on Communications (MICC 200), pp 84-89, Kuala Lumpur, Malaysia, 2-24 Octobr, 200. [25] J. M. C. Brito and I. S. Bonatti, A Simpl Adaptiv Error Control Schm for Wirlss ATM Ntworks, Intrnational Symposium on Tlcommunications (IST 200), pp , Thran, Iran, -3 Sptmbr, 200. [26] J. M. C. Brito and I. S. Bonatti, An Improvmnt in a Simpl Adaptiv Error Control Schm for Wirlss ATM Ntworks, Scond IASTED Intrnational Confrnc on Communication Systms and Ntworks, pp , Bnalmádna, Spain, 8-0 Sptmbr, [27] M. D ryckr, Asynchronous Transfr Mod (ATM): Solution for Broadband ISBN, 3rd Edition, Ellis Horwood LTD, 99. [28] D. Raychaudhuri, L. J. Frnch, R. J. Siracusa, S. K. Biswas, R. Yuan,. Narasimhan and C. A. Johnston, WATMnt: A rototyp Wirlss ATM Systm for Multimdia rsonal Communication, IEEE Journal on Slctd Aras in Communications, Vol. 5, No, pp , January, 997. Ivanil S. Bonatti was born in Mogi- Mirim, S, Brazil, in 95. H rcivd th B.Sc. (973) and M.Sc. (975) dgrs in Elctrical Enginring from th Univrsity of Campinas, UNICAM, Brazil, and th Doctorat n Automatiqu dgr from th Univrsity aul Sabatir, Toulous, Franc, in 98. H joind th School of Elctrical and Computr Enginring of th Univrsity of Campinas in 975, whr h is currntly a Full rofssor. His main intrsts ar signal procssing, circuit thory, simulation analysis and tlcommunication. José Marcos C. Brito rcivd his diploma in lctrical nginring from th National Institut of Tlcommunications (Inatl), Brazil, in 986, his M. Sc. dgr in lctrical nginring from Stat Univrsity of Campinas, Brazil, in 998, and his h.d. dgr in lctrical nginring from Stat Univrsity of Campinas in Sinc 986 h has bn a profssor at Inatl, whr h has hld svral managmnt positions, including vic-principal and dirctor for rsarch. Currntly h is a Full rofssor at Inatl. H has workd as a consultant for svral tlcommunications companis in Brazil and has publishd svral paprs in intrnational confrncs in th tlcommunications ara. H is th ditor-inchif of th Tlcommunications Journal ditd by Inatl and has srvd as a program committ mmbr in som intrnational confrncs. His currnt rsarch intrsts includ computr communications ntworks, multipl accss systms, modling and prformanc valuation of communication systms, wirlss ntworks and rror control schms.