An ILP Formulation for Reliability-Oriented High-Level Synthesis

Transcription

1 A ILP Foulatio fo Reliability-Oieted High-Level Sythesis S. Tosu *, O. Oztuk **, N. Masoui *, E. Avas *, M. Kadei **, Y. Xie **, ad W-L. Hug ** * Syacuse Uivesity ** Pesylvaia State Uivesity * {stosu,aasou,eavas}@ecs.sy.edu ** {kadei,yuaxie,oztuk,whug}@cse.psu.edu Abstact Reliability decisios take ealy i syste desig ca big sigificat beefits i tes of desig quality. This pape pesets a - itege liea pogaig (ILP) foulatio fo eliability-oieted high-level sythesis that addesses the soft eo poble. The poposed appoach ties to axiize eliability of the desig while obsevig the bouds o aea ad pefoace, ad akes use of ou eliability chaacteizatio of hadwae copoets such as addes ad ultiplies. We ipleeted the poposed appoach, pefoed expeiets with seveal exaple desigs, ad copaed the esults with those obtaied by a pio poposal. Ou esults show that icopoatig eliability as a fist-class etic duig high-level sythesis bigs sigificat ipoveets o the oveall desig eliability.. Itoductio Oe of the desig challeges i aoete VLSI ea is the guaatees fo eliability. With techology scalig, shikig geoeties, lowe powe voltage, highe fequecies ad highe desity cicuits all have a egative ipact o eliability: the ube of occueces of tasiet faults is iceased due to those factos. A ajo souce of the tasiet faults is soft eos, also called sigle evet upset (SEU), which ae iduced though thee diffeet adiatio souces: alpha paticles fo the atually occuig adioactive ipuities i device ateials, high-eegy cosic ay iduced eutos, ad euto iduced Boo fissio []. Powe-educig techiques eployed i ay ebedded systes ake these systes oe vuleable to soft eos [2]. Theefoe, thee is a clea eed fo soft eo-awae ebedded syste desig. I ode to have a obust desig, the soft eo poble ust be addessed at diffeet levels i a coodiated fashio, fo high-level specificatio to low-level ipleetatio. Oe of these levels that is paticulaly attactive ad oe beeficial is high-level sythesis (HLS), which is the pocess of deteiig the block-level (i.e., acoscopic) stuctue of the cicuit. While the past wok o HLS focused aily o pefoace, aea, ad powe costaits, eliability issues egadig soft eos have ot eceived uch attetio. Cosequetly, thee exist oly a few pio HLS studies that tageted at detectig/coectig soft eos. A coo chaacteistic of these techiques is that they eploy duplicatio (ude pefoace/aea bouds) duig HLS to icease esiliece to soft eos. Pio wok has ivestigated soft eo susceptibility of eoy eleets ad cobiatioal cicuits [3]. They showed that cobiatioal cicuits ae less susceptible to soft eos tha eoy eleets. This is because of thee ajo eo askig effects o cobiatioal cicuits; aely logical, electical, ad latchig-widow askig. O the othe had, Sivakua et al [4] deostate that the soft eo susceptibility of cobiatioal cicuits will be copaable to that of eoy cicuits by the yea of 2 with the cuet techology teds. This sigificat pedictio uges the copute desiges fo futhe eseach to educe the soft eo effects o data-path pat of the desigs sice the cuet potectio techiques fo cobiatioal cicuits itoduce oe aea, powe cosuptio, ad/o pefoace pealty tha those desiged fo eoy eleets. These obsevatios otivate us to coside the effects of soft eos o the poble of high-level data-path sythesis ad the oveall eliability fo the cobiatioal pat of the esultig desigs. Theefoe, the wok poposed i this pape is othogoal ad copleetay to techiques fo ipovig eliability of eoy copoets. I this pape, we take a fesh look at the soft eo-awae HLS poble, ad peset a appoach based o itege liea pogaig (ILP). As agaist the duplicatio-based pio wok i this aea, we assue the existece of ultiple vesios of a give opeato (a ode i the data-flow gaph), each vayig i tes of pefoace, aea, ad eliability etics. Ou appoach, usig ILP, deteies the ost suitable (i.e., ost eliable) vesio fo each data-flow gaph ode ude the give aea ad pefoace bouds. We also evaluate the oveall eliability of the esultig high-level desig. To test the effectiveess of ou appoach, we autoated it withi a custo HLS tool that pefos schedulig, esouce shaig, ad bidig. Ou expeietal evaluatio usig a set of saple desigs deostate that the poposed appoach ipoves the oveall desig eliability sigificatly, ove a soft eo-oblivious alteative. We also copae the esultig desigs fo ou ipleetatio with those obtaied though a pio wok that cosides oly ode duplicatio, ad discuss why a uified appoach that itegates both of these techiques ca geeate bette esults tha each idividual schee. The est of this pape is stuctued as follows. The ext sectio discusses the elated wok o ILP-based HLS ad eliability-awae HLS. Sectio 3 pesets backgoud o soft eos, discusses ou libay chaacteizatio, ad explais the eliability echais eployed to evaluate the oveall desig eliability. Sectio 4 gives the poble defiitio fo eliability-oieted HLS, ad pesets ou ILP foulatio. Sectio 5 gives ou expeietal evaluatio, ad fially Sectio 6 cocludes the pape. 2. Related wok Most of the pio wok o foulatig the HLS poble usig ILP aily focused o aea-pefoace o aea-pefoace-powe tadeoffs. Achatz odeled the high-level sythesis poble usig exteded - liea pogaig [5]. His odel hadles the ultifuctioal uits as well as uits with diffeet executio ties ude tie-costait o esouce-costait. OSCAR syste [6] also akes use of - itege pogaig fo solvig schedulig, bidig, ad allocatio. Sice the ube of vaiables ad iequalities i the ILP foulatio ca gow expoetially, applyig ILP to lage pobles ay be pobleatic. To educe the coputatio tie of the Poceedigs of the Sixth Iteatioal Syposiu o Quality Electoic Desig (ISQED 5) /5 $ 2. IEEE

2 algoith, [7] peseted a i-depth aalysis, ad poposed a well-stuctued ILP foulatio fo the HLS poble. Seveal studies also ivestigated the odule selectio poble usig ILP such as [5]. All of the studies etioed above coside oly aea ad pefoace optiizatios. Thee has ot bee ay pio ILP based foulatio, to the best of ou kowledge, cosideig eliability as a fist class citize i HLS faewok alog with aea ad pefoace costaits. Howeve, thee exist soe publicatios i this cotext that use heuistic ethods [8] [9]. These studies o eliable cicuit desig ake use of copoet edudacy. They typically use oe esouce (vesio) fo each type of opeatio with a fixed eliability, ad the oveall desig eliability is iceased by adoptig N Modula Redudacy (NMR). I [8], Oailoglu ad Kai itoduced a desig ethodology fo fault-toleat ASICs. They peseted two stategies that ae based o NMR. The fist stategy tagets at iiizig the oveall cost of the desig ude pefoace ad eliability costaits, while the secod oe ties to axiize the eliability give the cost ad pefoace costaits. Aothe ethod used to ipove the eliability of the high-level syste is to duplicate the etie stuctue fo the fault-detectig cicuits []. Studies usig this ethod copied the etie flow gaph, ad subsequetly used vaious stategies to iiize the oveall aea equieets of the fial desig. Fo exaple, [] exploited the feedo of opeatios i data-flow gaph, ad scheduled both the copies to educe the aea ovehead. Ou appoach diffes fo these pevious studies sice it akes use of a eliability-chaacteized libay that has diffeet vesios of esouces with diffeet aea, pefoace, ad eliability etics. The libay we use peits us choose the ost eliable esouces fo a specific task. I othe wods, istead of iceasig eliability though edudacy, we achieve eliable desig by usig diffeet vesios of the copoets (to the extet allowed by aea ad pefoace bouds). I additio, ou appoach is based o ILP, athe tha heuistic techiques. 3. Soft eos ad eliability I this sectio, we biefly discuss soft eos ad explai ou libay chaacteizatio ethod based o soft eo ate i a copoet. We also peset the echais used to calculate the eliability of a desig. 3.. Backgoud o soft eos A soft eo, also called Sigle Evet Upset (SEU), is a eo that is iduced though diffeet adiatio souces. It causes to have a glitch o the cicuit, usually esultig i a tasiet fault i the device. Soft eos occu whe the collected eegy Q at a paticula ode is geate tha a citical chage Q citical. Soft Eo Rate (SER) ca be estiated usig the cocept of citical chage. Hazucha ad Svesso [] poposed the followig odel to estiate the SER: Qcitical SER N flux CS exp, () Qs whee N flux is the itesity of the euto flux, CS is the aea of coss sectio of the ode, ad Q s is the chage collectio efficiecy that depeds o dopig. The SER of a copoet ca be educed by ipovig a paaete i Expessio (). Fo exaple, thee have bee studies [2][2] deostatig how supply voltage (theshold voltage) ca affect the SER of a copoet. Expeiets i these studies show that iceasig the supply voltage ay ipove SER. Howeve, it also advesely affects the obustess of cobiatioal logic. Theefoe, oe ay eed to appoach to the desig pocess fo a diffeet agle to ipove the eliability of the fial poduct. Soft eo susceptibility of diffeet ipleetatios of a copoet ay vay fo each vesio. Cosequetly, these copoets ay have diffeet eliability chaacteistic, which will be detailed i the followig subsectio. Based o this, we diect ouselves to fid oe eliable desigs by usig available copoets istead of chagig ay paaetes i Expessio () ad ot affectig the hadwae quality of the copoets. By doig so, ou appoach bigs bette eliability to the fial desig while ot educig its quality Reliability chaacteizatio based o soft eos Cuet libay chaacteizatio effots [3] focus aily o latecy, aea, ad powe. Howeve, it is equally ipotat to study the soft eo susceptibility of libay copoets so that oe ca coduct a tadeoff aalysis betwee eliability ad othe etics, which is citical fo ou puposes. Efficiet soft eo fault ijectio ad siulatio techiques [4] ca be used to evaluate the soft eo susceptibility of a libay copoet. Specifically, fo each copoet, each of the odes (gates) i the etlist ca be chaacteized idividually to deteie thei soft eo susceptibility by fault ijectio ad siulatio. Afte this step, by aalyzig the itecoectio of gates i the etlist, the oveall soft eo susceptibility of the desig ca be deteied. Fo ou esouce libay, we ipleeted thee diffeet addes (ipple-cay adde, Bet-Kug adde, ad Kogge-Stoe adde) ad two ultiplies (cay-save ultiplie ad Leap fog ultiplie), each havig diffeet aea, pefoace, ad eliability chaacteistics. We use a thee-step appoach illustated i Figue to estiate the eliabilities of these copoets ad thei diffeet ipleetatios. I the fist step, we deive the Q citical values fo cicuit siulatio. Fo exaple, we deteied the Q citical values fo ipple-cay, Bet-Kug, ad Kogge-Stoe addes as 59.46e-2 C, 29.7e-2 C, ad 37.29e-2 C, espectively. The, usig these Q citical values fo each ipleetatio, we estiate the SER values fo the coespodig ipleetatios usig Expessio (). With the sae techology geeatio, N flux ad CS ca be chose to be the sae fo diffeet cicuit ipleetatios. With the assuptio of uifo euto flux [2], Q s ca also be chose to be sae fo two cicuits. Thus, the SERs fo two cicuits that pefo the sae fuctioality ca be elated to each othe as follows: Qcitical Qcitical 2 SER = SER2 *exp{ }. (2) Q Qcitical Reliability SER Nflux CS exp 3 R( t) = exp{ λt} Figue. Q citical, SER, failue ate, ad eliability elatioship. s Qcitical Qs 2 SER λ =SER Failue ate 2 Poceedigs of the Sixth Iteatioal Syposiu o Quality Electoic Desig (ISQED 5) /5 $ 2. IEEE

3 The ext step is to elate the SER of each copoet to its eliability. Reliability is defied as the pobability with which a copoet will pefo its iteded fuctio satisfactoily fo a peiod of tie [t,t], give that the copoet was wokig popely at tie t. To calculate the eliability of a desig, we should deteie its failue ate, which is the pobability with which the desig will fail i the ext tie uit, give that it has bee wokig popely i the cuet oe. We ca elate the eliability of a copoet to its failue ate by the followig distibutio fuctio: R( t) = exp{ λt}. (3) We use the SER of a copoet as its failue ate, assuig that evey soft eo will esult i a failue. This is show as the secod step i Figue. The, we deteie the eliability of a copoet, which is the thid step i the sae figue. Note that the eliability of the ipple-cay adde is set to.999; ad the eliabilities of othe copoets ae deteied based o this value, usig thee steps depicted i Figue. We used the MAX layout edito tool ad the HSPICE siulato to ipleet ad siulate the diffeet vesios of copoets. Table shows the oalized delay ad aea values ude colus two ad thee, espectively. The colu fou gives the eliability values fo each esouce; estiated usig the steps explaied above. Sice we wat to copae ou appoach with a edudacy-based solutio, we pefoed expeiets with duplicated esouces as well. The aea of a duplicated esouce is assued to be twice the size of its oigial (o-duplicated) vesio, igoig the aea of itecoectio ad the checke cicuity. The eliability of a duplicated esouce ca be calculated usig the followig equatio: R d = R + R2 R R2 (4) Fo exaple, while the eliability of adde is.999 without ay edudacy, its duplicated vesio has a eliability of The aea ad eliability values of the duplicated esouces ae show ude the colus five ad six of Table. I all of ou expeiets, we use the values give i this table Desig Reliability I ode to copae the eliability of two alteate desigs with potetially diffeet vesios of esouces, we eed a echais to evaluate the oveall eliability of a desig. I high-level sythesis, to have a successful executio of a etie desig, all the copoets of the desig ust succeed (i.e., opeate without failue). Theefoe, to expess the eliability of the desig, we adopt the followig foula: R s = R i Table. Aea, delay, ad eliability values fo diffeet adde ad ultiplie vesios. Resouce type Delay (cc) Without duplicatio Aea (Uit) Reliability (5) With duplicatio Aea (Uit) Reliability Adde Adde Adde Multiplie Multiplie It should be ephasized that we oly coside o-hieachical data-flow gaphs i ou expeiets, i.e., we use data-flow gaphs that do ot cotai ay bachig o iteatio costucts. 4. Poble defiitio ad ILP foulatio I this sectio, we defie the poble of eliability-oieted high-level sythesis, ad explai ou - ILP foulatio fo the stated poble. ILP is usually used i the optiizatio pobles, i which evey fuctio ust be liea, ad solutios to each vaiable ust be iteges. If each vaiable is esticted to be eithe o i the ILP, it is called - ILP, which also kow as ZILP. 4.. Poble defiitio Iputs to ou high-level sythesis faewok ae a data-flow gaph ad a esouce libay. The data-flow gaph is a pola diected acyclic gaph G(V,E), whee the sets V={v i ;,,,} ad E={(v i,v j ); i,j=,,,} ae the vetex (ode) set ad edge set, espectively. While the vetex set epesets the oe-to-oe coespodece betwee the opeatios ad odes, the edge set epesets the data depedecies aog odes. The secod iput to the faewok is the esouce libay, give i Table. Each esouce i this table diffes fo othe esouces by havig diffeet aea, delay, ad/o eliability values. Note that we also have ultiple ipleetatios of a esouce with diffeet aea, delay, ad eliability values i this esouce libay. Thee ae also aea ad pefoace costaits (epeseted by A ad L, espectively) that ae specified by the desige. The esultig desig ust satisfy both the aea ad pefoace costaits. The poble addessed by the eliability-oieted HLS is to schedule the data-flow gaph with available esouces such that the aea ad pefoace costaits ae et ad the eliability of the oveall desig is axiized. To achieve this, ou HLS faewok selects the ost eliable esouces fo the esouce libay, obsevig the bouds ILP foulatio To ake ou ILP foulatios easy to follow, we stat by pesetig the otatio used i ou foulatios. Table 2 lists the costats ad vaiables used, ad thei defiitios. Fo the uified schedulig ad bidig poble, we defie two biay decisio vaiables subscipted usig two idices X = {x is ;,,,; s=,2,..,l+} ad B = {b i ;,,,; =,2,,}, whee the fist idex fo both the vaiables epesets the ae of the ode (vetex), icludig souce (v ) ad sik (v ) vetices. The secod idex i vaiable x epesets the stat tie of the opeatio. We stat by schedulig the souce ode at cycle, ad schedule the sik ode at a give latecy L plus oe (L+). The idices i vaiable x idicate which opeatio will stat at which cycle; i.e., x is is oe if ad oly if ode i stats at step s. I vaiable b, idicates the esouce that ca be apped to ode i. Note that the esouce libay ca povide a vey lage ube of esouces fo a opeatio, which ca be used by ou appoach as log as the esultig desig is withi the bouds as idicated by the total aea costait. The idices i vaiable b idicate which ode is boud to which esouce type; i.e., b i is oe if ad oly if ode i is boud to esouce. Afte havig defied the vaiables ad costats used i 3 Poceedigs of the Sixth Iteatioal Syposiu o Quality Electoic Desig (ISQED 5) /5 $ 2. IEEE

4 TABLE 2. The costats ad vaiables used i ou ILP foulatio. Notatio L A a R N i t d j T y x is b i k is the foulatio, we ca ow peset the costaits ad objective fuctios. Fist, we foulate the stat tie of each ode. I the schedule, each opeatio has to be stated oce. Cosequetly, the followig stadad expessio states this costait [5]: L + x is s= i : = ; i (6) We also equie each x vaiable to be a o-egative itege: x {,}; i ; s L + (7) is We the eed to foulate the bidig ifoatio. Each opeatio i the fial desig should be boud to oe ad oly oe esouce, which ca be expessed as follows [5]: b i = i : = ; i (8) Note that i this foulatio, we oly bid the odes to the esouces with coespodig type. We also equie each vaiable b to be a o-egative itege: b {,}; i ; (9) i Sice ou esouce libay has ultiple ipleetatios of a give opeatio type, thee ae ultiple possibilities fo a ode s executio delay. Thus, we use the followig expessio fo expessig the delay of each ode: j () I ode to esue coect schedulig, the sequecig costaits ust also be satisfied. A sequecig costait states that the stat tie of opeatio i ust be lage tha o equal to the stat tie of ay of its iediate pedecesso j plus d j. L+ i, j : s xis s x js d j ; s= s= () i, j : ( v, v ) E i Defiitio Maxiu allowable latecy Maxiu allowable aea Nube of odes i the data-flow gaph Nube of esouces i the esouce libay fo each type Aea of esouce Reliability of esouce Reliability of ode i Delay of esouce Delay of ode j Oveall eliability of the desig Nube of type esouces used i the desig Vaiable associated with schedulig ifoatio of ode i x is is if ad oly if ode j is scheduled to step s; othewise. Vaiable associated with bidig ifoatio of ode i b i is if ad oly if ode i is boud to esouce ; othewise. Vaiable associated with schedulig ad bidig ifoatio of ode i k is is if ad oly if ode i is scheduled i step s ad boud to esouce ; othewise. d = j t b j = L+ j Fially, we have to expess the aea costait. To do this, we have to fid the axiu ube of istaces fo each ; esouce used i the schedule to deteie the total aea of the desig. The followig expessio is used fo this pupose: : s= i (2) Sice a liea solve caot solve the o-liea iequality give i Expessio (2), we defie a vaiable with thee idices, k is such that k is is if ode i is scheduled at step s, ad is boud to esouce. This vaiable ca be expessed as follows: i, s, j : xis + bi kis ; (3) i ; s L +; Afte this, the k is values ae plugged ito the left had side of Expessio (2) so that the foulatio becoes liea. Afte fidig the istaces of each esouce, the total aea of the desig is foud by addig the poduct of the aeas of esouces ad thei istaces used i the desig by Expessio (4). Obviously, the total aea cosuptio ust be boud by A. = a y A (4) Havig specified the ecessay costaits, we ext give ou objective fuctio, which ais to axiize the oveall eliability of the desig. To do this, we should assig the eliabilities of coespodig esouces to each ode: N = R b ; i (5) i = i The, we eed to deteie the eliability of the oveall desig by ultiplyig the eliabilities of each ode, as show i Expessio (6). Howeve, this equatio caot be solved by ay ILP solve sice it is a o-liea fuctio. MAX: T = N i (6) Alteatively, we ay have used a logaithic equatio, give i the followig expessio: log T = log( N i ) = log N (7) This equatio ay seve fo the sae pupose as Expessio (6). Howeve, we also eed to e-wite Expessio (5) i a logaithic fashio to be cosistet with Expessio (7). Sice the logaithic tes could ot be used i Expessio (5), we use the suatio of the eliabilities of each ode, istead of takig thei poduct as ou objective fuctio. This ca be expessed as follows: MAX: T = N i i (8) We calculate the total eliability of the desig afte ou ILP solve gives a solutio. Fo the exaple desigs we tested, we veified by had that Expessios (6) ad (8) esult i the sae fial desig. I fact, sice the eliability values of the copoets ae vey close to (oe), Expessio (8) ca be eployed safely to fid the optial desigs. We ipleeted the ILP foulatios usig a publicly available Mixed Itege Pogaig (MIP) solve []. 5. Expeietal esults L x is b i y ; I this sectio, we peset expeietal esults 4 Poceedigs of the Sixth Iteatioal Syposiu o Quality Electoic Desig (ISQED 5) /5 $ 2. IEEE

5 illustatig the ipact of the poposed appoach by copaig it with a alteate schedulig schee. We also copae ou esultig desigs with those obtaied fo the pio wok that eploys edudacy-based eliability ehaceet. I ou expeiets, we used two high-level sythesis bechaks: a autoegessive lattice filte (AR) ad a 6 poit elliptic wave filte (EW). Fo the esouce libay, we use the esouces listed i Table. We fist illustate the ipact of ou appoach o two diffeet desigs, i.e., the AR, ad EW filtes. The, we peset a copaiso of ou appoach with the solutio peseted i [8]. We also show the esults whe ou appoach is cobied with the ethod peseted i [8]. Note that, we eploy duplicated esouces oly i the last expeiet. I the fist expeiet, we schedule the AR filte with two diffeet appoaches. Figue 2(a) shows the fist appoach that uses oly oe ipleetatio (vesio) fo each type of opeato (ode). We choose this schedulig schee to show how ou appoach beefits fo eployig ultiple ipleetatios of copoets. I Figue 2(a), specifically, we estict ouselves to type 3 addes ad type 2 ultiplies, ad pefo schedulig ad bidig without cosideig eliability. Note that, if we have used othe adde o ultiplie vesios, we would ot be able to eet the aea o pefoace costait. I copaiso, the schedulig esulted fo ou eliability-oieted appoach is show i Figue 2(b). The latecy ad aea bouds fo these two desigs ae 8 clock cycles ad 24 uits, espectively. The esultig aea fo the fist desig is 24 uits (two addes of type 3 ad fou ultiplies of type 2), while its eliability is.564. O the othe had, ou desig has a eliability of.5834, epesetig a 3% ipoveet ove the fist desig; ad its aea is the sae as the fist schedule. To achieve highe eliability, ou solutio uses oe adde of type, oe adde of type 3, fou ultiplies of type, ad oe ultiplie of 2. The addes of type 3 i Figue 2 ad Figue 3 ae filled with dake colo to distiguish the fo the addes of type. I ou ext expeiet, we evaluate two possible schedules fo the EW filte with a 4 clock cycles of latecy ad 8 uits of aea bouds. The two schedules ae illustated i Figue 3. The schedule i Figue 3(a) esults i a eliability of.45587, equiig a aea of 6 uits (thee addes of type 2). Note that, we caot eploy othe vesios of addes fo this expeiet if we ae to eet the specified aea ad pefoace costaits. Ou appoach (show i Figue 3(b)) leads to a total aea of 8 uits (two addes of type, oe adde of type 2, ad oe adde of type), ad achieves a oveall eliability of.8767, a 77% ipoveet ove the fist schedule. x Step x2 x3 x4 Step x5 x7 Step x8 x Step 4 x x9 x2 +24 Step x6 x2 Step 6 x2 x9 x Step Step (a) Figue 2. Two possible schedules fo AR filte with L=8 ad A=24. x +5 x2 x x6 x x x9 x2 +24 x x2 x2 x (b) x4 x x8 x7 Step Step Step 3 Step Step Step Step Step Step Step +8 Step Step Step 3 Step (a) Figue 3. Two possible schedules fo EW filte with L=4 ad A=8. These two exaples show two ipotat cotibutios: Icopoatig eliability as a fist-class paaete ito the HLS bigs sigificat ipoveets o the oveall desig eliability, ad By eployig ultiple ipleetatios of esouces, each havig diffeet eliability chaacteistic, oe ca ipove the eliability of fial desig. I ou last expeiet, we ake two copaisos. Fist, we copae ou ethod with the oe poposed i [8] by schedulig the AR filte with vaious aea ad pefoace bouds. The easo we copae ou appoach with [8] is that it uses eliability as a ueical etic as ou appoach does, ad to the best of ou kowledge, it is the oly study i this cotext pio to ou eseach. While the ethod peseted i [8] uses edudacy to ipove oveall desig eliability, we do ot eploy ay edudacy i ou desigs. Ou secod copaiso is desiged to show the ipact of a uified schee (i.e., we cobied the ethod poposed i [8] ad ous). Specifically, we use edudacy (based o [8]) followig ou solutio explaied i this pape as fa as the aea costait peits. That is, fist, ou appoach fids a solutio without duplicatio, ad the we add edudat esouces as log as we eet aea boud. The, we copae the esults of this uified schee with those obtaied though [8]. The esults fo this expeiet ae show i Table 3. The colus oe ad two i this table list the specified latecy ad aea costaits, espectively. The colu thee shows the eliability values obtaied by [8], ad the colu fou gives ou oveall desig eliabilities. The colu five gives the pecetage eliability ipoveet povided by ou ethod ove [8]. As ca be obseved fo this colu, ou ethod obtais oe eliable desigs ost of the tie, eve though we do ot exploit ay edudacy. Howeve, as we stat iceasig the aea boud, the eliability values foud by [8] also icease ad stat to outpefo ou ethod. Note that, a egative value i this colu eas that the eliability value obtaied by [8] is bette tha ous. The easo fo egative values is that whe we have tight pefoace ad aea bouds ad we have to choose the ost eliable esouce fo a opeatio, [8] selects a (b) Poceedigs of the Sixth Iteatioal Syposiu o Quality Electoic Desig (ISQED 5) /5 $ 2. IEEE

6 L TABLE 3. Reliability values ad ipoveets ude diffeet latecy ad aea bouds. Bouds A Ref [8] Ou ethod Ipv (%) Ou ethod + [8] Ipv (%) Solutio tie(s) duplicated esouce with highe eliability while we have to select a o-duplicated vesio (Recall that we estict ouselves with oly o-duplicated esouces i this expeiet.) Fo exaple, fo a adde selectio, [8] selects a duplicated vesio of adde of type 2 while we select a o-duplicated vesio of adde of type 3, which cosues the sae aea but is less eliable tha the duplicated vesio of adde of type 2. I the colu six, we show the eliability values obtaied by the uified ethod, which is the cobiatio of ou ethod ad [8]. The ipoveet coig fo this cobied ethod ove [8] is show i colu seve. These ubes show that the cobiatio of these two ethods gives bette esults tha the ethod peseted i [8]. As ca be obseved fo this table that, soe of the eliability values i colu fou ad colu six ae the sae. This is because thee is ot a aea slack that ca be exploited to eploy edudacy to the desig ude the give aea costait. This expeiet poves the effectiveess of ou appoach, which bigs sigificat eliability values to the fial desig. We ca coclude fo these values that usig ultiple ipleetatios of the esouces, the desig eliability ca be ipoved eve we do ot eploy ay edudacy. I a vey tight aea ad pefoace bouds, ou appoach bigs up to 62% ipoveet i eliability. Fially, the colu eight gives the CPU tie of ou ethod fo each desig i secods, which is a ipotat facto fo ILP based solutios. I geeal, the tie coplexity of ILP is vey poo copaed to heuistic appoaches. Howeve, ILP ca fid the optiu o ea to optiu solutios. As ca be see fo this colu, the ILP faewok fids the solutios i easoable aout of tie fo the AR filte. Note that, these solutio ties (i Table 3) ae withi the toleable liits. 6. Coclusios Eve scalig pocess techology cobied with powe-savig techiques such as voltage scalig ad copoet shut-dow akes cicuits oe vuleable to soft eos tha i the past. To have a oe eliable desig, eliability eeds to be addessed as a fist class citize i both hadwae ad softwae. This pape focuses o high-level sythesis ad pesets a eliability-oieted appoach to addess the gowig soft eo poble. The ai idea behid this appoach is to icease the eliability of the desig as uch as possible, bouded oly by allowable aea ad latecy. As opposed to the pio wok o the topic, the poposed faewok accoodates diffeet vesios of the sae type of esouce, each diffeig i pefoace, aea, ad/o eliability. Ou expeietal evaluatio idetifies the cases whee oe ca expect the poposed appoach to be bette tha the pio poposal. We also discuss how ou appoach ca be cobied with the pio wok to achieve eve futhe ipoveets o eliability of the desig ude cosideatio. 7. Refeeces [] J. F. Ziegle et.al. IBM expeiets i soft fails i copute electoics ( ), IBM Joual of Reseach ad Developet, 996. [2] V. Degalahal, R. Rajaa, N. Vijaykisha, Y. Xie, ad M. J. Iwi, The effect of theshold voltages o soft eo ate, 5th Iteatioal Syposiu o Quality Electoic Desig, Mach, 24. [3] K. Johasso, P. Dyeklev, B. Gabo, M. Calvet, S. Foutie, ad O. Feuillate, I-flight ad goud testig of sigle evet upset sesitivity i static RAM s, IEEE Tasactios o Nuclea Sciece, 45: , Jue 998. [4] P. Sivakua, M. Kistle, S. W. Keckle, D. C. Buge, ad L. Alvisi, Modelig the Effect of Techology Teds o the Soft Eo Rate of Cobiatioal Logic", Iteatioal Cofeece o Depedable Systes ad Netwoks (DSN), Jue, 22. [5] H. Achatz, Exteded / LP foulatio fo the schedulig poble i high level sythesis, EURO-DAC 93 with EURO-VHDL 3, 993. [6] B. Ladweh, P. Mawedel, ad R. Doe, OSCAR: Optiu siultaeous schedulig, allocatio ad esouce bidig based o itege pogaig, EURO-DAC 94 with EURO-VHDL 94, 994. [7] S. Chaudhui, R. A. Walke, ad L. Raachada, Aalyzig ad exploitig the stuctue of the costaits i the ILP appoach to the schedulig poble, IEEE tas. o VLSI, 994. [8] A. Oailoglu ad R. Kai, A Desig Methodology Fo The High-level Sythesis Of Fault-toleat Asics, VLSI Sigal Pocessig V, 992. [9] L. Guea, M. Potkojak, ad J. Rabaey, High level sythesis fo ecofiguable data path stuctues, Copute-Aided Desig, 993 [] A. Atola, V. Piui, ad M. Sai, High-level sythesis of data paths with cocuet eo detectio, Defect ad Fault Toleace i VLSI Systes, 998. [] P. Hazucha ad C. Svesso, Optiized test cicuits fo SER chaacteizatio of a aufactuig pocess, Solid-State Cicuits, 2. [2] P. Hazucha, K. Johasso, ad C Svesso, "Neuto-Iduced Soft Eos i CMOS Meoies ude Reduced Bias", IEEE Tas. Nucl. Sci., vol. 45, pp , Dec [3] B. Ackalloo ad D. Gaitode, A oveview of libay chaacteizatio i sei-custo desig, Poceedigs of the IEEE Custo Itegated Cicuits Cofeece, 998. [4] R. Leveugle ad A. Aai, Ealy Fault Ijectio i Digital, Aalog ad Mixed Sigal Cicuits: a Global Flow, Poceedigs of Desig Autoatio ad Test i Euope, 24. [5] G. De Micheli, Sythesis ad Optiizatio of Digital Cicuits, McGaw-Hill, 994. [6] M. Bekelaa, K. Eiklad, ad P. Notebaet, lp_solve: Ope souce (Mixed-Itege) Liea Pogaig syste, Vesio 5... dated May 24 6 Poceedigs of the Sixth Iteatioal Syposiu o Quality Electoic Desig (ISQED 5) /5 $ 2. IEEE