The Throughput of Hybrd-ARQ n Block Fadng under Modulaton Constrants Tark Ghanm and Matthew C. Valent Lane Dept. of Comp. Sc. and Elect. Eng. West Vrgna Unversty Morgantown, WV 26506 6109 Emal: mvalent@wvu.edu Abstract In a semnal paper publshed n 2001, Care and Tunnett derved an nformaton theoretc bound on the throughput of hybrd-arq n the presence of block fadng. However, because the results placed no constrants on the modulaton used, the nput to the channel was Gaussan. The purpose of ths paper s to nvestgate the mpact of modulaton constrants on the throughput of hybrd-arq n a block fadng envronment. Frst, we consder the mpact of modulaton constrants on nformaton outage probablty for a block fadng channel wth a fxed rate codeword. Then, we consder the effect of modulaton constrants upon the throughput of hybrd-arq, where the rate of each codeword vares dependng on the nstantaneous channel condtons. These theoretcal bounds are compared aganst the smulated performance of HSDPA, a newly standardzed hybrd- ARQ protocol that uses QPSK and 16-QAM bt nterleaved turbo-coded modulaton. The results ndcate how much of the dfference between HSDPA and the prevous unconstraned modulaton bound s due to the use of the turbo-code and how much s due to the modulaton constrants. I. INTRODUCTION Hybrd-ARQ s a technque for combnng forward error correcton (FEC) codng wth an automatc repeat request (ARQ) protocol [1]. A message s encoded by a low rate mother code and then parttoned nto several blocks. Blocks are sent one by one untl enough nformaton s accumulated at the destnaton to correctly decode the message. Often, the channel s uncorrelated from one block to the next, n whch case a block fadng model may be assumed. A key performance metrc for hybrd-arq s ts throughput, whch s the number of bts conveyed per unt tme. In [2], Care and Tunnett derved nformaton-theoretc bounds on the throughput of hybrd-arq n block fadng. The results bult upon related work on the performance of standard block fadng channels [3], [4],.e. channels wth a fxed codeword sze and number of blocks per codeword. The results n [2] placed no constrants upon modulaton, and as a consequence, the nput to the channel was assumed to be Gaussan dstrbuted. However, practcal systems do not use Gaussan-dstrbuted modulaton, and the computaton of nformaton-theoretc lmts on the throughput of hybrd-arq wth practcal modulaton constrants has untl now remaned an open problem. The man motvaton behnd the present paper s the emergence of the Hgh Speed Data Packet Access (HSDPA) standard [5], [6], whch s part of the UMTS famly of standards under development by the Thrd Generaton Partnershp Project (3GPP). In HSDPA, messages are frst encoded wth a bnary turbo code and then punctured by a rate matchng algorthm to create the frst transmtted block. If the destnaton s unable to decode the ntal block, then the codeword s agan punctured by the rate matchng algorthm, though by selectng a dfferent set of rate matchng parameters, a dfferent set of code bts can be ncluded n the second transmtted block. Blocks contnue to be generated by rate matchng wth dfferent parameters and sent untl ether the destnaton correctly decodes the message or an upper lmt on the number of retransmssons s reached. HSDPA uses ether QPSK or (gray-labelled) 16-QAM modulaton. Because the encoder s bnary and separated from the modulator by a btwse nterleaver, ths s an example of bt-nterleaved coded-modulaton (BICM) [7]. As shown n [7], the performance of a BICM-constraned system can dffer sgnfcantly from that of a system wth an unconstraned Gaussan nput, especally at hgh spectral effcency. The purpose of ths paper s to nvestgate how modulaton constrants effect performance of block fadng channels n general (an ssue that has also been recently dscussed n [8]), and more specfcally, the throughput of hybrd-arq over a block fadng channel. To accomplsh ths goal, we frst begn n Secton II wth an exposton of our system model, and then contnue n Secton III wth a revew of the BICM-constraned capacty of smple addtve whte Gaussan nose (AWGN) channels. Secton IV dscusses the nformaton outage probablty of block fadng wth both unconstraned and constellaton-constraned nputs, and Secton V bulds upon these results to derve the throughput and latency of hybrd-arq under modulaton constrants, thereby generalzng the results of [2]. Numercal results n Secton VI compare the smulated throughput of HSDPA aganst the unconstraned bound of [2] and the modulatonconstraned bound developed n ths paper. Fnally conclusons and suggestons for future work are gven n Secton VII. II. SYSTEM MODEL The system model s as shown n Fg. 1. The system uses bt-nterleaved coded modulaton [7] and hybrd-arq [2]. The transmtter passes a length K bnary message u nto a bnary encoder, producng a codeword c of length N bts. The codeword s btwse nterleaved, producng the vector c, whch
u c' c Encoder M odu l a t or Feedback Channel û λ' λ Fg. 1. D ecoder l D em odu l a t or System model. π denotes nterleavng at the bt level. s passed nto an M-ary modulator. The modulator produces a length N/ log 2 M vector x of complex M-ary symbols drawn from the sgnal set S. The modulated codeword s broken nto B max equal-length blocks, denoted x[b], 1 b B max. The length of each block s L = N/(B max log 2 M) symbols and the rate of each block s R = K/L. The transmtter sends the frst block x[1], and f the recever s able to successfully decode t, an acknowledgement wll be sent back through a feedback channel (we assume here that the feedback channel s error and delay-free and that an deal error detectng code allows the recever to dscrmnate between correctly and ncorrectly decoded messages). If the transmtter receves an acknowledgement, t wll move on to the next message; otherwse, t wll send the next block from the current message. Ths process contnues untl ether the message s receved correctly or the last (B max ) block s transmtted. The b th block s transmtted wth average energy per symbol E s = E{ x 2 } over a block fadng channel so that the receved sgnal s: h ν x y + y[b] = h[b]x[b] + ν (1) where ν s a vector of complex Gaussan nose whose dmensons match x[b] and whose components are zero-mean..d. crcularly symmetrc Gaussan wth varance N o /2 n each complex drecton, and h[b] s a complex scalar channel gan assumed to be ndependent from block to block and constant for the duraton of each block. Wthout loss of generalty, E{ h[b] 2 } = 1 so that the average receved energy per symbol s the same as the transmtted symbol energy. Each receved symbol n y[b] s passed through a demodulator that produces log-lkelhood rato estmates of each of the log 2 M bts assocated wth the symbol. Snce demodulaton s on a symbol-by-symbol bass, consder the demodulaton process for a sngle symbol y. For each possble x m, 1 m M, a log-lkelhood s formed: Λ m = log p(x m y) p(x m y) = log x S p(x y) (2) where p(x) s the pdf of x. Lettng the lkelhood f(x y) = κp(x y) for any arbtrary constant κ that s common for all postulated symbols, and applyng Bayes rule, then (2) can be more convenently rewrtten as Λ m = log f(y x m ) x S f(y x) = log f(y x m ) log x S f(y x) = log f(y x m ) max [log f(y x)] (3) x S where the max-star operator s as defned n [9], { } max {x } = log e x. (4) Coherent detecton s mplemented by usng: log f(y x) = E s N o y hx 2. (5) Notce n Fg. 1 that the recever has perfect channel state nformaton (CSI) but that the transmtter does not use any CSI (asde from the ACK sgnal sent over the feedback channel). Next, the recever transforms the set of M log-lkelhoods that are calculated for each receved symbol nto a set of log 2 M btwse log-lkelhood ratos (LLRs), one for each code bt assocated wth the symbol. To calculate the LLR for the th bt of receved symbol y, frst partton the symbol set S, whch s the set of symbols whose th bt s a 0, and S (1), whch s the set of symbols whose th bt s a 1. The LLR of the th bt, 1 log 2 M, s then: nto two dsjont sets, S (0) λ = log p(c = 1 y) p(c = 0 y) p(x y) x S = log (1) p(x y). (6) x S (0) When symbols are equally lkely, ths may be expressed as λ = max [log f(y x)] max [log f(y x)]. (7) x S (1) x S (0) After the b th block has been receved, then the correspondng bt lkelhoods for all blocks that have been receved so far are passed nto a decoder. The blocks could be encoded n such a way that all B max blocks are dentcal (a repetton code), n whch case the blocks wll be dversty-combned at the recever by addng up the LLR s of each block. More generally, ncremental redundancy could be used, whereby each block s obtaned by puncturng a low rate mother code. Wth ncremental redundancy, a dfferent part of the codeword s transmtted each tme, and after the b th block, a recever wll pass the rate R b = R/b code that t has untl then receved through ts decoder (code-combnng). III. AWGN CAPACITY The mutual nformaton between channel nput X and output Y s defned as [10]: p(x, y) I(X, Y ) = p(x, y) log 2 dxdy. (8) p(x)p(y)
The capacty of a channel s found by maxmzng the mutual nformaton over all possble nput dstrbutons: C = max I(X, Y ). (9) p(x) When there are no constrants on the nput sgnal and the channel s AWGN, (9) s maxmzed by lettng the nput p(x) take on a Gaussan dstrbuton. Ths results n the classc unconstraned AWGN channel capacty: C(γ) = log 2 (1 + γ) (10) where γ = E s /N o s the SNR and the capacty takes on unts of bts per channel use (.e. transmtted symbol). Rather than usng Gaussan dstrbuted symbols, practcal systems use symbols drawn from the sgnal set S, usually wth equal probablty. Under such modulaton constrants, p(x) s a fxed functon of S, and snce there s nothng to maxmze over, the capacty s merely the mutual nformaton gven by (8) wth p(x) determned by the modulaton constrant. After some manpulaton, (8) and (9), can be wrtten n terms of the symbol lkelhood Λ m as the expectaton C(γ) = E xm,ν [log M + log p(x m y)] = log M + E xm,ν [Λ m ] nats/symbol = log 2 M + E x m,ν [Λ m ] bts/symbol (11) log 2 where the expectaton s over all symbols x m S and complex nose samples ν wth SNR equal to γ. Ths expresson represents the coded modulaton (CM) capacty and can be evaluated ether by numercal ntegraton [3], [11] or Monte Carlo ntegraton [7]. If the system s further constraned to use BICM [7], then the channel s essentally transformed nto log 2 M parallel bnary channels. The capacty of the th bnary channel, 1 log 2 M s C (γ) = E c,ν [log 2 + log p(c y)] nats/symbol (12) where the expectaton s over the two possble code bts c {0, 1} and the complex nose samples ν wth SNR γ. After some manpulaton, ths can be expressed n terms of the bnary LLR λ as: C (γ) = log(2) E c,ν [max {0, ( 1) c λ }] nats/symbol = 1 E c,ν [max {0, ( 1) c λ }] bts/symbol. log 2 (13) Snce the capactes of parallel Gaussan channels add [10], the overall capacty of the BICM system s found by addng the capactes of the ndvdual bnary channels: C(γ) = log 2 M =1 C (γ). (14) As an example, the capacty when S s constraned to be ether QPSK or 16-QAM s shown n Fg. 2. For comparson purposes, the unconstraned capacty (10) s also shown. For Capacty 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 16QAM, CM (sold lne) Unconstraned 16QAM, BICM w/ SP 16QAM, BICM w/ gray labellng QPSK 0-10 -5 0 5 10 15 20 Es/No n db Fg. 2. Capacty of QPSK, 16-QAM, and unconstraned (Gaussan-nput) modulaton n AWGN. For 16-QAM, the CM capacty s shown as s the BICM capactes for two types of symbol mappngs (gray-labellng and setparttonng (SP)). 16-QAM, both the CM and BICM capactes are shown. Whle the CM capacty does not depend on how bts are mapped to symbols, for BICM t does. The BICM-constraned capacty for two typcal symbol mappngs are shown, gray-labellng and set-parttonng (SP). Whle both BICM capactes are nferor to the CM capacty, the BICM capacty wth gray-labellng s very close to the CM capacty, especally for C(γ) > 2. IV. BLOCK FADING In block fadng, the codeword s broken nto B blocks and each block s sent over an ndependent channel. Because the fadng coeffcent h[b] of the b th block s constant for the entre duraton of the block, the channel durng one block s condtonally Gaussan (condtoned on h[b]). However, snce the fadng coeffcent s random, then so s the nstantaneous SNR of the b th block, whch we denote γ b h[b] 2 E s /N 0, and therefore so s the correspondng capacty C(γ b ). For Raylegh block fadng, h[b] s Raylegh and h[b] 2 s exponentally dstrbuted. When code-combnng s used, then the capactes of the B blocks add, snce each block s sent over an ndependent Gaussan channel. The resultng capacty s: ( C(γ 1,..., γ B ) = 1 B ) C(γ b ) (15) B b=1 where the 1 B term s needed because blocks are orthogonal and therefore effectvely occupy only 1/B th of the channel. For dversty combnng, the SNRs add and so the capacty when B blocks are transmtted s: ( C(γ 1,..., γ B ) = 1 B ) B C γ b. (16) b=1
When there are no modulaton constrants, the capactes n (15) and (16) are found from the unconstraned AWGN capacty (10), whle when there are modulaton constrants equaton (11) or equatons (13) and (14) must be used for CM and BICM, respectvely. When B s fnte, the channel s not ergodc, and therefore a Shannon-sense channel capacty does not exst. For fnte B, a more relevant performance metrc s the nformaton outage probablty, defned n [3] and [4] as the probablty that the nstantaneous capacty C(γ 1,..., γ B ) s less than the rate R B = R/B, p 0 (B) = P [C(γ 1,..., γ B ) < R B ]. (17) Informaton Outage Probablty 10 0 10-1 10-2 10-3 10-4 10-5 B=10 B=4 Modulaton Constraned Input Unconstraned Gaussan Input B=3 B=2 B=1 Whenever C(γ 1,..., γ B ) < R B, an nformaton outage occurs, and relable sgnalng s not possble. The nformaton outage probablty s an nformaton theoretc bound on the frame error rate (FER) n block fadng, and thus no system can have a FER that s better than the nformaton outage probablty. In the example shown n Fg. 3, the nformaton outage probablty of code-combnng n Raylegh block fadng s plotted aganst SNR for rate R B = 2 bts per symbol and B = {1, 2, 3, 4, 10}. For each value of B, two curves are shown, one for an unconstraned Gaussan nput [obtaned by substtutng (10) nto (15) wth R B = 2], and the other for a BICM constraned nput usng gray-labelled 16-QAM [obtaned by substtutng (13) nto (14) and (15)]. On ths loglog scale, each curve becomes a straght lne at hgh SNR. The slope of the lne s d, where d s an nteger n [0, B] and s called the block dversty or SNR exponent. As dscussed n [8], for an unconstraned Gaussan nput channel, d = B, but under modulaton constrants the dversty s upper-bounded by the Sngleton bound ( d = 1 + B 1 R ) B. (18) log 2 M Snce n ths case R B / log 2 M = 1/2, d = 1, 2, 2, 3 and 6 for B = 1, 2, 3, 4 and 10, respectvely. Ths behavor can be observed n the fgure. For B = 1 and 2, the outage probablty under modulaton constrants s worse than the unconstraned case, but asymptotcally the two curves for the same value of B have the same slope. However, for B = 3 not only s the constraned case worse than the unconstraned case, but asymptotcally t has the same slope as the B = 2 unconstraned case. Smlarly, the B = 4 constraned case has the same slope as the B = 3 unconstraned case. For B = 10, the asymptotc slope for the constraned case s ndeed 6, though ths s not obvous by lookng at the fgure because slope 6 and 10 look smlar to the eye. V. HYBRID-ARQ Let the random varable B ndcate the number of hybrd- ARQ transmssons untl the packet s successfully receved. Intally, consder the case that there s no lmt on the number of transmssons. For B to equal b, the frst b 1 attempts must 10-6 0 10 20 30 40 50 Es/No n db Fg. 3. Informaton outage probablty vs. SNR for unconstraned and graylabelled 16QAM modulaton n Raylegh block fadng wth rate R B = 2. fal whle the b th attempt must succeed. Thus, the pmf of B s b 1 p B [b] = (1 p 0 (b)) p 0 () for b 1. (19) Often, an upper lmt B max s placed on the number of hybrd-arq transmssons. If the message s not receved after B max blocks have been transmtted, then an error s logged, and the system moves on to the next message. The pmf of B wth constrant B max on the number of transmssons s b 1 ξ (1 p p B [b] = 0 (b)) p 0 () for 1 b B max =1 0 otherwse, (20) =1 where ξ s a normalzaton factor requred to make p B [b] a vald pmf: [ Bmax b 1 1 ξ = (1 p 0 (b)) p 0 ()]. (21) =1 =1 Let τ be the tme between the start of consecutve blocks (whch ncludes the tme to transmt the block, process t, send an acknowledgement, and process the acknowledgement). Then the throughput, n bts per second, s: η = K τe[b] (22) where E[B] s the expected value of B, and K s the number of nformaton bts per message. A more meanngful metrc s the throughput effcency, whch s the rato of correct bts to transmtted bts: η eff = 1 p 0(B max ). (23) E[B]
TABLE I MAXIMUM THROUGHPUT (kbps) FOR THE FIXED REFERENCE CHANNEL QPSK 16-QAM H-Set 1 534 777 H-Set 2 801 1166 H-Set 3 1601 2332 Another metrc of nterest s the latency, whch s the tme between correctly decoded messages, and s gven by τ/η eff seconds. Note that when usng hybrd-arq, R B = R/B and so the upper-bound on dversty gven by (18) becomes d = 1 + B R log 2 M. (24) Ths mples that as long as R < log 2 M (whch must be true n practcal systems) then d s upper bounded by B and there s no loss n dversty n hybrd-arq systems due to usng modulaton constrants. VI. LIMITS ON THE THROUGHPUT OF HSDPA In ths secton, the throughput effcency of HSDPA (obtaned through computer smulatons) s compared aganst the correspondng nformaton theoretc bounds (both unconstraned and modulaton-constraned). Wth HSDPA, the message s frst encoded by the rate 1/3 UMTS turbo code [12]. A two stage rate matchng algorthm s used to puncture the codeword, whch s then modulated (after btwse nterleavng) usng ether QPSK or 16-QAM. For each modulaton type, there are eght ways to perform rate matchng, whch s specfed by a three bt varable called the redundancy verson [5]. In the case of 16-QAM, gray-labellng s used and rate matchng can be used to essentally rearrange the sgnal constellaton mappng. When a retransmsson s requested, the rate matchng algorthm can ether be run wth the same redundancy verson, resultng n a repetton code whch s dversty-combned at the recever, or a dfferent redundancy verson can be used for each transmsson, n whch case codecombnng s used. Key parameters, such as the message sze (K), block length after rate matchng (L), sequence of redundancy versons, and tme between the start of consecutve blocks (τ), were chosen to comply wth the 3GPP approval standard [13]. There are a total of sx testsets defned n [13], termed H-Set 1 through H-Set 6. In ths secton, we gve throughput results for H- Set 1 through 3, whch dffer only n the value of τ. The maxmum throughput for these three H-Sets, whch occurs as E[B] 1, or equvalently as E s /N o, s gven n Table I. For each case, the number of nformaton bts s K = 3202 for QPSK and K = 4664 for 16-QAM. After rate matchng, the block sze s L = 2400 QPSK symbols or L = 1920 16-QAM symbols. The maxmum number of hybrd-arq transmssons per message s B max = 4 and each block s punctured usng a dfferent redundancy verson (code-combnng). The tme between the start of consecutve blocks s τ = 6, 4, and 2 msec for H-Set 1, 2, and 3, respectvely. Normalzed throughput 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 QPSK 16-QAM Unconstraned Gaussan Input Modulaton Constraned Input Smulated HSDPA Performance 0-10 -5 0 5 10 15 20 25 30 Es/No n db Fg. 4. Throughput effcency of HSDPA H-Sets 1 through 3 n Raylegh block fadng usng QPSK or 16-QAM modulaton. For each modulaton type, the unconstraned and modulaton-constraned theoretcal lmts are compared aganst the smulated performance of the HSDPA system. Fg. 4 shows throughput effcency versus SNR n Raylegh block fadng for H-Sets 1 through 3 usng both QPSK and 16- QAM modulaton. Snce H-Sets 1 through 3 dffer only n the value of τ, all three have the same throughput effcency. The fgure shows two groups of three curves. The group on the left s for QPSK and the group on the rght s for 16-QAM. Note that QPSK has better throughput effcency than 16-QAM n ths applcaton because t has a lower per-block code rate (R = 3202/2400 for QPSK and 4664/1920 for QAM). For each modulaton type, three curves are shown. The leftmost curve s the nformaton-theoretc lmt on throughput wth an unconstraned (.e. Gaussan-dstrbuted) nput, whle the mddle curve s the nformaton-theoretc lmt wth a modulatonconstraned nput. The rghtmost curve s the throughput of the smulated HSDPA system n block fadng. The results shown n Fg. 4 ndcate how much of the performance dfference between HSDPA and the correspondng theoretcal lmts s due to the modulaton constrants and how much s due to the use of the turbo code. For nstance, wth QPSK, a throughput effcency η eff = 0.5 s acheved at E s /N 0 = 0.77, 1.12, and 2.05 db for the unconstraned, modulaton-constraned, and actual HSDPA cases, respectvely. Ths mples that whle HSDPA has a 1.28 db loss compared to the unconstraned theoretc bound, about 0.35 db of ths loss can be attrbuted to the modulaton constrant, whle the rest s attrbuted to the turbo code. Smlarly, for 16-QAM, a throughput effcency η eff = 0.5 s acheved at E s /N o = 4.88, 5.44, and 6.48 db for the unconstraned, modulaton-constraned, and actual HSDPA cases, respectvely. Ths ndcates that of the 1.60 db dfference between HSDPA and the unconstraned theoretc bound, about 0.56 db of ths loss s due to the modulaton constrant. It s nterestng to note that for QPSK, the loss due to the
modulaton constrant dmnshes at low throughput effcency (e.g. η eff < 0.2), whle for QAM t does not (except at extremely small η eff ). These results suggest that the modulaton constrant has more of a negatve effect when usng QAM sgnalng than when usng QPSK sgnallng, at least for the HSDPA system consdered here. VII. CONCLUSIONS When examnng the throughput of any practcal hybrd- ARQ system n block fadng, there s always a loss relatve to the nformaton theoretc bounds derved by Care and Tunnett [2]. In the case of HSDPA, ths loss s n the range of 1-2 db. Whle there are several causes for ths loss, these causes can be roughly parttoned nto those that are due to the modulaton constrants and those that are due to the use of a practcal code. Ths paper presented a methodology for determnng the nformaton theoretc throughput bound under modulaton constrants, thereby allowng the relatve throughput losses due to modulaton and codng to be separated. In the case of HSDPA, about 0.5 to 0.6 db of the loss s due to usng a 16-QAM modulaton constrant, whle up to 0.4 db of the loss s due to usng QPSK modulaton constrants. As for the losses due to causes other than modulaton, there are several factors. Frst, both the unconstraned and modulaton-constraned throughput bounds were found by usng expressons for the AWGN Shannon-sense capacty of each block. As such, these expressons are derved under the assumpton of an nfnte block length. However, practcal systems must use a fnte block length (e.g. n HSDPA t s 2400 QPSK symbols or 1920 QAM symbols). Thus some of the loss s due to fnte block length effects, and the amount of ths loss can be determned usng an extenson of the spherepackng approachng descrbed n [14]. Another ssue wth HSDPA s that whle the rate matchng algorthm can be used to produce up to eght dstnct blocks for each modulaton type, these blocks are not mutually exclusve,.e. some code bts wll appear n more than one block. As a consequence, the processng at the recever wll actually be a combnaton of code-combnng and dversty-combnng. Ths problem can be allevated by usng a rate compatble code, such as a rate compatble turbo code [15], whch wll have dstnct blocks and s therefore amenable to pure code-combnng. One weakness of usng rate compatble codng s that t mposes a fnte upper lmt on the maxmum number of retransmssons B max ; ths drawback can possbly be allevated by usng a rateless code such as an LT code [16] or a Raptor code [17]. In addton to fnte block length effects and presence of repeated code bts, the other losses relatve to the nformaton theoretc bounds can be attrbuted to the code mperfectness as defned by [18]. Whle the purpose of ths paper has been to examne the effects of modulaton constrants upon the theoretcal throughput lmts of conventonal, pont-to-pont, hybrd-arq, the results can easly be extended to study hybrd-arq based relayng protocols, such as the HARBINGER protocol proposed n [19]. In a relayng network, addtonal relay termnals assst the transmsson of the message from source to destnaton. Whle the ntal hybrd-arq transmsson must always come from the source, each retransmssons may come from any relay that overhears the message. Thus the tme-dversty benefts of hybrd-arq are combned wth the spatal-dversty of relayng. Whle the results n [19] assumed an unconstraned channel nput, the results from ths paper could be used to study the mpact of modulaton constrants on hybrd-arq relayng protocols. ACKNOWLEDGMENT The authors would lke to thank Dr. Mke McCloud from Tensorcomm, Inc., and Sh Cheng and Roht Iyer Seshadr from WVU s Wreless Communcatons Research Lab for ther techncal gudance. REFERENCES [1] S. Wcker, Error Control Systems for Dgtal Communcatons and Storage. Englewood Clffs, NJ: Prentce Hall, Inc., 1995. [2] G. Care and D. Tunnett, The throughput of hybrd-arq protocols for the Gaussan collson channel, IEEE Trans. Inform. 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