The Hardware Implementation of Devices Forming Discrete Signals with Multi-Level Correlation Function
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1 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 Te Hardare Ipleetato of Devce Forg Dcrete Sgal t Mlt-Level Correlato Fcto Alee Srov Profeor te Departet of Softare Krovorad Natoal Teccal Uvert Krovorad Ukrae Abtract: Algebrac approac to td te forato of large aeble of dcrete gal t lt-level correlato fcto c baed o te ecto of crclar orbt of grop code tded Te ber ad vale of de -lobe level of te correlato fcto of te geerated eqece ad te poer of te aebl gal are detered b reote ad trctral properte of poloal rg over fte feld Propoal for te ardare pleetato of devce forg dcrete g al t lt-fcto correlato are developed Keord: eeble of dgtal gal lt-level correlato fcto Itrodcto A prog drecto te developet of algebrac etod of te teor of dcrete gal te e of advaced ateatcal apparat of te teor of fte feld ad partclar te teor of poloal rg c allo aocatg te correlato properte of te eqece geerated fro te grop ad te trctral properte of te code eqece [ 4] Te tde carred ot t ork oed tat trved algebrac approac to te te of dcrete gal baed o ecto of crclar orbt of te grop code allo creatg large aeble of eqece te correlato properte of c ave lt-level trctre Te teed gal ave te ot practcal teret ltple acce rado cotrol te [5 7] Te e of large aeble of dcrete gal t te proved properte ll gfcatl creae bcrber capact of rado cotrol te t code cael dvo Propoal for ardare pleetato of devce forg dcrete gal t lt-level correlato fcto are developed t ork It o tat te developed olto allo to geerate a eqece t proved correlato ad aebl properte ad to practcall pleet te developed [ 4] etod of forg of dgtal gal Algebrac approac to te forato of dcrete eqece t ltlevel correlato fcto Te propoed [ 4] algebrac approac to te forato of large aeble of dcrete gal t lt-level correlato fcto baed o te ecto of crclar orbt of grop code Te ber ad vale of de -lobe level of te correlato fcto of te geerated eqece ad te poer of gal aeble are detered b reote ad trctral properte of poloal rg over fte feld Let' brefl eae tee provo cotttg te teoretcal ba for te forato of dcrete gal Grop code qel detered b leader (repreetatve of t copoet cclc orbt A orbt ereafter refer to te et of code ord eqvalet to eac oter t repect to te operato of te cclc ft Uder te ecto of te orbt of te grop code let dertad te coce of oe repreetatve (leader of eac orbt Dtace (correlato properte of te t fored et of leader are detered b reote properte of grop code eret te eqvalece of cclc ft operato abet b defto of orbt ecto Let et t propert te ba of te aebl of dcrete gal forato Sectoal dagra of oero cclc orbt of grop code o Fg Fg o te decopoto of te vector pace GF q o te et of o-terectg orbt V L te grop code V repreetato trog te o of a fte ber of orbt ad te cee of coog of orbtal leader oe arbtrar v v v repreetatve fro eac cclc bet V M (for coveece te code ord Cv c c c are arked b to dce: v te ber of orbt V v of te code V v ere v te ber of code ord te orbt v v M V v te ber of a code ord te orbt I 5-5(ole Deceber Page 7
2 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 V C V C C C C S V C C C C S V V C C C C S S W V M C M C M C M C Ml S M V M+ V L CM+ CM+ CM+ CM+ l+ C L C L C L C LL Fg Scee of oero cclc orbt ecto of a grop code for te forato of a aebl of dcrete gal S SM ere Sv C v v M ad te electo of a de t approprate C detered b te rle of ecto of te v-t cclc grop code orbt Repreetatve of te orbt of te elected for te et S S v Let coder te bar cae e retrct orelve to te properte of te et S S S SM fored b te ecto of te v v crclar orbt of bar grop code Te eleet of te fored of dcrete eqece (dgtal gal S v v c let defe te eleet of te elected code ord (te leader of te orbt a follo: v c Let ppoe tat te codered ( k d code V a a egt pectr of: A( A( A( A(d ( A(d A(d A( ere A te ber of code ord te code V t te egt Te te et of dgtal gal S S S SM fored b te ecto of cclc orbt of code V a correlato ad aebl properte correpodg to te follog tateet [ 4] Stateet Sde lobe of te perodc fcto of ato (PFAC ad tal (PFMC correlato gal aebl S S S ave te follog vale: SM for toe d d tat A( PFMC PFAC ( For all c dd tat A( te de lobe ad PFAC ad PFMC ll ever be v v I 5-5(ole Deceber Page 8
3 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 Te poer M of te aebl S S boded belo b te epreo: S defed b te ber of o-ero orbt of te code V ad SM M ( Te eqalt old cae of te a perod of te eqece of all te orbt forg te code e f te code V a et of orbt fored b eqece of a legt (-eqece Let coder te ot geeral cae ere te bar grop k d GF gve b ceckg poloal of: k code der f f f (4 ere f f f arbtrar ro of te follog al poloal eleet GF GF GF repectvel ere te order of te eleet ltplcatve grop of a fte feld GF a prtve eleet of te fte feld GF eqal to te order of te Let coder tot lo of geeralt tat Let defe te ceck ad geerator poloal a follo: j j g j Sceatcall te proce of forg of te ceck ad geerator poloal o Fg Te bol v tad for te ber of te clae of cojgate eleet tat ake p a lt plcatve grop of a fte feld GF (eleet clae (eleet correpodg j j Te frt cla cota cojgac (c detere te prtve eleet Te follog j cota j cojgac ( j defed a te allet potve teger for c te eqalt: j j od j If te order of te ltplcatve grop of a pre ber tat e: pre ber te: j: A gle eleet of te feld for a addtoal cojgate cla of oe eleet Fg o te correpodg dtrbto of te eleet of a fte feld te poloal fte feld of te frt cojgate clae are te root of te ceck poloal c old te root of te ceck poloal ( od( doe tat : a j dvde evel j v For eac j v j ad g Eleet of a A rage of eleet of a fte feld detered b te larget vale for c te codto od od od } { I 5-5(ole Deceber Page 9
4 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 g j j j j j v v v v Fg Scee of forato of ceck ad geerator poloal of te grop code j j v v v v g j j j Fg Dtrbto of te eleet of te fte feld to ceck ad geerator poloal of te grop code I geeral te root of poloal ece: ad accordgl: f f are te rage: f vale t d t Te correpodg code paraeter of a grop code are a follo: k d (5 Let etate te egt pectr of te code Verfcato poloal of te code t te paraeter (5 cota ceck poloal of all te code a a cofactor t te ceck poloal f f f It follo tat all te code ord fro te grop code t f f f are code ord of codered code t paraeter (5 e oero copoet of te egt pectr are fored b a cceve addto ( order of addto of te cofactor te poloal f f f of te correpodg par of eleet (for all : ere: a A( A( od od od } { We e ave oe o-ero copoet of te egt pectr A( c correpod to Te codered ork [ 4] cae of bldg tree ad fve-level dcrete gal correpod to: I 5-5(ole Deceber Page 4
5 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 I 5-5(ole Deceber Page 4 : A( A( : ( A ( A T te tree ad fve-level dgtal gal are a pecal cae of cotrctg of large aeble of dcrete gal t lt-level correlato fcto Te geeral epreo for etatg te egt rage of te grop code pecfed b a ceck poloal (4 let pt do a : A( Te correpodg epreo o valg te de-lobe perodc correlato fcto geerall take te for:
6 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 I 5-5(ole Deceber Page 4 od od od a ( ( ( od od od a PFAC PFMC (6 T te geerated b te propoed etod dcrete gal ave ltlevel featre of ato ad tal-correlato Te vale of te lateral eo take a fte ber of vale gve b te egt properte of a ed grop code Let etate te poer of te aebl of te fored dgtal gal Te poer of te ed code k tere are altogeter: k of oero code ord If e ae tat eac code ord a te a perod ad eac cclc orbt cota eactl code ord te te epreo for te etate of te poer of te aebl of te fored gal becoe: M ( ( Te aal of te lat epreo o tat te e of grop code allo creatg large aeble of dcrete gal Addg of a al poloal a aoter cofactor te ceck poloal creae te poer of te aebl ( ere te ber of te added poloal Developet of propoal for te ardare pleetato of devce forg dcrete gal b a propoed etod Te developed etod of forg of dgtal gal allo bldg large aeble of eakl correlated bar eqece Let coder te poblt of practcal forato of large aeble of eakl correlated dcrete gal ad cotrct g te correpodg ardare devce for bar eqece geeratg I cae of lt-level eqece e get te follog cee of forato of dcrete gal (Fg 4 Te devce blt trog coectg of ft regter to te adder otpt A rg dagra to ake approprate provo te regter rg feedback ft elected b te coeffcet of prtve poloal of degree repectvel I t cae te legt of te bar eqece eqal to ad to for te oe eed to e ft regter te ft regter t bar dgt Te tal tate of te ft regter et te ode of te fored eqece
7 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 Fcto of te feedback ft regter are et b coeffcet of prtve poloal of degree: ere f f f c are defed b ter root f f f al poloal of eleet repectvel fro te ed feld GF Fg 4 Block dagra of te forato of dcrete gal t lt-level correlato fcto Te order of eleet eleet of te fte feld GF Te devce ork te dced above aer ad allo creatg: eqece of legt eqal te order of te ltplcatve grop of a fte feld GF M ( ( a prtve 4 Coclo T te core of a codcted reearc practcal ggeto regardg te pleetato of te ardare devce forg dcrete eqece ave bee developed Te deged cee are pleeted coptatoall b effcet coverter for eaple baed o crct t a ft regter ad a adder (ee Fg 4 7 Te allo creatg large aeble of dcrete gal t proved correlato ad aebl properte Terefore te developed propoal let to practcall pleet te developed etod of forg dcrete gal I 5-5(ole Deceber Page 4
![Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 Referece [] Ketov AA Srov AA Sa V N Dgtal Sgal t Mlt-Level Correlato Fcto // Rado: Ukr Iterag Sc ad Eg Sat Karkov: KNUR Ie 66 P 4-5 []](/docs-images/74/70200477/images/8-1.jpg "Ketov AA Srov AA Sa V N Forato of Dcrete Sgal Wt Mlt-Fcto Correlato // Iforato proceg te K: KAFU Vol 5(95 P 5-6 [] Ketov AA Ue of Cople Dcrete Sgal for Stegaograpc Iforato Secrt / AA Ketov AA Srov //")
8 Iteratoal Joral Of Coptatoal Egeerg Reearc (jceroleco Vol Ie 8 Referece [] Ketov AA Srov AA Sa V N Dgtal Sgal t Mlt-Level Correlato Fcto // Rado: Ukr Iterag Sc ad Eg Sat Karkov: KNUR Ie 66 P 4-5 [] Ketov AA Srov AA Sa V N Forato of Dcrete Sgal Wt Mlt-Fcto Correlato // Iforato proceg te K: KAFU Vol 5(95 P 5-6 [] Ketov AA Ue of Cople Dcrete Sgal for Stegaograpc Iforato Secrt / AA Ketov AA Srov // Iteratoal Joral of Egeerg Practcal Edcato Vole Ie USA Idaa: Scece ad Egeerg Pblg Copa P -5 [4] AA Srov Coparatve Stde of Metod for te Ste of Dgtal Sgal t Specal Correlato Properte / AA Srov EV Meleko // Abtract of V Iteratoal Scetfc ad Teccal Spo "Ne Tecologe Telecocato" (NIICT-Carpata- Kv 7- Jaar Kv: NIICT P 8-8 [5] Grak MV Frolov VI Tecolog CDMA Te Ftre of Moble Ste Ukrae Te World of Cocato 998 # P 4-4 [6] Naeko NI Staev JV Ketov AA Eveev SP Teor Of Sgal-Code Strctre K: KAFU [7] Sklar B Dgtal Cocato Teoretcal Ba ad Practcal Applcato M: W lla 4p Ator Nae Alee Srov a bor 977 Gradated fro Karkv Mltar Uvert t a degree Atoated Cotrol Ste 999 Caddate of Teccal Sc ece (PD Profeor of Departet of Softare of Krovorad Natoal Teccal Uvert Ukrae Feld of teret: forato ecrt ad rotg e I 5-5(ole Deceber Page 44
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