M) A 13' 20R STA IST ICAL DATA PROCESSING SYSTE[M MlnDl ING ANDRELIARBItIY(U 'STANFORD UNIV CA I KAILAT FT At.JUN 83 AFOSR-TR 83 0935 F49620 79 C 0058

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Bol AF BaNs 1W. ouum or NaaP -Su) Snl

Cm~~~ 'lbsV WSAM ofU~ AMsaro DesOib) herei was; eCloe' seofa t ethipobs instaistcaldat prcesingandsysem odeing wih prtCuMSpFect. h

19. pKeyOMsenttion wil be in ON,, me sdetions onein toe OEeeM"*t o

the&i oofrsearcha esiraieori me. kailore svera a1 nand prblm oif:

1. Anaysis of Nonstatimmay sip"a prooesse8. Aloritlas for gats on~se ost. en bash

omt.1amwml'=

CUF 'AcvYv CLAMWSCAIQU OPP yMfPAOu9uMbwWMm o ag.ae.~ LASSIFIED

3. Reliable VLSI Comting Structures4. Algorithmn and Architectures for Statistical and Data Processing

XTIS GRA&IDTXC TABUnrannouncedJustification

Distribution/ 9W~ .~s m

A APOSUTh 83-0 93 5 h

mar 1 s - Jame ^S 1963SttltlalDo" Prsu Ib Sam Mlsde : Ad RehbOW~

Rebert IL GrowAbbes 31 Gamng

7he, aim of research drbed heres was explore svel fadaniental prob.

lena. in statistical data processing and, syste m odulig It paricla apets

e results obtained have almost, completely bees decibe in publishe jwmrsal

Fand conference papers, so this report will focus on a summary of major results.

The presentation will be in separate, sqctomPENs F rrl s -to the dart of

the, co-priscipal ivestigators, - T. Kaflath, R. Gray, A. El Geam anKe Mart:

Aalysi of SPAtioar S i e om.

9,.&- Algorihm 1hr Data Coonw-sJ

9-.* RA" VnX Computing ftneturesOw L

,9- .Api4#a a *mn fa Sttistical and Dat ?roceinw

1. As*A1n of Neat rhes toebasde PrNOMSe (T. Kafmib

the OaW of t psmeothbas besf to develop a Tuisty of issal P Mn

algestbe w" it mp s" C an ~ r prose..., redue wd.sptslmy

deab Id a0uuelk w A AM*Oft oby&

83 1 29 2 0,

Cb F -sk 1 prcesss baed o

deopa Im &%td IiiTdy6 4kewi MY-rcmg

1.Chra tiation, and apaduh~re Abf-nbimx ro..bsd

hnotion 'of displacemenit rak of a covaianc was utilized to construct

efficient parametrization Of ammitaimary diuctete-tme secoad-order process.

geveraldist Ideft Mori ed 40164 shaidfg a' omm set Schur

COCejk which Sri a guea~alm4te~la., r~leia orprta

eovrdtixs) coefficients, aseeod wit W" th, s noaei Ike cur

coellicienits, ad an additiona sot of tmei44in eaeies seiVe ains

in lattie-fam modeling ad whilmma kiensfrqmsaim mws Those

lattice filt. now d omh fa pm r setomu; th0* tlme~axatiom

requied lse gr owth is tia of the Le a"e.

illamatdo the igmicame ami vewmihl *6 theMu W ~ e

Thi amaytea Poeedue, madoef hemalal by flchw (o"7 hrjelm

theerath uAwlmmat has be &amu~vre wr b. n dm'

kmm It emans isn11M *ete W tim aft" M~ n~e'7 4 t 7171,7-an~~~emia~i =a y~ ssel~a no u AN& Am5

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sun. *-n ~ --. 4-

-AIR FR= OLIrncOr SOWII MUM (*70)*nzle 01P IRUMWT?*z to melThis to&VwIoaa report has bess reviewed and Isapproved tor publ to release 1AN AIR190-12.Distribution Is wgl~itd.

4- NAMAt . uChief, ftesbaial fteuuwatiu "vision

numerOus effaIsS of the Peedur M to ated it to Wcke dm

It &bes Spar" S $WMs of_ My results Li the theoY of tmetse seattet.

of statlsiary prect"OnZ ms~f~~V-s~wiae btaineA by lNer

time avauiaut (LII ktg GttaloS ryM Proesses, Posses the same structumral

pssc~ v"u w e dt quui-atehlb7 a s, articular cm ae lattice models

of Mowe cwmoault, but atil share SMY Or"pe"e Of utaiar'y ovarlances.

Another Outeotue og the amis&of matatinary proc...s is the formula-

tiwo of a -Mawd tuofseta abifory autprcss Our results

ncdeas piiiatcsteptitydvhe tkeory of asympvtotcally a.

-, aympotkatsas sAtoay aid Paumsbsjroceses. Our

anly provides also a *W&V4 ~~m~t'et Wieera W enle harmomic

anluf*, Sbrowd gk* 1oft na 1 prou

Se~ealapwhe". boo vdtts 6gog.t~es, 044a wlA a pat

a" ILebs ~ i6m* 1 toapar" It die All 1 me.ia em

*I~~~Is~~i*.sf 1,ei1 MAus Is n S 3 a aote Paper is

MONm.t~a~hCeoe W

t WIN,

. .~ .....

th ea * OW imWWodb w 4rfSMW*M ds

uipPtAinawshwh the

adaptve Ut., dkfetly o~mpw *%pdt imdowl "~ mob*u ja on We

bave dwvehpw 'mm mw W akt &We4.wdw, i*q abpumm ie

4w, 04-"hy-Jh~e 44A9Av OWNi *A, sbuim eIm $I elw qiedow per

iteatip aad ehbit biter vwAsmei pmopus h Aepb un u

K~ba 44a a~lti of urV LJWAud AdMOM:ser bW1 I N* hmUM t"e

stochatic-padhma or US ada$5vbwidwh pf W~d.w _4A 14t mem now,

behaviw r a umode imareaLe.

wide rap of praeo* affaesIOm s tam e~a~ * 6W Xainwk

In Ase coursof *s theaumw " 'Oth~msvwdbi

the Faa ;-Kha4Ih~h ~ ~ ~ d P ir,,e ;~ ~ m ,~ .f IW~ - m~

W& se The -dd at ow gumiel lisiks gok am b amw$ .hw

...... MO " 0a

zo1.

simple miodification of the new &Ipdltmmo, 1 au'Llj~fuy Wdtmof e

"m"m of thorn b"ii cosmlitwop throsto # spart-cssimt is am o rmitte to

reduce the elects of noise upon a good nial c Wdais.

In related work, sa egtteatuseqaspocdr sdvepdfr

the adaptive 6adjust t of.a bhat**span e~d equsliwer A (FM) tnmbol

hte~elatoCC. the du&e thft L r!@e ep a- s" by, td& wew procedur. to

reduce computatiamal requiremnts and to Improe comvergmsnc. For a T/p FSM,

a facor of p Impovuuiemt in 4itwsp" timeis attUnd adi" to Soe =&~cAm-

awl FBI vusbuss of the eustequaoo algthzin o FahOsmt aa Lju jif! ead

of Satoriw and Pack 11"4'~ AddftluAl redoo$lam in LOomlPstet"* require

musats are acheved by a upecial eatlm-suv modlcatom for the pauband

-N"Nyu" FSM structre of Mueller and Wwmew Te pocedure In ibm to be

mat ebe.Uy S.me I ~tv R rosasialo 4d*e fat

e~ct.eIes W O alr dMs h .du apt~m~tqim of

tho new procedure (T/4 FM) bs bA to be appi bowdovqy as tMai of

60 icA do-adt alI at 0116I, bodu " ndWebonstn fIN) Mas&

t 41

io I

*wso Is #A IN

-

1.-4

M. L Vwulu amd I7. Ka"ht, -~On GiewWUii"mu Rwsimn.., 1=~f r. ou AvtimComb,, VA AC-U., so. 3, pp. 334M, Aamt M!LS

B. Pert ned T. K~sa", '%rmlhsod Latiw Mpdtbim for Lewbdpnous StmIdeatiea"~,* MW Tr. AS5P, Vet. A58P41, so 1, pp, 1281Sk Frnq 1183h

W. RL Kwom, A. AL flid wed Ti. Kabb, -*bfb ft&F*kp via dwMw

T. Ka"i nd IL )PocM *mfAhpws. ip*si Amr asegmst P*uemb I& EarmwxAndpi. w efs ~i~n flw P. Manma kDbt VIelm, ii. by IL Sahb and V. MmiawebiNorah Ilma& M12.

T. Kailmob ad L. Linu&g -Two.PFtm Smtiag Fanslp by Daslato f theHtonms 00016W' 3.1 J. OiNWb: VOL. 36In 4, lP6 tf4f3, Oct~bdrt 82

B. PeraI, -Ile Un of PwWs -einb4 PMmalkd tUatls AlgulSmi?, a= 2rve. amAWt~m. Combt., Vet. AC-27, so, 4, pp. 1"410 Asuat 1182.

C. B~la.,"A UAW TWOWuu4"aVt A l3Ia iforiis Uldutesaos 3W.1 i~rsuI Cewtrt,

C. Ssimmos, "-A Ad* L4Q Maelssbr fur Samidblm Pime ftdma, Imtwnsia.

takn f kmm&*mk Aedhal **. AM I'me. o. AAYW, V.6. ABaS, .a

"'T -A AL-L- O- -

T. a&*mh Up~hm or W NJ1WW.hIW Mo -eum &RAWt Waf VAIK 04

VOL Skm 1& 6 sg w ~ .~8 ONKI wa wu~e' iV~W h

........ .....

ATM W~ai

~~7 77, .,

Traw. Avim Guusty. Vol AC4s, w4, pp. 111,Augmt MI.

K. Wax, "TAe helmoe of Time. Dehy Dstwea Two Sigmi with Ramioms Relative PhseeShbt' MW Tram&. on Aouad , Spook& 6 S#Wo Preenusba eL~ AM-U, no. 8, pp. 4W-MI,

Ph D~sate, Y. aspla aed Y. K~amp, "Guouaised Isbu Repreentisms of Matriu.Valued Fu.tioms SUM L. A*p D~imo MuM, Val., s. 1 S pp6 W47,W km 1081.

V. U. Raftl, 3& Kp~dt ad T. RaM~ OpbedeWP~ Adaptive Lib. hobwmer for aSlaumoidal SIWW k adbad Neh.', AM r..,. .. 0Mebi 6 fpce, Val. CAS-2k %*. 6,pp. 6434-0, Jun. 11061. Als 1KW Tram on ASS, VoL ASSP-IS, so. 3, pp. 702-710 kmg

T. Kala, -Redheler Scsaring Theory anid Linar State. Space EstImation Problems',Rkverchc &1 Automauics, Specia ame an Math. Physics and System Theory, VoL 10, no. 2, pp.136.166, December 1979 (appeared 1061).

D.T.L. Lee, M. Meat ad B. Friedlander 'Recursive Leadt Squares Ladder Estimation A*&.rithus' spal joint ham. of I=E Trans. Circuits and Spitrem, Vel. CAS, No. 6, pp. W6-081,jun. 1061.

G. Verghese mmd T. KAMlt, 'Rational Matri Structue', I=E Trans. Avlem. Ceosr., Vol. AC.26,no. 2, pp. 434-430, AtarI 1961

S. Wood ad Xi Mouf *A Fast lm lstatift of a Mflnimum Variance Estimao for Computer.ised Tomegrapby Image RecnRUcti, fE Trans. B1-Me"ia Emgiseari, VoL BUMS2,pp. 86.66,February 1os1.

T. Kabth, -Som Aternatie Is Recusive Resain, Ing. L. Centiro& Vol. 32, no. 2, pp. 311.328, Avg"a IM6.

0. C. Varghse, &. Frledle aid T. Kalath 'Senthein Thesmy and Lbnea LestSqueresEhtinlonP M.D Th. Estimates, I= Trut Anbus. Cenlr., Val. 2k, no. 4, Wp 7940%

S-Y. Keg sad T. Kailet, 'Put Pueecis Melbods for bGima Desin Probm Is Lbnea Sys-Ji tom Theecy', Automatics, Vol. 1, no, 4. w 3406,5* lIlL

T. Ks"t, Reiw al 'Vactushnthm Metbd hr Diserete Ssquentia heheati' by 0l. Dies.mim, MWTrusss h~r. V*, Vol fl4S, me. 1, pp 1.1, Jan ISK

T. IKallat 3& Levy, L. Lung ad Ai Maet. 'Tbe Faetubale ad Representas of OperatorsIn Tb. Algbr Geeaed tv TeepbsaentW, ANI. AppL NMg, Vol M? I&o. Wp 467.

3.D. Ash.. anil T. Xdkab 'iTu.. fNewo tyntb Via Deal Spectral Facut ea',AM rresu. Cbuu* 9 OpL, VAL CAS~A ms 13 pp lUP Oct. iVl

3a P dFedeg, N I 1'4 . Ke"~ A L I.. s *Ng bMe Wvuh Pandase hr UM"iseChbIn 6 %W of Ih* Dhkue 600n T~f MMbbu, Usee Abt$ .WkMWd* Ap#6w,VA .1, Wp 0%d Oat. MW

3.Lev T. LuBell L. I*"s ad N. AbmP 'P O mvub m btttiu

-wbom *"ot 4......... -

Oil~ -.---.- 174 , -aA

at

W-t 4 4xK vt,

~~~~ ,ApI itv &*pst

4*144 v%*-.

~ t ~bat.tY4-~ oI3Vrfl r4C.Iahb it4fi k kteo ;i *k maAi

,~. r .irca~ . . , *

W'I t44 "V$~ jortr1 V.rM t -

K ~ ~~~~~~~~ vo ~ r:~I 4 4.tjC

~6- tt ~~-s ~ I ~ V3t(~. AaE~*@7mw

~~AK A* 00~'

t -

Pubilbd Camhwrmse Pae.,

J. 14 Ciof ad T. Kailath, "Fast, Phido~rder, LintSquares Agoitm for Adaptive Fibter-INS 95 CSS?. pp. 87*68, Duis., MA, APOi 1IN&

M. Wax and T. Ksat, "E11cieat; lnveruion of Doubly Bloc Toeplits Mat&i,' 185 ICASS,pp 170-.173, April 1ISM Boane, MA.

M. Wax, T-J. Shins ad T. Kaflth, "Covariance Elgenstructure Appoach to 2-D HarmonicRetriffal, 1589 ICASSP 4949,ApE 03, vvftks MA.L

V. U. Reddy, T-J. Shan and T. Kadlt, "Application of 14.4usd Leaatqusre Algorithm toAdaptive Esh. CancebA&IOU 195IA 5?, pp. 6-58, Apt~ 10%3 flet., MA.

M. Wax, T-J. Sha ad T. Kailath, "Location and Spectral Density Estimation of MultipleSources,' Sixteenth Asilemar Cof on Circuit*, System. and Computers, pp. 322-325, PacificGrove, CA, November 1961

W. H. Kwou, A. M. Bmuckatein ad T. Kailath, "Stabilizing State-Feedback Design via the Mov-ing Horizon Method', 21st IEEE Conference on Decision & Control, Oado, FL, Doe. 8-14b

T. Kailath and H. Lev-rM, "Constant-Parameter Lattice Pilters for Nouttionary Processes,'3rd voue of 0.11.d t odeo. Mehkmuiiq... per L Automsfigue e'Asslpe it Spees, d etoTraftement do Sigw4 CNRS N.&sd Cen)t, Bille-Us, France, Sept.1282.

T. Kaflthb 'Real Time Statistical Signal Processing, Pr... Workaep on Information and Dee-lieu, best. of Infrm. Sciences, Academia Sinica, pp. 123-136, Taipei, Taiwan, Aug. 17,1981.

T. Kailath, - Rocent Developments in Statistical Signal Processing', Proc. IFAC Sp,,. on DigialContra& Pergaamon Press, London, 1962.

V. U. Reddy, F. K. Soong, A. Kt Peterson and T. Kailath, "Application of Leasto-Squares Algo-rithms to Adaptive Eeho Cancefltlion', hit 7.Symp. on Microwev.. .34 Comm., K~haragper,India, Doe. 29631, 191.

V. U. Raddy, B. Fgnrdt and T. Ks"~, 'VOa the Adaptive mpestal of Puarekos luar-amok Retrieval Mietd', IWl Svqp. on Morowase ad Comm., Kharagpsr, ks. De. 3041,

* ~1941. Alm. presented at the 15D Au~nw Coqf em Circuit, Soe .34 Computers, Now. 9-11,1981.

* H.~ Low-Mri sod T. Maind, 'On Generafsedl Ushe and Lvs-Ss Alwbh~ms Or Quais-timasy Pressem, M91 11W Couferee on Doe~.. end Ce.1v4 pp. 187-Oft San DlqsCA, Ducmber 1941.

T. KAlsth "TimuVand Thae'bwaerlst LaWs. Pb..e far Newsktlsuuy Preses', Pro.Foot Alps&% m Le' ..., Dpmkldtims, pM 417-494, Ameb, Pftes Uspt. 1-M5 MSLI I -R epr R""W Ousb of Medal. M.Ebemipwo w ht£ALeWmuitqo £~b bl*'Do~e Esi Loreteesuu Ds 5p*4 VAi %. od L 9. Landsu, 417.4%4 00%3 faeso IM

IL Lo'M a6dT. PKal Ib, " e Apsu0sMM 46 N. dh Pft@=s, huWerh~ep so Aflff 14, N lo a , O3s.~ Avg 1% USL

.10-

H. Lev-Ari and T. Kailatk, "Schur nad Levinson Algorithm for Nostdme Pr.em', Pm.1981 I E Cer. en Aceetic, Speech and S pgd Procswin pp. 86.S4, Atlanta, " March1981.

M. Wax, "ne Estimate of Time Det BEtw o Sib ih Random Redive PheShift', 1981 Int'l. Coat. on Acoustics, Speech & Signal Procesing, Atbata, GA, March 1981.

H. Levi-Ari and T. Kalath, "Ladder-Form Filters for Non tnsdonnr Process', 1 AWN Cw.on Dec en Control, pp. 90.91, Abquerque, New Mexico, December 160.

Y. Genia and S. Kun, "Ration, Aa with Hanhel- m Criterion', 111*f i C.on Deeben 8 Conlr., pp. 486-4M, Auqeqe, New Mexico, December 1960.

Y. Genis, 'Owo-Dimeuonal Rdectlos Coellients and HankNorm oproxim ', Pre.1080 European Con. en Cirevi Thg. 6 Doeos, Vol. 1, pp. 47.483, Warsaw, Poland, Sept. 15,1980.

Ph. Debarte, Y. Geaia sad Y. Kamp, "A New Algorithm to Perform LU Decomposition withApplication in 2-D Digital Filtering',EEE M In . Smp. en Cireit 6 Sde1em, pp. 210-212, Hoe.ton, TX, April 1960

G. C. Vershese and T. Kailath, "Rationsl Matrix Structure', Proc. 1811 IEEE Dec. 8 Coou.Conifer., pp. 1008-1012, Ft. Lauderdale, Florida, Dec. 1979.

G. C. Verabese and T. Kalat, "Eiseavector Chain- for Finite and dmite Zeros of RationalMatie, Proc. 1811. IEEE Dee. 5 Contr. Con., pp. 31-32, Ft. Lauderdale, Florida, Dec. 1979.

• .I .* sr '. - - - -- ' , 'P '

, . . - , ,

,, . .r. ... .. ... . ..i. ...

AempisdPapers

M. Wax, "Position-Location from Sems with Position Uncertainty.' I=E Trans. AES.

T. Kailath and M. Wax, "A Note on the Complementary Model of Weinert and Dessi,' IEEE

I Trans. Astern. Contr., Vol. AC-29, no.8.

T. Kailath, "Signal Procezrumg in the VLSI Era,' to appear in Modemn Signal Processing andVLSI, ed. by S. Y. Kung, H. Whitehouse and T. Kailath, Prentice-HD, 1964M. Wax and T. Kailath, "Diret Approach to the Two-Filter Smoothing Formulas,' fnjel J.ControL

A. M. Bruckstein and T. Kailath, "Modeling Rate-Modulated Selfexcitiug Pont Processs,,Conference en Syetem#, Man and Cybernetic, Delhi, India, Dec. 31, 1063.

H. Ley-Aui and T. Kailath, "Spectral Analysis of Nonstationary Processes," IEEE Imte4T SIMy.an Inform. Thyt., St. Jo wite, Quebec, Canada, Sept. 1#81.

M. Was, T-J. Shan avid T. Kailath, "Covarianee Eigenetructure Approach to Detection and Ewfi-motion byt Paeeive Arrays,' Pt. I. Diretion-ef-Arrival and Fr. queneat FAetmation of Multiple Nar-reoband Sources,* IEEE International Sgymp. en Inferm. Thu. Canada.

Ml. Was, T-J. Shan and T. Kailath, "Cewarianee Bigenetructure Approach to Deecio and E~ti-mation byt Passive Arrayse,* Pt. II. Source Location and Spectra( Density Estimaation of WidebandSources,* IEEE International Sun.,. on Inform. Thy., Canada.

B. Egardt, T. Kailath and V. U. Reddyt, "Hisgh-Revolution Spectral Analysis "apn Malti-Step Adap-tive Prediction,* Circuits, Sytemsen and Signal Proeeesinp.

Al. Was and T. Kailath, "Efficient Inversiom of Dovblat Block Toeplits Matrix~," IEE Trans. onAcoustic, Speech and Signal Processing,

Ml. Wax and T. Kailath, "Optimum Localization of Multiple Sevre in Passive Angie,' IEEETrans. ASS?.

. Lev-Ars and T. Kalt, "Lattice Filter Parametrization and Made&#n of NonotatisnaryPreeeses,' INE Tram. Informn. Thyt., VoL IT-8O, no. 1, 15M

T. Kailath, L. Ljung and M. Marf, 'Recurive Input-Output and St at e-S, ac Solution, forContinous-111m. Linear Est&ate Problem.', JIM Tram. Autam. Contr., Vol. 08, September

Iff

-n-

2. Algorlthms for Data Comprsdo. (. M. Grqy)

Research Objectives

The general goal of this project has been to develop computer-aided design

algorithms for data compression sytew and to study the reative performance,

complexity, and rate of such systms. Where possible, comparisons have also

been made with theoretical bounds and with traditional approaches. Particular

emphasis has been placed on vector quantisation (vector coding, block coding,

multidimensional quantization) systems for speech waveforms, for finear predic-

tive speech parameters, and for various random proceses.

Major A ompl MEAS

As detailed in the annual reports and in the folowing flat of publications,

the research effrt has been exceedingl fruitful in laying the groundwork for

computer aided design of a variety of data eompvlom Wytei. algorithm

of Linde, Buzo, and Gray (IM) for the design of locally optimum vector quan.

tizers which was developed with the support of this cotract has been extended

both by our Stanford group Ad by a severoelsue sItutha to devrp

moderate complexity I"w rto sd Toy low tote "et SMP~Usion qseM OW

speech wavedoran, voice aodes variom raadom puemem, ad, most recently,

* imag. Our pomp pomnerd e bie a*m md th of Uis =t impottant

varitlos tre sAre cods sd I I!des cod., h atiW to the melts of

this rm pre t, the ,ldatei e, deps by t. proe hos boee

mod in ote proe ad eter hiIlWem to sal mw .ppeatdto NywA. J

-13-

speech recognition systems based on vector qmantitatios and not requiring

dynamic time warping have been developed at the Naval Research Laboratory,

the University of Mexico, Osaks University, and Bell Laboratories using varis-

tions on our algorithms. Now low complexity image coding systems of rates less

than one bit per pixel have been developed using our algorithms at the University

of California, by our group, and by Mitsubishi Corp.

Part of the accomplishment of this project was the development of extensive

software for vector quantizer design and data compression simulations. This

software has been shared and extensively used by the Naval Research Labora-

tory.

During the Ainal year of this contract the emphasis has been on the develop-

ment of shape/gain vector quantizers, an example of product code quantization

systems that operate in a memoryless fashion on successive data vectors and

separately quantize a scalar gain -n and a vector shape term. The quantiza-

tions are coupled by the distortion measure so that the eucoder is optimal for

codes with this structure. An iterative improvement algorithm was developed to

yield locally optimum codes of the desired structure. The goal of this style of

code is twofold: To provide better dynamic range by separately treating the

energy and to provide a mesas of designing higher rate and hence better quality

vector quantizers with reasonable computational complexity and memory require

meats. Then codes capable of providing better peformance for a ixed rate

and complexity than the ordinary high omplexity vector quastim& -P.kei-

mary results for thes system wer is b Sab n and Gray (Is) ad a

414-

paper has recently bees submitted for subn~ds for publiuatlm A cop d thin

pape will be forwarded to the Air Force when complete as an epilogue to this

"a rPort

With the exception of the final paper being prepared, Al of the principal

research resuls developed during the course of this project have been reported ina

the open literature. Preliminary portion of the Ainal paper may*be found In the

conference proceediap of the paper by Sabia and Grm (1063.

With the termination of this contradt, the linage coding and the speech cod-

ing and recogniion work will continued with the support of the Army Research

Office and the Joint Services Electronics Program. Unlike the reearch reported

here, the future reearch will ocum on feedback var quatmr and Gatostate

vector quantizen instead of-the memoyls. vector quanthm of Ibi project. Li

and VLSI iraplememtatmim of vector quatlalm stm, with and without

mmy will be costhwued with'te support of A*e 5ht Service ElectroMles lo.

gram

Nbhbd Jourami (or book) Papms

Y. Linds, A. flea. wad R. KL Gray,$"An aipwtUbm for vector quanthze design,'MU Tresawm oan umuelise VoL. OOM4 pp. 84-46, January 10M.

Y. Yamada, S. Tazaki, and R. AL Gray, "Asymptotic performace of block qua.-tUlm with a differ... 4istortio =morw%* EN Tra~dions am hut rmetie

Mor.t, Vol I-2S, pp. 6-14, Jell. 1060.

A. Duzo, A. IL Grayj Jr., R. M. Grey, sad J. D. Market, "Speech coding bawed%pom vector qPatou*o AU Trauaetiew on Acemusic., Speech and Signa

speech coigwit a umum diuhualastiom fraindoto esr,MME Trweinem oniufemetione Thwi , Vol. IT-27, no. 6, pp. 708-721, Nov.1061.

G. Rebolhedo, R. Kt Gray, and L. P. Bug, "A multirate vain. digitizer basedupon vector quatization,* &BEE Thnsediem em Conmumc iem.o, Vol. COM-30, pp. 721-727, Apei 1063

H. Abut, ft. hL Gray, ad G. Rebolledo, "Vector quantization of speech andspeech-like waveforms,' MWE flemeectivas em Acousfic., Speech, anud Signal Pro-cesan, Vol. ASSP-30, so. 3-, pp.423-435, June 1I6.

Aeceptd Papers

Rt. KL Gray, ltauteualato, in Multiwe Anlg*-V, P.R. Krbh-21"1h UP, North-1301aud to ap0pear.

ft...oe .I Gry ..eto ..aiata, lE SP Mapmme,4 to appear.

IPmblhei od1sm PlIPei

R. K r, A. IL GrW J,I md~ a Q LoW QD.M isih hNo

7.Kww A w., LIL ms d.D "ft Ma

Aspe w.. oad *Ab w- -0Mu, J00, AP4 ML

RI. KGray, "Te~erbdblock sourcsem..," Awmfdi 1W00 A~evoCeuJresc, Aflertom IL, Oct 190.

IL Abut, It. KL Gra, and CL R*sAhis, "Veat., quwmmatsd of speech andspeecha. wavduema' 131 1ff omitmeim Ipmyede on hwwmWtThe*M. Sat Moici4Fb WL in

G. ReAlleo ad R. IL GMa, "Vector qw~dtlas appied to speech codiqIbid.

IL Abut, R. IL GMy, MAd G. RebOfleis "Vejor qmsathlOs Of sPeech

eCasi, Atalanta, GA, AprillMR.

G. Rebofledo R. IL Gray, ad I P. But~ "A suimlo"40t4 hsea Predictivevocoder boed uwas vests quuc ssidem4* mmdle a eicm

M. J. Sabin ad R. IL Gral "An alpritba for the duip at product code vectorquatizer' 1W Ituhm Mam.. n m porutiem MMer, LesArea, Framce, um USE.

M. i.8abis ad R. K. Gway "Product code veduhmR qumas for *6eecwaveform cdgCOqfsvrac Resu'd Glcm I& pp. 107-10910 December

Paper" Uadu Revbw

U. . Sabin, sid R. K Gray, "Poduc code vector qumatlser for waveform madvoice eodlu5e I= Tw'ms, on AWS, Jim 116

~ a *~~-'~r~O ) -

~ ~ ~1~~My ~ MA

a. Rellable, VIA Coemftg I@ U m w (A. U Gkom4

Reusuc Objectives

The following topics have beend~ ma ivestigation: Mi Coding for memories

with stuck-at defects and raadom erwors when the defect information is provided

to the encoder or to the decoder. (Hi) The improvemnent is storap capacity

achieved by skipping defective or some partially defective uwmory ei (Mi) The

complexity of encoding and decoding circuitry. (iv) The ame and delay penaltin

involved in structuring VLSI arrays. (v) Communication complexity of comput-

ing.

majorAcoplhet

(i) Heegard III hos uxaansix clas of Maer block codes (LDC) for improv-

ing the reliable slurap of laformatom In a computer moemory with stuck-at

defects and some. go examined LEO'.whim the "Wde nformation about the

state of the defects &YAvaiabe o the decoder or to She acoder. In the former

cast etuk-at ce Ad as errnre 1 twt teebubpewfor deeodieg the LOC's 'with

crowre nd er roi6.a be .m.by* H iasodee" a clas of modifled Kear

block Sweu ClAM96*MW- seme dss d era. wam the beath. mad ature

of As dbaf Is*toem.p4

I *..

,5 -4,

A elm at ndled Oft cutl Wo kmbmse in 7UI The bH td fo

theme cycle codes was derived ad ewmpbyed to ostruct ULDCs with specified

boasds on the mxn... distances.

(Hi) in jpj, the proposer and Grams, considered a DOiam composed of N

discrete ceells, each characterized. by a defect state.# drawn independently

according to () . The probabilt of retrieving a symbol v given a and the

stored symbol s is completel speiled by p(l s,@). The selector identifies a

subset of *good' ello wbich aiome are used to store data, in an effort to improve

the reliable storage rate of the mnemory.

EN4CODER / SELECTOR MEMORY

DEOE

22.13

2~ Rt4

0A

Idl

ntt

lu* ., A-s

, 7

-Iit and omilY it the Oh NU is used. The symbols Ii,... *sNI me stored in

order in the selected cells. A stmrag rate R is achieved if there exists a

sequence of (2RN,rN) codes, selection rule p(. Isa) and decoding rules such that

the probability error tends to zero.

The storage capacity is established for independent selection rules

NvA~u Is) - ][I p(mi jei) . It is then shown that the capacity is higher for the more

general clas of causal rules Anu Is) - 11 pAvgi t...) P. However, for the cellinua

consisting of two binary symmetric channels (BSC's), the capacity for causal rules

is achieved by an independent rule. A uimilar result hold for any two-state cten

when the state is knoi~n to the decoder.

For arbitrary selection rules, rates higher than those possible 'With causa

rules awe achievable, even for two-state BSC cells. The capacity for arbitrary

rules is as yet unknown.

(iii) Ahbswede has proved the Mlias f3J - Winograd 141 result for probability

o( error criteion. The capaity so.. ,whene A the number of

infomation bits, (results mot writtm up).

(it) tIn Jtbb projoser sad Grefte imvesigated the asymptotic penalties of

testeuilg omotemeous VW.S wap for yield eahameemmat Bach element of

ase tabg WagsI &a is &Wewt edeeie I",binimd probalt p.-

A Oxid 6asti R of the dimS. wte to be emted tot a pwoedwl rep.

4 m1i 0* .o bon"d a"q 6" . qj.uom.. Let 10fl m. 14 f w 0m

..... ....

of the longest connection and t be the nmber of wlrkg tiracks needed to

accomplish the interconnection. It is shwn that:

(1) Connecting a chain of K elaments tom, a hiear anry of N elements

requires d - (XIeg) and I - track running paralel to the array.

(2) Connecting a linear army of K fixed 1/0 ports to distinct non-detective elements frm a parale array requires 4 - f(gN)p and

(3) Connecting K elements from an N-element linar array to K from aparallel N-element armay, in pairs, requires only constant d and I.

DEFECTIVE ACTIVE

I N ELEMENTS

Fi.2.&: Couneetloa of a chain fro aa N-element linear array.

PORT

Tracks

all

;41 R..4vq -

io i

Fi.2.c: Pairwise connection of two parallel N-element linear arrys.

Fig. 2Ad Comectio oa chsinof K-il elaemtafrhom a 4X4 aM-v

U~ ~ ..df 1 OO--b m60aIA vq

* 7-

(4) Cambeetlmg a shah .1 K dinmts bm a NXX wqr require cow$to" an m e ow Ae betwee 2 hinemtq this problur b cely*rted& to the peNrcobio "eehiu of itema" ph*S~.k

14 A* -de *Ibb caso, lg1s bAd Almedn thev bpu* n~ cm and tat* prusited whic coet h-ans wih polbmwt approaig-me. The alkItkm n bn lo(m aim

MI QOnni"Wsga KXK op~en Ae kIebi an. NXN waM in shws totequkm 'i1. In 4"it s owma that *wait E-Os41vN)

onya oetat nbe at tras are neeoed& Th proof minla~atmaxiaumIowmuauuncut theoem for ppn wit rando= c"pull-

(v) In flthe piopose proed tha if (X,Y) wre two SAnt. alphabem.rn

I" dswrwv ith(POW) >S fokwAN (zsv)(X XY), and Ita fuctioMFXY)

is 04enraa% *ft af o n X to r aeesoy to compute

F(XY) rdol am$be,*m -iww t av* to N(X Ir). The rush

hold it the toma~ is wWi0orm IV ,* nwo

L, ay ef~ Psm sW Ir and V Sm a adV reepee

-xr iv, s v-'* tha OW bi th 14 RP WO LFj

41~~ ~ "~:*~-

-23-

RZFERENCES

[11 C. Heegard, "Linear Block Codes for Memory with Defects,* to appear inIEEE Transection. on Information Theoryj.

121 J. Greene, A. El Garnal, "Storage Rates For a Memory with a Selector,"to appear in IEETransaction. on Inform ation Thew'j.

[31 P. Elias, "Computation in the presence of noise," IBM Journal, pp. 346-363, October 196.

[4] S. Winograd, "Coding for logical operations," IMM Journal, pp. 430-438,October 1962.

151 J. Greene, A. El Garnal, "Configuration of VLSI Arrays in the Presence ofDefects," to appear in Journal of ACM.

151J . Greene, A. El Carnal, "Configuration of VLSI Arrays in the Presence ofDefects, Part U1,- in preparation.

11 A. El Canal, "A Simple Proof of the Ablawede-Csizar One-Bit Theorem,'toapea in IEM Traneaction. on Information Theor.

181 A. El Garnal and K Pang, "Communication Complexity of Computingthe Hamming Distance,' to appear in SIUM Journal of Comp~utiny

#.Algorlthms and Architecturs for Statleal ad Data Procuuing

(M. morn)

Professor Morf has moved to Yale University. He will be sending his portion

of the final report directly.

However, a list of Ph.D. students partially supported under this contract,

and a list of publications in the contract period are given here.

425-

Ph. D. STUDENTS

Hadidi, M.T. " Contributlowm to the Anlysis and Modeling of Mul-tickanie Autogreive Stationary Processes, June

Nehorai, A. "Algorithms for System Identification and SourceLoctlon," June 1083

Delorne, J.M. "Algorithms for Finite Shift-Rank Proces" Sep-tember 1082.

Ahmned, H. "1VLS Architectures For Real-Time Signal Process-ing," June 1083

Lee, D.T.L. "Ladder Form Relsalmso Fast Algorthm- InEstnitlo,"August 1080.

.............................

4-8

Published Journal (or book) Papers

J.-M. Delosme and Martin Modf, "Fast Algorithms for Finite Shift-RankProce.... A Geometric Approach," published in the 1QM volume of the serieson Published by TeSauaialsI and Moels fey Centrvol Sysecms Analysisand Signal Processing, " CNRS Editions, Paris, pp. 499427. (invited)

D.T.L. Lee, M. Modf and R Friedlander, "Recursive Least Squares Ladder Esti-mation Algorithmns," special joint ise of SEEE Trans. Circuits and Systems,Vol. CAS, No. 6, June 1Q61 pp. 467-41.

Accepted Papers

T. Kailath, L. Ljung, M. Modf, "Recursive Input..Outpint and State-Space Solu-tions for Continuous-Time Linear Estimation. Problems," MEEE Transactien onAutomatic CoteL (Aceajita4 resesd eed vesalmilt.4)

Publishe Costbreae Paper.

J.-M. Deloeme and M. Mail, "A Unified Stochatic Description of Efficient, Alpo.ritlinu for Secnd-Order Procmwes," P~oc. Werk&ep en Feet A4tr&sP feyLine a an.., Ammso.., France, September 21426, 131, pp. 1&1-13.22.

M. MkW and J..M. Deloern, "Matrix Decompositions and Inverson via Eleam-utary SIgnature-Orotfinl TransfraISUM" Pree. 15WM Somposium, San Fran-cisc, CA, May 1061. (Invited)

* S, Wood and lL Arl, "A Fat I m ntation of a Minimum Variace Fatima-tor for Comaterised Tomography, Imag Recnstrcto w Trans. We..Mdial g., Vl BM&SNo. 2.Fbruary l, pp.* .

It. Mail, "Doublin Aig"la fow TWopt and Reted Equa~tis, iee. 'ItsICASSP Denver, 00# Apt~ 9-U113,f Mp 96443

I pool

427-

D.T.L. Lee and M. Modf, "A Novel Innovatioms Band Tin-Dooaah Pitch Detec-tion," Free. 1DR ICASSP, Denver, CO, April 9-11, 1960, pp. 4044.

M. Modf and D.T.L. Lee, "Recursive Square-Root Ladder Estimation Algo-* rithms," Proe. IMO ICASSP, Deaver, CO, April 9-11, 1960, pp. 1006-1017.

7-7Is

W 17, -77