Analisis Pengaruh Penggunaan Metode Tunneling PPTP & L2TP Terhadap Peningkatan QoS pada Streaming video di Streaming Server Online.
%DQGZLGWK(IILFLHQF\,PSURYHPHQWRI2QOLQH*DPHV
E\WKHXVHRI7XQQHOLQJ&RPSUHVVLQJDQG
0XOWLSOH[LQJ7HFKQLTXHV
-RVH6DOGDQD-HQLIHU0XULOOR-XOLiQ)HUQiQGH]1DYDMDV-RVp5XL]0DV-RVp,$]QDU(GXDUGR9LUXHWH1DYDUUR
&RPPXQLFDWLRQ7HFKQRORJLHV*URXS *7& ±$UDJRQ,QVWRI(QJLQHHULQJ5HVHDUFK ,$
'SW,(&$GD%\URQ%XLOGLQJ&368QLY=DUDJR]D
=DUDJR]D6SDLQ
^MVDOGDQDMHQLIHUPXULOORQDYDMDVMUXL]MLD]QDUHYLUXHWH`#XQL]DUHV
$EVWUDFW²7KH HQWHUSULVHV WKDW GHYHORS RQOLQH JDPHV QHHG
FKDUDFWHULVWLFV OLNH SHULRGLFLW\ ORFDOLW\ DQG VHOIVLPLODULW\
KDUGZDUH DQG EDQGZLGWK UHVRXUFHV LQ RUGHU WR JLYH D JRRG
$QRWKHUFRQFOXVLRQLVWKDWWKH\KDYH OHVVEDQGZLGWKDQGUHDO
VHUYLFH WR WKH XVHUV 7KHVH JDPHV SURGXFH D KLJK UDWH RI VPDOO
WLPHUHTXLUHPHQWVWKDQ)36
8'3 SDFNHWV IURP WKH FOLHQW WR WKH VHUYHU VR WKH RYHUKHDG LV
VLJQLILFDQW 7KH DFWLRQV RI WKH SOD\HUV KDYH WR EH SURSDJDWHG WR
WKHVHUYHUDQGWRWKHUHVW RIWKHSOD\HUVLQ DYHU\VKRUWWLPH VR
QHWZRUN GHOD\V DUH YHU\ FULWLFDO 7KLV ZRUN SUHVHQWV D PHWKRG
WKDW VDYHV EDQGZLGWK E\ WKH DGGLWLRQ RI D ORFDO DJHQW ZKLFK
TXHXHV SDFNHWV FRPSUHVVHV KHDGHUV DQG XVHV D WXQQHO WR VHQG D
QXPEHURI SDFNHWVLQWRD PXOWLSOH[HGRQH 7KHEHKDYLRXURIWKH
V\VWHP KDV EHHQ VWXGLHG IRU ,3Y DQG ,3Y VKRZLQJ WKDW
VLJQLILFDQWEDQGZLGWKVDYLQJVFDQEHDFKLHYHG)RUFHUWDLQWLWOHV
XS WR RI WKH EDQGZLGWK FDQ EH VDYHG IRU ,3Y 7KLV
SHUFHQWDJH JURZV XS WR IRU ,3Y DV WKLV SURWRFRO KDV D
ELJJHU RYHUKHDG 7KH FRVW RI WKHVH EDQGZLGWK VDYLQJV LV WKH
DGGLWLRQ RI D QHZ GHOD\ZKLFK KDV DQ XSSHU ERXQG WKDW FDQ EH
PRGLILHG6RWKHUHLVDWUDGHRII WKHELJJHUWKHDGGHGGHOD\VWKH
ELJJHUWKHEDQGZLGWKVDYLQJV2QWKHRWKHUKDQGWKHWHVWVVKRZ
WKDWLIWKHQXPEHURISOD\HUVLVELJHQRXJKWKHDGGHGGHOD\VFDQ
EHDFFHSWDEOHLQWHUPVRIXVHU¶VH[SHULHQFH
.H\ZRUGVJDPLQJ GHOD\ PXOWLSOH[LQJ FRPSUHVVLQJ
PHDVXUHPHQW QHWZRUNJDPHV 4XDOLW\RI([SHULHQFH )LUVW3HUVRQ
6KRRWHU
,
,1752'8&7,21
2QOLQHJDPLQJYLD,QWHUQHWLVDVHUYLFHWKDWJURZVTXLFNO\
ZRUOGZLGH7KHUHDUHVRPHWLWOHVZKLFKKDYHPLOOLRQVRIXVHUV
VR WKH HQWHUSULVHV WKDW GHYHORS WKH JDPHV KDYH WR IDFH D
GLIILFXOW SUREOHP ZKHQHYHU D QHZ WLWOH LV UHOHDVHG WKH\ QHHG
KDUGZDUH DQG EDQGZLGWK UHVRXUFHV LQ RUGHU WR DYRLG WKH
VDWXUDWLRQRIWKHLULQIUDVWUXFWXUH$VWKHVXFFHVVRIDQHZWLWOHLV
QRW YHU\ SUHGLFWDEOH WKH\ PD\ KDYH WR RYHUSURYLVLRQ WKHVH
UHVRXUFHVEHFDXVHWKHXVHUVWKDWEX\WKHJDPHKDYHWRUHFHLYH
DJRRGVHUYLFH,Q>@DVWXG\RIWKHEHKDYLRURIWKHJDPHUVZDV
SUHVHQWHGDQGWKHDXWKRUVFRQFOXGHGWKDWWKH\DUHYHU\GLIILFXOW
WRVDWLVI\ LIWKH\KDYHFRQQHFWLRQSUREOHPVWKH\XVXDOO\OHDYH
DQGQHYHUUHWXUQDQGWKH\GRQRWWHQGWREHOR\DOWRDVHUYHU
7ZR RI WKH PRVW SRSXODU JHQUHV RI RQOLQH JDPHV DUH
00253*V 0DVVLYH 0XOWLSOD\HU 2QOLQH 5ROH 3OD\LQJ
*DPHV DQG)36 )LUVW3HUVRQ6KRRWHUV 5HIHUHQFH>@VWXGLHG
WKH WUDIILF RI 00253*V FRQFOXGLQJ WKDW WKH\ KDYH VRPH
7KLV ZRUN KDV EHHQ SDUWLDOO\ ILQDQFHG E\ &38)/,3, 3URMHFW 0,&,11
7,1 0%$&7R,3 3URMHFW RI $UDJRQ ,' $JHQF\ DQG ,EHUFDMD
2EUD 6RFLDO DQG 1'&,3,44R( 3URMHFW RI &DWHGUD 7HOHIRQLFD 8QLY RI
=DUDJR]D
SPECTS 2011
227
,Q)36WKHDFWLRQVRIWKHSOD\HUVKDYHWREHSURSDJDWHGWR
WKHVHUYHUDQGWRWKHUHVWRIWKHSOD\HUVLQDYHU\VKRUWWLPHVR
QHWZRUN GHOD\V DUH YHU\ FULWLFDO7KHVH JDPHV SURGXFH D KLJK
UDWHRIVPDOO8'3SDFNHWV W\SLFDOO\VRPHWHQVRIE\WHV IURP
WKH FOLHQW WR WKH VHUYHU VR WKH RYHUKHDG FDXVHG E\ ,38'3
KHDGHUV LV VLJQLILFDQW 6HUYHU WR FOLHQW SDFNHWV DUH W\SLFDOO\
ELJJHU
7KHUHDUHVRPHVFHQDULRVZKHUHPDQ\SOD\HUVRIWKHVDPH
JDPH VKDUH WKH SDWK IURP WKH DFFHVV QHWZRUN WR WKH JDPH
VHUYHU HJ ,QWHUQHW &DIpV ZKLFK DUH YHU\ SRSXODU LQ PDQ\
FRXQWULHVIUHTXHQWO\KDYHFRPSXWHUVDEOHWRUXQRQOLQHJDPHV
DQGJDPHUVXVXDOO\JRWKHUHWRSOD\LQJURXSV )LJDDQGE
7KH WUDIILF EHWZHHQ VHUYHUV RI WKH VDPH JDPH LV DQRWKHU
VFHQDULR ZKHUH WKH SDFNHWV RI PDQ\ SOD\HUV VKDUH WKH VDPH
SDWK )LJF
7KHWUDIILFRIWKHVHJURXSVRISOD\HUVFRXOGEHFRPSUHVVHG
DQG PXOWLSOH[HG LQ RUGHU WR VDYH EDQGZLGWK WDNLQJ LQWR
DFFRXQWWKDWWKHDFFHVVQHWZRUNLVXVXDOO\WKHERWWOHQHFN$QG
LQ FDVH RI '6/ WKH XSOLQN KDV QRUPDOO\ OHVV EDQGZLGWK WKDQ
WKH GRZQOLQN %\ WKH DGGLWLRQ RI D ORFDO DJHQW ZKLFK TXHXHV
SDFNHWVFRPSUHVVHVKHDGHUVDQGVHQGVPXOWLSOHSDFNHWVLQWRD
ELJJHU RQH VRPH EDQGZLGWK VDYLQJ FRXOG EH DFKLHYHG DW WKH
FRVWRIDGGLQJQHZGHOD\VPDLQO\FDXVHGE\WKHUHWHQWLRQWLPH
DWWKHTXHXH
,QRUGHUWRDYRLGZRUNORDGWRWKHFHQWUDOJDPHVHUYHUVRPH
SURSRVDOV>@>@LQFOXGHGQHWZRUNHOHPHQWV SUR[LHV QH[WWR
WKHDFFHVVQHWZRUN,QFRQWUDVWWKHORFDODJHQWSURSRVHGLQWKH
FXUUHQWZRUNFRXOGEHGLVWULEXWHGZLWKWKHJDPHDSSOLFDWLRQLQ
WKHVDPHZD\DVORFDOVHUYHUVDUHGLVWULEXWHGZLWKFHUWDLQWLWOHV
7KHWXQQHOIURPWKHFOLHQWVWRWKHVHUYHUFRXOGHLWKHUEHFUHDWHG
E\ D GHGLFDWHG PDFKLQH )LJ D RU E\ WKH FRPSXWHU RI D
SOD\HU )LJE WKXVDYRLGLQJWKHFRVWRIDQHZPDFKLQH
$W WKHRWKHU VLGH WKH VHUYHUZRXOG KDYHWR LPSOHPHQW WKH
GHPXOWLSOH[HU DQG GHFRPSUHVVRU ZKLFK ZRXOG LPSO\ VRPH
SURFHVVLQJ FDSDFLW\ DQG VSDFH WR VWRUH WKH FRQWH[W RI HDFK
IORZ LHWKH LQIRUPDWLRQ QHFHVVDU\WRUHEXLOG WKH FRPSUHVVHG
KHDGHUV VRPHWHQVRIE\WHVDVZHZLOOVHH>@ 7KLVZLOOQRW
LPSO\ D VFDODELOLW\ SUREOHP DV WKH VHUYHU DOUHDG\ VWRUHV WKH
VWDWH RI WKH JDPH IRU HDFK SOD\HU 2Q WKH RWKHU KDQG WKH
VDYLQJVLQWHUPVRIEDQGZLGWKDQGSDFNHWVSHUVHFRQGPD\DOVR
EHEHQHILFLDOIRUWKHVHUYHU
,IWKHQXPEHURISOD\HUVLVELJHQRXJKLWFDQEHH[SHFWHG
WKDWZKLOHDGGLQJVPDOOGHOD\VDELJQXPEHURISDFNHWVFRXOG
EH PXOWLSOH[HG LQWR D ELJJHU RQH %DQGZLGWK VDYLQJ QRW RQO\
DIIHFWVWKH JDPLQJWUDIILFEXWLWFDQDOVREHEHQHILFLDOIRUWKH
EDFNJURXQG WUDIILF ZKLFK VKDUHV WKH DFFHVV ZLWK LW
)XUWKHUPRUH PXOWLSOH[LQJ KDV DQRWKHU DGYDQWDJH WKH QXPEHU
RISDFNHWVSHUVHFRQGWKHURXWHUKDVWRPDQDJHZLOOEHUHGXFHG
7KHUH H[LVW RWKHU DSSOLFDWLRQV DQG VFHQDULRV ZKHUH PDQ\
UHDOWLPH IORZV VKDUH WKH VDPH SDWK HJ 9R,3 WUXQNLQJ DQG
WKH XVH RI PXOWLSOH[LQJ DQG FRPSUHVVLQJ WHFKQLTXHV KDV EHHQ
SURSRVHG DQG HYHQ VWDQGDUGL]HG >@ IRU WKHP 0DQ\ RQOLQH
JDPHVSUHVHQWVLPLODUWUDIILFSDWWHUQVJHQHUDWLQJDKLJKUDWHRI
WLQ\ SDFNHWV DQG WKXVSUHVHQWLQJ D ELJRYHUKHDG7KH QRYHOW\
RI WKH SUHVHQW ZRUN LV WKH XVH RI VLPLODU PXOWLSOH[LQJ
WHFKQLTXHV IRU WKHVH JDPHV¶ WUDIILF LQ ZKLFK VLJQLILFDQW JDLQV
FDQDOVREHREWDLQHGZLWKRXWORVLQJTXDOLW\
:HZLOOPDLQO\VWXG\WKHVFHQDULRVSUHVHQWHGLQ)LJDDQG
EEXWPRVWRIWKHFRQFOXVLRQVFDQDOVREHDSSOLHGWRWKHWKLUG
RQH )LJF 2QO\FOLHQWWRVHUYHUWUDIILFLVVWXGLHGDVELJJHU
VDYLQJVFDQEHREWDLQHGDQGLQPDQ\VFHQDULRV HJ'6/ LWLV
WUDQVPLWWHG YLD WKH PRVW UHVWULFWLYH OLQN :H KDYH WR PHDVXUH
WKH LPSDLUPHQWV RQ WKH SDUDPHWHUV WKDW GHWHUPLQH WKH TXDOLW\
H[SHULHQFHGE\XVHUVLQRUGHUWRSURSHUO\WXQHWKHSDUDPHWHUV
WKDWGHILQHWKHWUDGHRIIEHWZHHQEDQGZLGWKVDYLQJDQGTXDOLW\
$OWKRXJK WKLV WHFKQLTXH FRXOG EH DSSOLHG WR RWKHU JDPH
JHQUHV ZH ZLOO XVH )36 WUDIILF LQ WKLV ZRUN DV WKHVH JDPHV
KDYH YHU\ VWULQJHQW UHDOWLPH UHTXLUHPHQWV 7KH VXEMHFWLYH
TXDOLW\ PDLQO\ GHSHQGV RQ GHOD\ DQG SDFNHW ORVV >@ 7KH
6\VWHP 5HVSRQVH 7LPH 657 WKH WLPH WKH V\VWHP QHHGV WR
GHWHFWDXVHUHYHQWWRSURFHVVLWDQGWRVHQGWKHXSGDWHGJDPH
VWDWHWRWKHORFDORXWSXWGHYLFH KDVWREHPDLQWDLQHGXQGHUD
FHUWDLQYDOXH
7KHUHVWRIWKHZRUNLVRUJDQL]HGDVIROORZV 1H[WVHFWLRQ
SUHVHQWV WKH UHODWHG ZRUNV 6HFWLRQ ,,, H[SODLQV WKH SURSRVHG
WXQQHOLQJ FRPSUHVVLQJ DQG PXOWLSOH[LQJ PHWKRG 6HFWLRQ ,9
GHWDLOVWKHUHVXOWV7KHSDSHUHQGVZLWKWKHFRQFOXVLRQV
,,
/RFDO
DJHQW
$FFHVV
QHWZRUN
3OD\HUV
,QWHUQHW
3OD\HUV
$FFHVV
QHWZRUN
3OD\HUDQG
ORFDODJHQW
$ 2QOLQH*DPLQJ7UDIILF
7KHUHLVDVLJQLILFDQWDPRXQWRIOLWHUDWXUHUHJDUGLQJWRWKH
WUDIILFRIRQOLQHJDPHV:HZLOORQO\FRQVLGHUDFWLYHWUDIILFLH
WKH RQH JHQHUDWHG RQFH WKH JDPH KDV VWDUWHG 7KLV WUDIILF
SUHVHQWVWZRGLIIHUHQWEHKDYLRUV ILUVWWKHFOLHQWDSSOLFDWLRQLV
LQ FKDUJH RI FRPPXQLFDWLQJ WKH DFWLRQV RI WKH SOD\HUV WR WKH
VHUYHU XVLQJ VPDOO SDFNHWV ZLWK D VPDOO SHULRG 6HFRQG WKH
VHUYHUFDOFXODWHVWKHQHZVWDWHRIWKHJDPHDQGEURDGFDVWVLWWR
DOOWKHSOD\HUVXVLQJELJJHUSDFNHWVZKRVHVL]HGHSHQGVRQWKH
QXPEHURISOD\HUV5HI >@SUHVHQWHGDPHWKRGWRH[WUDSRODWH
VHUYHUWRFOLHQWWUDIILFREWDLQHGIURPHPSLULFDOPHDVXUHPHQWV
7KH\ REWDLQHG VL]H GLVWULEXWLRQV IRU DQ 1SOD\HU JDPH IURP
PHDVXUHGWUDIILFRIDQGSOD\HUV,QWKDWZRUNLWLVDOVRVDLG
WKDW WKH FOLHQW WR VHUYHU VL]H GLVWULEXWLRQLVLQGHSHQGHQWRI WKH
QXPEHURISOD\HUV
*DPH6HUYHU
D
,QWHUQHW
*DPH6HUYHU
,Q > @ D PLOOLRQ SDFNHW WUDFH RI &RXQWHU6WULNH ZDV
DQDO\]HG DQG D FRQFOXVLRQ ZDV WKDW WKH GHVLJQ RI WKH JDPH
WDUJHWV WKH VDWXUDWLRQ RI WKH ERWWOHQHFN ZKLFK LV WKH ODVWPLOH
OLQN $OVR LQ >@ WKH FKDUDFWHULVWLFV RI PDQ\ RQOLQH JDPHV
ZHUHDQDO\]HGLQWHUPVRISDFNHWVL]HDQGLQWHUSDFNHWWLPH,Q
>@DVXUYH\RIGLIIHUHQWWUDIILFPRGHOVIRUSRSXODUJDPHV
FDQEHIRXQG7KHVHVWXGLHVVKRZWKDWWKHVHJDPHVJHQHUDWHD
KLJK UDWH RI VPDOO SDFNHWV 7KLV EHKDYLRXU SURGXFHV D ELJ
RYHUKHDG VREDQGZLGWK VDYLQJV FDQEHDFKLHYHGE\ PHDQVRI
KHDGHUFRPSUHVVLQJDQGPXOWLSOH[LQJ
E
*DPH
3UR[\
&HQWUDO*DPH
6HUYHU
*DPH
3UR[\
,Q > @LWLV DOVR VDLG WKDW WKH PDLQ ERWWOHQHFN LV IUHTXHQWO\
WKHQXPEHURISDFNHWVSHUVHFRQGWKDWDURXWHUFDQPDQDJHDQG
QRW WKH EDQGZLGWK RI WKH DFFHVV OLQH 5RXWHUV DUH XVXDOO\
GHVLJQHG IRU ELJ SDFNHWV DQG FDQ H[SHULHQFH SUREOHPV ZKHQ
PDQDJLQJEXUVWVRIVPDOOSDFNHWV
*DPH
3UR[\
3OD\HUV
F
)LJXUH 6FHQDULRVZKHUHPDQ\SOD\HUVVKDUHWKHVDPHSDWK D SOD\HUV
VKDULQJDQDFFHVVQHWZRUNXVLQJDORFDODJHQWE SOD\HUVXVLQJWKHFRPSXWHU
RIDQRWKHURQHLQRUGHUWRFUHDWHWKHWXQQHOF 7UDIILFEHWZHHQSUR[\VHUYHUVRI
WKHVDPHJDPH7KLFNOLQHVUHSUHVHQWWKHWUDIILFRIDQXPEHURISOD\HUV
SPECTS 2011
5(/$7(':25.6
228
% ,QIUDVWUXFWXUHIRU6XSSRUWLQJ2QOLQH*DPHV
7KH SUREOHP RI WKH LQIUDVWUXFWXUH WKDW VXSSRUWV WKH JDPHV
KDVDOVREHHQVWXGLHGLQVRPHZRUNV)URPWKHSRLQWRIYLHZRI
WKHXVHU5HI>@SUHVHQWHGDQDOJRULWKPWRDOORZWKHFOLHQWWR
DGDSWLYHO\VHOHFWWKHEHVWVHUYHUIRUDFHUWDLQRQOLQHJDPH7KLV
FRXOGDOORZDJURXSRIXVHUVWRSOD\LQWKHVDPHVHUYHUDQGXVH
PXOWLSOH[LQJWHFKQLTXHV
PDNHV WKH LPSOHPHQWDWLRQ PRUH GLIILFXOW >@ DQG PD\ DGG
ELJJHUSURFHVVLQJGHOD\V
)URP WKH SRLQW RI YLHZ RI WKH VHUYHU WKHUH DUH WZR
DUFKLWHFWXUHV WR VXSSRUW WKLV VHUYLFH FHQWUDOL]HG DQG
GLVWULEXWHG,QWKHILUVWRQHWKHUHLVDVHUYHUWKDWPDLQWDLQVWKH
VWDWHRIWKHJDPHDQGGLVWULEXWHVLWWRWKHSOD\HUV7KHSUREOHP
LV WKDW WKH VHUYHU UHSUHVHQWV D ERWWOHQHFN ,Q GLVWULEXWHG
DUFKLWHFWXUHV >@ WKHUH LV QR QHHG IRU D FHQWUDO VHUYHU DV WKH
SOD\HUV H[FKDQJH WKH LQIRUPDWLRQ %XW WKLV DUFKLWHFWXUH LV
JHQHUDOO\QRWXVHGLQFRPPHUFLDOJDPHV
,Q WKLV VHFWLRQ ZH ZLOO H[SODLQ WKH SURSRVHG FRPSUHVVLQJ
DQGPXOWLSOH[LQJPHWKRG$VWXG\RIWKHEDQGZLGWKHIILFLHQF\
ZKLFKFDQEHDFKLHYHGLVDOVRSUHVHQWHG
7KHSUREOHPRIWKHVFDODELOLW\RIWKHUHTXLUHGLQIUDVWUXFWXUH
IRUWKHVHJDPHVZDVDOVRVWXGLHGE\0DXYHHWDO>@DQGWKH\
SURSRVHG WKH XVH RI SUR[LHV LQ RUGHU WR SURYLGH FRQJHVWLRQ
FRQWURO UREXVWQHVV UHGXFH GHOD\V DQG DYRLG FKHDWLQJ 6RPH
SUR[LHVFRXOGEHGLVWULEXWHGQH[WWRWKHSOD\HUVDYRLGLQJVRPH
ZRUNORDGWRWKHFHQWUDOVHUYHU5HI>@DOVRSURSRVHGWKHXVHRI
ERRVWHUER[HV ZKLFK ZRXOG EH QH[W WR WKH URXWHU DQG FRXOG
NQRZ WKH VWDWH RI WKH QHWZRUN EHLQJ DEOH WR JLYH QHWZRUN
VXSSRUW WR WKH DSSOLFDWLRQV $V VDLG LQ WKH LQWURGXFWLRQ WKH
VROXWLRQ SURSRVHG LQ WKH FXUUHQW ZRUN FRXOG HYHQ UXQ LQ WKH
PDFKLQHRIDSOD\HU
& &RPSUHVVLQJ$OJRULWKPV
6RPH ,(7) VWDQGDUGV WKDW FRPSUHVV KHDGHUV ZHUH
GHYHORSHG PDQ\ \HDUV DJR ILUVW 9-+& >@ SUHVHQWHG D
PHWKRG WR FRPSUHVV ,37&3 KHDGHUV 6RPH \HDUV ODWHU ,3+&
>@ ZDV DOVR DEOH WR FRPSUHVV 8'3 DQG ,3Y KHDGHUV $W WKH
VDPH PRPHQW &573 ZDV SUHVHQWHG LQ RUGHU WR FRPSUHVV
,38'3573 KHDGHUV DQG VRPH \HDUV ODWHU LW ZDV HQKDQFHG
DQGQDPHG(&573%XWWKHVHWZRSURWRFROVDUHQRWVXLWDEOHIRU
FRPSUHVVLQJ JDPLQJ WUDIILF DV LW LV QRW 573 7KHUH ZDV DQ
LQWHUHVWLQJSURSRVDO>@RIXVLQJDSURWRFROVLPLODUWR573IRU
RQOLQHJDPLQJ$QDGYDQWDJHRIWKLVSURSRVDOLVWKHSRVVLELOLW\
RIUHXVLQJJHQHULFVHUYLFHVDYRLGLQJWKHQHHGRILPSOHPHQWLQJ
WKHPIRUHYHU\JDPH%XWQRZDGD\VFRPPHUFLDOJDPHVPDLQO\
XVH,38'3SDFNHWV
7KHVH DOJRULWKPV FRPSUHVV KHDGHUV LQ D KRSE\KRS ZD\
XVLQJWKHKLJKUHGXQGDQF\RI,37&3DQG8'3KHDGHUILHOGVLQ
RUGHU WR DYRLG VHQGLQJ VRPH RI WKHP $ FRQWH[W LV GHILQHG
ZKLFKLVILUVWWUDQVPLWWHGIURPWKHVHQGHUWRGHGHVWLQDWLRQZLWK
WKHILUVWKHDGHUV7KHGLIIHUHQWKHDGHUILHOGVDUHFODVVLILHGLQWR
QRQFKDQJHUDQGRPGHOWDDQGLQIHUUHG7KHILUVWRQHVDUHRQO\
VHQW LQ IXOO KHDGHUV 5DQGRP KHDGHUV DUH VHQW ZLWKRXW
FRPSUHVVLRQ ZKLOH GHOWD RQHV DUH FRGLILHG XVLQJ OHVV E\WHV
WKDQWKHRULJLQDOVL]HRIWKHILHOG)LQDOO\LQIHUUHGKHDGHUVFDQ
EHREWDLQHGIURPWKHILHOGVRIRWKHUOD\HUVHJWKHOHQJWKRIWKH
SDFNHWFDQEHREWDLQHGIURPWKHOHYHOFRUUHVSRQGLQJILHOG
52+&Y>@LVDPRUHUHFHQWVWDQGDUGZKLFKLVDOVRDEOH
WRFRPSUHVV,38'3573KHDGHUVDQG,38'3RQHV,WUHGXFHV
WKH LPSDFW RI FRQWH[W GHV\QFKURQL]DWLRQ E\ SURYLGLQJ D
IHHGEDFNPHFKDQLVPIURPWKHGHFRPSUHVVRUWRWKHFRPSUHVVRU
,WXVHVWKUHHGLIIHUHQWFRPSUHVVLRQOHYHOVZKLFKFRUUHVSRQGWR
RSHUDWLRQ PRGHV ,QLWLDOL]DWLRQ DQG 5HIUHVK )LUVW 2UGHU DQG
6HFRQG2UGHU,QWKHODVWOHYHOWKHKHDGHUFDQEHFRPSUHVVHG
WR MXVW RQH E\WH >@ 7KH XVH RI WKHVH DGYDQFHG WHFKQLTXHV
SPECTS 2011
229
,,, &2035(66,1*$1'08/7,3/(;,1*0(7+2'
$ 7XQQHOLQJ&RPSUHVVLQJDQG0XOWLSOH[LQJ$OJRULWKP
,Q5)&>@WKH,(7)DSSURYHG7XQQHOHG&RPSUHVVHG
573 7&573 LQRUGHUWRFRPSUHVVDQGPXOWLSOH[573IORZV
)LUVW (&573 FRPSUHVVLQJ LV DSSOLHG DQG PDQ\ SDFNHWV DUH
LQFOXGHG LQWR WKH VDPH RQH XVLQJ 3330X[ )LQDOO\ D /73
WXQQHO LV XVHG LQ RUGHU WR VHQG WKH ZKROH PXOWLSOH[HG SDFNHW
HQGWRHQG
:HKDYHXVHGDVLPLODUVFKHPHEXWLQRXUFDVHWKHWUDIILFLV
QRW 573 VR ZH FDQ RQO\ FRPSUHVV ,38'3 KHDGHUV XVLQJ
,3+&RU52+&Y:HZLOOFDOOWKLVPHWKRG7XQQHO&RPSUHVV
0XOWLSOH[ IURP QRZ 7&0 )LJ VKRZV WKH SURWRFRO VWDFN
DQGWKH VWUXFWXUHRI D7&0 SDFNHW,W FDQ EH GLYLGHG LQWR WKH
QH[WSDUWV
x
x
x
x
Common Header (CH):&RUUHVSRQGVWRWKH,3/73
DQGWKH333KHDGHUV
PPPMux header (MH):,WLVLQFOXGHGDWWKHEHJLQQLQJ
RIHDFKFRPSUHVVHGSDFNHW
Reduced header (RH):,WFRUUHVSRQGVWRWKH,38'3
FRPSUHVVHGKHDGHURIHDFKRULJLQDOSDFNHW
Payload (P): ,W LV WKH 8'3 SD\ORDG RI WKH RULJLQDO
SDFNHWVJHQHUDWHGE\WKHDSSOLFDWLRQ
% 7KHRUHWLFDO$QDO\VLVRIWKH3URSRVHG0HWKRG
:H ZLOO QH[W PDNH DQ DQDO\VLV RI WKH EDQGZLGWK VDYLQJ
ZKLFKFDQEHDFKLHYHGE\WKHXVHRIWKLVWHFKQLTXH:HDVVXPH
WKDW WKH PXOWLSOH[HG SDFNHW VL]H ZLOO QHYHU EH DERYH
E\WHVZKLFKLVFHUWDLQIRUWKHWUDIILFVRIWKLVZRUN
$V VDLG LQ WKH LQWURGXFWLRQ SDFNHW GHOD\ KDV D YHU\ ELJ
LPSRUWDQFH IRU WKLV VHUYLFH 6R ZH KDYH XVHG D PXOWLSOH[LQJ
SROLF\WKDWPDLQWDLQVSDFNHWGHOD\XQGHUDQXSSHUERXQG,QWKH
PXOWLSOH[HULWLVGHILQHGDSHULRGQDPHG 7DQGDPXOWLSOH[HG
3D\ORDG
3D\ORDG
&RPSU+HDGHU
8'3
&RPSU+HDGHU
,3
3330X[
333
/73
,3
/73
KHDGHU
,3KHDGHU
&+
333
KHD
GHU
333
0X[
&RPSU
+HDGHU
3D\ORDG
0+
5+
3
333
0X[
&RPSU
+HDGHU
3D\ORDG
0+
5+
3
)LJXUH 7&0SURWRFROVWDFNDQGVFKHPHRIDPXOWLSOH[HGSDFNHW
1DWLYH
WUDIILF
SHULRG
SHULRG
SHULRG
SHULRG
0XOWLSOH[HG
WUDIILF
)LJXUH %HKDYLRURIWKHPXOWLSOH[LQJSROLF\
SDFNHW LV VHQW DW WKH HQG RI HDFK SHULRG LQFOXGLQJ DOO WKH
DUULYHGRQHV )LJ 7KHUH DUH WZR H[FHSWLRQV LI WKHUH LVQR
SDFNHW WR PXOWLSOH[ QRWKLQJ ZLOO EH VHQW DQG LI WKHUH LV RQO\
RQH SDFNHW LW ZLOO EH VHQW LQ LWV QDWLYH IRUP DV WKH XVH RI D
WXQQHOZRXOGPDNHLWEHELJJHU
:HZLOOUHIHUWRWKHSDFNHWVJHQHUDWHGE\WKHDSSOLFDWLRQDV
QDWLYHLQFRQWUDVWWRPXOWLSOH[HG PX[ RQHV:LWKWKLVSROLF\
WKH DYHUDJH UHWHQWLRQ GHOD\ ZLOO EH 7 DQG LWV XSSHU ERXQG
ZLOOEH7
$Q LQWHUHVWLQJ SDUDPHWHU LV WKH EDQGZLGWK UHODWLRQVKLS
%:5ZKLFKLVWKHGLYLVLRQRIPX[DQGQDWLYHEDQGZLGWKV:H
ZLOOGHQRWHWKHQXPEHURIDUULYHGSDFNHWVLQDSHULRGDVN1+
GHQRWHVWKHVL]HRIDQ,38'3KHDGHU,QRUGHUWRREWDLQ%:5
ZH ZLOO ILUVW FDOFXODWH WKH QXPEHU RI E\WHV VHQW LQ D SHULRG
ZKHQ PXOWLSOH[LQJ LV DSSOLHG VR ZH KDYH WR GLVWLQJXLVK WKH
FDVHRIKDYLQJRQHSDFNHW
VL]HPX[ 3U N 1+(>3@
3U N! >&+(>N_N!@ 0+(>5+@(>3@ @
1H[W WKH H[SHFWHG YDOXH RI WKH VL]H RI WKH QDWLYH SDFNHWV
DUULYHGLV
VL]HQDWLYH (>N@ 1+(>3@
%:5D
2Q EHKDOI RI FODULW\ ZH ZLOO QRW LQFOXGH KHUH WKH
FDOFXODWLRQ RI (>N_N!@ 3U N DQG 3U N! 7KHVH
FDOFXODWLRQV DUH LQFOXGHG LQ WKH $SSHQGL[ $V VKRZQ WKHUH
WKH\PD\YDU\GHSHQGLQJRQWKHEHKDYLRURIHDFKJDPH
,QRUGHUWRJHWQXPHULFDODQGJUDSKLFDOUHVXOWVZHZLOOQRZ
XVH WKH UHDO SDUDPHWHUV RI VRPH FRPPHUFLDO JDPHV DQG WKH
RQHVXVHGLQWKHSURSRVHGSURWRFROV
x
1+ E\WHV IRU ,3Y8'3 DQG E\WHV IRU
,3Y8'3
x
&+ E\WHVIRU,3Y FRUUHVSRQGWR,3WR/73
DQGWR333KHDGHU)RU,3Y&+ E\WHV
x
0+ E\WHVFRUUHVSRQGLQJWR3330X[
x
(>3@ 7KH YDOXH RI WKH 8'3 SD\ORDG GHSHQGV RQ WKH
DSSOLFDWLRQXVHG
x
(>N@ 7KHQXPEHURISDFNHWVSHUVHFRQGJHQHUDWHGE\
WKH1SOD\HUVRIWKHJDPH
x
(>5+@ ,Q WKLV H[DPSOH WR EH LQ WKH ZRUVW FDVH ZH
KDYHFRQVLGHUHG,3+&FRPSUHVVLQJ8'3KHDGHUVWR
E\WHV E\ XVLQJ RQO\ ELWV IRU WKH &,' ILHOG DQG
DYRLGLQJ WKH RSWLRQDO FKHFNVXP ,3Y DQG ,3Y
KHDGHUVFDQDOVREHFRPSUHVVHGWRE\WHV6RZHZLOO
FRQVLGHU E\WHV DYHUDJH IRU FRPSUHVVHG KHDGHUV DQG
RUE\WHVIRUIXOOKHDGHUVZKLFKDUHVHQWHYHU\
VHFRQGV WKH GHIDXOW )B0$;B7,0( SDUDPHWHU RI
,3+&
&+
3U N
3U N!
(>N @
(>N @ 1+ (> 3@
3U N!
(>N _ N ! @ 0+ (> 5+ @ (> 3@
(>N @
1+ (> 3@
7KHILUVWWHUPLVFDXVHGE\WKHGHFLVLRQRIQRWPXOWLSOH[LQJ
ZKHQ KDYLQJ RQO\RQHSDFNHW 7KH VHFRQGRQHH[SUHVVHV KRZ
WKHFRPPRQKHDGHULVVKDUHGE\WKHZKROHSDFNHW,WEHFRPHV
VPDOOHU DV WKH QXPEHU RI PXOWLSOH[HG SDFNHWV LQFUHDVHV 7KH
WKLUG WHUP GHSHQGV RQ WKH FRPSUHVVLQJ DOJRULWKP DQG LQ WKH
DYHUDJHSDFNHWVL]HJHQHUDWHGE\WKHDSSOLFDWLRQ
6RLI ZH KDYHDELJ QXPEHURI XVHUVRUDELJ SHULRG WKH
QXPEHURISDFNHWV ZLOO EHELJ DQG WKH ILUVW DQG VHFRQG WHUPV
ZLOO EHFRPH QHJOLJLEOH 5HJDUGLQJ WR WKH WKLUG RQH 3U N!
ZLOO DOPRVWEH DQG WKH VDPH ZLOO KDSSHQ WR (>N_N!@(>N@
6RZHFDQREWDLQWKHH[SUHVVLRQIRUDQDV\PSWRWHIRU%:5
SPECTS 2011
230
:HREVHUYHWKDWWKHVPDOOHUWKHYDOXHRI(>3@WKHVPDOOHU
WKHYDOXHRIWKHDV\PSWRWH6RWKHSUHVHQWHGWHFKQLTXHVKRXOG
KDYH DJRRGEHKDYLRULQDSSOLFDWLRQVWKDWJHQHUDWHD KLJKUDWH
RI VPDOO SDFNHWV DV )36 JDPHV GR /RJLFDOO\ LW LV H[SHFWHG
WKDW WKHELJJHU WKH QXPEHURISOD\HUV WKHEHWWHUWKH EHKDYLRU
DV WKH VDPH QXPEHU RI SDFNHWV FDQ EH PXOWLSOH[HG ZLWK OHVV
DGGHGGHOD\V$QGWKHLQFUHDVHRI7ZLOODOVREHEHQHILFLDOIRU
%:5 EXW ZH FDQ QRW LQFUHDVH LW LQGHILQLWHO\ DV SOD\HUV DUH
YHU\VHQVLWLYHWRGHOD\
$QGGLYLGLQJ DQG ZHREWDLQ%:5
%:5
0+ (> 5+ @ (> 3@
1+ (> 3@
8VLQJWKHVHYDOXHVZHREWDLQWKHYDOXHVVKRZQLQ7DEOH
7KH\DUHWKHYDOXHVRIWKHDV\PSWRWHLHWKHEHVW%:5WKDWFDQ
EH DFKLHYHG LI WKH QXPEHU RI XVHUV DQG WKH SHULRG DUH ELJ
7$%/(,
*DPH
%:5$6@ >@ ,Q RXU FDVH WKH
WUDFHVKDYHEHHQREWDLQHGZLWK2SHQ*/UHQGHULQJZKLFKLVWKH
PRVWFRPPRQRQHDQGKDVLQWHUSDFNHWWLPHVRIPVDQG
PVZLWKDRISUREDELOLW\HDFK7KLVPDNHVWKHYDOXHRI O
EHSDFNHWVSHUVHFRQG7KHDQDO\VLVRIWKHSUREDELOLWLHVIRU
WKLVWUDIILFKDVEHHQLQFOXGHGLQWKH$SSHQGL[VXEVHFWLRQ%
0XOWLSOH[HG
FRPSUHVVHG
DQGWXQQHOHG
3OD\HU
3OD\HUWR1
3OD\HU
SHULRG
3OD\HU1
3OD\HU1
)LJXUH 0HWKRGXVHGWREXLOGWKHWUDFHV
%DQGZLGWK5HODWLRQVKLS%:5
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
%:5
SHULRG PV
232
,QWHUSDFNHWWLPHKLVWRJUDP
LQWHUSDFNHWWLPH PV
)LJXUH +LVWRJUDPRILQWHUSDFNHWWLPHLQPV
SPECTS 2011
)LJXUH &RPSDUDWLYHRIWKHWKHRUHWLFDODQGWKHVLPXODWLRQUHVXOWVRI%:5
QXPEHURISDFNHWV
$VLPXODWLRQKDVEHHQFRQGXFWHGXVLQJ0DWODELQRUGHUWR
REWDLQWKHFRPSUHVVHGDQGPXOWLSOH[HGWUDIILFWUDFHVDVVKRZQ
LQ)LJ)LUVWWKHWUDFHLVVHSDUDWHGLQWRWKHLQGLYLGXDOWUDFHV
RI WKH GLIIHUHQW SOD\HUV DQG WKH VHUYHU WR FOLHQW WUDIILF LV
HOLPLQDWHG )RU JHQHUDWLQJ WKH WUDIILF IRU WKH WHVWV ZH H[WUDFW
WKHJHQHUDWLRQWLPHWKHXVHUDQGWKHVL]HRIWKHSDFNHWIURPWKH
UHDOWUDFHV1H[W,38'3FRPSUHVVLQJLVDSSOLHGWRHDFKIORZ
)LQDOO\ XVLQJ WKH SHULRG 7 WKH VL]HV DQG WLPHV RI WKH
PXOWLSOH[HGSDFNHWVDUHFDOFXODWHG
3OD\HU
,38'3
KHDGHUV
FRPSUHVVHG
1RWXVHG
,Q RUGHU WR FRPSDUH WKH VLPXODWLRQ UHVXOWV ZLWK WKH
WKHRUHWLFDORQHV ZH KDYH XVHG WKH VDPH JDPH LQWKLV VHFWLRQ
+DOI /LIH &RXQWHU 6WULNH 7KH WUDIILF WUDFHV KDYH EHHQ
REWDLQHG IURP &$,$ SURMHFW HJ WKH WUDFH IRU SOD\HUVLVLQ
>@ 7KHUH DUH DYDLODEOH WUDFHV IURP WR SOD\HUV7KHUH LV
DQ RIIVHW RI WKH ILUVW SDFNHWV DQG RQO\ WKH QH[W
QXPEHUBRIBSOD\HUV SDFNHWV DUHLQFOXGHG WR HQVXUH WKDW
DOOWKHSDFNHWVFRUUHVSRQGWRDFWLYHJDPHWUDIILFZKLFKLVWKH
RQHZHDUHVWXG\LQJ
,Q RUGHU WR REWDLQ WUDFHV IRU PRUH SOD\HUV ZH KDYH DGGHG
VRPH RI WKHP HJ ZH KDYH REWDLQHG D WUDFH RI SOD\HUV LQ
GHGXVW VFHQDULR E\ WKH DGGLWLRQ RI WKH WUDFHV RI DQG
SOD\HUV LQ WKH VDPH VFHQDULR 7KLV FDQ EH GRQH GXH WR D
SURSHUW\ RI WKH FOLHQW WR VHUYHU WUDIILF ZKRVH GLVWULEXWLRQ LV
LQGHSHQGHQW RI WKH QXPEHU RI SOD\HUV >@ >@ WKH FOLHQW WR
VHUYHUWUDIILFRIDSOD\HUJDPHZLOOEHVLPLODUWRWKHDGGLWLRQ
RIWKUHHJDPHVRI DQGSOD\HUV/RJLFDOO\ZHKDYHFXWWKH
WLPH RI WKH WUDFHV WR WKH VKRUWHVW RQH REWDLQLQJ WUDFHV RI
VHFRQGV
3OD\HU
3OD\HUWR1
&OLHQWWRVHUYHU
7TXHXH
6HUYHUWRFOLHQW
7UHWHQWLRQ 7SURFHVV
3DFNHWVSHUVHFRQG
7KHPHWKRGKDVEHHQWHVWHGZLWKWKHWUDIILFRI)36JDPHV
EHFDXVH WKHVH DSSOLFDWLRQV KDYH YHU\ VWULQJHQW WHPSRUDO
FRQVWUDLQWVDVSOD\HUVGHPDQGDKLJKLQWHUDFWLYLW\6LPXODWLRQV
KDYHEHHQFRQGXFWHGLQRUGHUWRVWXG\WKHEDQGZLGWKVDYLQJV
DQG WKHUHVXOWV VKRZ WKDW WKHEDQGZLGWK FDQEHUHGXFHG XS WR
IRU ,3Y DQG RYHU IRU ,3Y 7KH DGGHG GHOD\V FDQ
UHPDLQVPDOOLIWKHQXPEHURISOD\HUVVKDULQJWKHVDPHSDWKLV
ELJHQRXJK$VDIXWXUHOLQHZHFRQVLGHUWKHGHSOR\PHQWRIDQ
DOJRULWKPWKDWG\QDPLFDOO\DGMXVWVWKHPXOWLSOH[LQJSDUDPHWHUV
GHSHQGLQJRQWKHQXPEHURISOD\HUVDQGWKHQHWZRUNVWDWLVWLFV
DVGHOD\DQGSDFNHWORVV
SOD\HUV
SOD\HUV
SOD\HUV
SOD\HUV
SSV
$33(1',;
QDWLYH
3HULRGLQPV
)LJXUH 3DFNHWVSHUVHFRQGPDQDJHGE\WKHDFFHVVURXWHU
+HUH ZH SUHVHQW WKH FDOFXODWLRQV QHFHVVDU\ WR REWDLQ DQ
DQDO\WLFDO H[SUHVVLRQ RI (>N_N!@ ZKLFK LV UHTXLUHG WR EXLOG
WKH JUDSKV RI %:5 SUHVHQWHG LQ VHFWLRQ ,,, )LUVW ZH REWDLQ
(>N@DV
SOD\HUV
3DFNHWVL]HLQE\WHV
SOD\HUV
(>N@ 3U N (>N_N @3U N (>N_N @
SOD\HUV
SOD\HUV
E\WHV
3U N! (>N_N!@
$QGWDNLQJLQWRDFFRXQWWKDW(>N_N @ DQG(>N_N @
ZHREWDLQ
(>N_N!@
QDWLYH
3HULRGLQPV
)LJXUH6L]HRIPX[SDFNHWV
)LJ SUHVHQWVWKHQXPEHURISDFNHWVSHUVHFRQGPDQDJHG
E\WKHDFFHVVURXWHU$VH[SODLQHGLQVHFWLRQ,,$DUHGXFWLRQ
RI WKLVSDUDPHWHUFDQDOVREHLQWHUHVWLQJ:HREVHUYHWKDW WKH
ELJJHU WKH SHULRG WKH VPDOOHU WKH DPRXQW RI SDFNHWV SHU
VHFRQGZKLFKWHQGVWREHWKHLQYHUVHRIWKHSHULRGGHVSLWHWKH
QXPEHU RI SOD\HUV )LJ SUHVHQWV WKH SDFNHW VL]H ZKLFK
JURZVOLQHDUO\ZLWKWKHSHULRG
9
&21&/86,216
7KLV ZRUN KDV SUHVHQWHG D WXQQHOLQJ FRPSUHVVLQJ DQG
PXOWLSOH[LQJPHWKRGZKLFKFDQEHXVHGWRDFKLHYHEDQGZLGWK
VDYLQJV E\ FRPSUHVVLQJ KHDGHUV DQG JURXSLQJ SDFNHWV LQWR
ELJJHURQHV,WFDQEHXVHIXOLQRUGHUWRUHGXFHWKHRYHUKHDGRI
RQOLQH JDPLQJ WUDIILF DV WKHVH DSSOLFDWLRQV XVXDOO\ JHQHUDWH D
KLJK UDWH RI VPDOO SDFNHWV 7KH PHWKRG XVHV DQ ,38'3
FRPSUHVVLQJSURWRFROPXOWLSOH[LQJZLWK3330X[DQGD/73
WXQQHOLQRUGHUWRZRUNHQGWRHQG
7KH HQWHUSULVHV ZKLFK GHYHORS JDPHV FRXOG EH LQWHUHVWHG
RQUHGXFLQJWKHEDQGZLGWKDQGDOVRWKHQXPEHURISDFNHWVSHU
VHFRQG WKH\ KDYH WR PDQDJH7KH EDQGZLGWK VDYLQJVFDQ DOVR
EH LQWHUHVWLQJ LQ RUGHU WR REWDLQ D EHWWHU EHKDYLRU LQ DFFHVV
QHWZRUNVZLWKOLPLWHGEDQGZLGWK
233
6RZHQHHGWRREWDLQWKHH[SUHVVLRQVIRU3U N 3U N
DQG3U N! ,QWKHSUHYLRXVDQDO\VLVZHKDYHGHILQHGNDVWKH
WRWDOQXPEHURISDFNHWVDUULYHGWRWKHPXOWLSOH[HULHWKHVXP
RI WKH SDFNHWV IURP HDFK SOD\HU 1RZ ZH GHILQH O DV WKH
QXPEHU RI SDFNHWV RI D VLQJOH SOD\HU :H FRQVLGHU WKDW WKH 1
GLIIHUHQW SOD\HUV¶ SDFNHW DUULYDOV DUH LQGHSHQGHQW VR (>N@ 1
(>O@ 1O7
$ &RQVWDQWSDFNHWUDWH
7KH GLIIHUHQW SUREDELOLWLHV GHSHQG RQ WKH VWDWLVWLFDO
GLVWULEXWLRQRIWKH LQWHUSDFNHWGHOD\RIWKH VWXGLHGJDPH:H
ZLOOFRQVLGHUDFRQVWDQWSDFNHWUDWHDVLWRFFXUVLQPDQ\JDPHV
>@/HWWEHWKHLQWHUSDFNHWWLPH:HZLOOFRQVLGHU7 WLQ
RUGHUWRDYRLGELJDGGHGGHOD\VVRWKHPD[LPXPYDOXHRIOLV
DQGFRQVHTXHQWO\
(>O@ O7 3U O 3U O
,IZHKDYH7WWKHQ3U O VRXVLQJ
3U O (>O@ O7
3U O 3U O O7
$QGLIZHKDYH7!WWKHQ3U O VRNQRZLQJWKDWWKH
VXPRIWKHSUREDELOLWLHVLVDQGXVLQJ ZHREWDLQ
SPECTS 2011
(>N @ 3U N
3U N !
3U O (>N@ ±O7
3U O 3U O (>N@± O7
>@
$QGQRZZHFDQILQG3U N
3U N >3U O @ 1
>@
%XW3U N LVQXOOLIWKHUHLVPRUHWKDQRQHSOD\HUDQG7!W
DV HYHU\ SOD\HU ZLOO KDYH VHQW DW OHDVW RQH SDFNHW GXULQJ WKH
SHULRG6RWKHH[SUHVVLRQIRU3U N IRU7WLV
§1·
3U N _7W ¨¨ ¸¸ 3U O >3U O @ 1
©¹
>@
>@
>@
% 7ZRSRVVLEOHLQWHUSDFNHWWLPHV
,Q WKLV VXEVHFWLRQ ZH FRQVLGHU WKH FDVH RI D JDPH WKDW
JHQHUDWHVSDFNHWVXVLQJWZRGLIIHUHQWLQWHUSDFNHWWLPHV/HWW
EH WKH VPDOOHVW RQH DQG W WKH ELJJHVW RQH DQG S DQG S WKH
UHVSHFWLYHSUREDELOLWLHVRIKDYLQJWDQGW:HZLOOFRQVLGHUDV
KDSSHQVLQWKHJDPHFRQVLGHUHGLQWKLVZRUNWKDW7 WDQG
W W,QWKLVFDVHZHKDYHWKHQH[WYDOXHIRUO
O
SW S W
>@
> @
>@
>@
>@
:HZLOOQRZGLVWLQJXLVKWZRFDVHV)LUVWLIZHKDYH7 W
WKHQZHKDYHWKHVDPHFDVHDVLQ DQG DV3U O
,Q WKH FDVH W 7 W ZH KDYH WR ILQG 3U O LH WKH
SUREDELOLW\ RI KDYLQJ QR SDFNHWV LQ D SHULRG 7 ZKLFK ZLOO EH
WKH SUREDELOLW\ RI WKH SHULRG EHJLQQLQJ GXULQJ WKH ILUVW W7
VHFRQGVRIDQ LQWHUSDFNHW WLPH RIGXUDWLRQ W VR FRQVLGHULQJ
WKDWWKHFRQVHFXWLYHLQWHUSDFNHWWLPHVDUHLQGHSHQGHQW
3U O S
W 7
SW S W
SO W7
>@
>@
>@
>@
$QG QRZ XVLQJ DQG NQRZLQJ WKDW WKH VXP RI WKH
SUREDELOLWLHVKDVWREHZHZLOOEHDEOHWRREWDLQ
3U O O>7S 7W @
3U O SO 7W
>@
>@
> @
)LQDOO\ DQG FDQ EH XVHG LQ RUGHU WR REWDLQ WKH
SUREDELOLWLHVRIWKHGLIIHUHQWYDOXHVRIN
>@
5()(5(1&(6
>@
>@ & &KDPEHUV : )HQJ 6 6DKX ' 6DKD 0HDVXUHPHQWEDVHG
&KDUDFWHUL]DWLRQRID&ROOHFWLRQRI2QOLQH*DPHV,Q3URFHHGLQJVRIWKH
WK $&0 6,*&20 FRQIHUHQFH RQ ,QWHUQHW 0HDVXUHPHQW ,0&¶
86(1,;$VVRFLDWLRQ%HUNHOH\
>@ . &KHQ 3 +XDQJ & /HL *DPH WUDIILF DQDO\VLV $Q 00253*
SHUVSHFWLYH ,Q 3URFHHGLQJV RI WKH LQWHUQDWLRQDO ZRUNVKRS RQ 1HWZRUN
>@
SPECTS 2011
234
DQG RSHUDWLQJ V\VWHPV VXSSRUW IRU GLJLWDO DXGLR DQG YLGHR
1266'$9¶ SS $&01HZ
E\WKHXVHRI7XQQHOLQJ&RPSUHVVLQJDQG
0XOWLSOH[LQJ7HFKQLTXHV
-RVH6DOGDQD-HQLIHU0XULOOR-XOLiQ)HUQiQGH]1DYDMDV-RVp5XL]0DV-RVp,$]QDU(GXDUGR9LUXHWH1DYDUUR
&RPPXQLFDWLRQ7HFKQRORJLHV*URXS *7& ±$UDJRQ,QVWRI(QJLQHHULQJ5HVHDUFK ,$
'SW,(&$GD%\URQ%XLOGLQJ&368QLY=DUDJR]D
=DUDJR]D6SDLQ
^MVDOGDQDMHQLIHUPXULOORQDYDMDVMUXL]MLD]QDUHYLUXHWH`#XQL]DUHV
$EVWUDFW²7KH HQWHUSULVHV WKDW GHYHORS RQOLQH JDPHV QHHG
FKDUDFWHULVWLFV OLNH SHULRGLFLW\ ORFDOLW\ DQG VHOIVLPLODULW\
KDUGZDUH DQG EDQGZLGWK UHVRXUFHV LQ RUGHU WR JLYH D JRRG
$QRWKHUFRQFOXVLRQLVWKDWWKH\KDYH OHVVEDQGZLGWKDQGUHDO
VHUYLFH WR WKH XVHUV 7KHVH JDPHV SURGXFH D KLJK UDWH RI VPDOO
WLPHUHTXLUHPHQWVWKDQ)36
8'3 SDFNHWV IURP WKH FOLHQW WR WKH VHUYHU VR WKH RYHUKHDG LV
VLJQLILFDQW 7KH DFWLRQV RI WKH SOD\HUV KDYH WR EH SURSDJDWHG WR
WKHVHUYHUDQGWRWKHUHVW RIWKHSOD\HUVLQ DYHU\VKRUWWLPH VR
QHWZRUN GHOD\V DUH YHU\ FULWLFDO 7KLV ZRUN SUHVHQWV D PHWKRG
WKDW VDYHV EDQGZLGWK E\ WKH DGGLWLRQ RI D ORFDO DJHQW ZKLFK
TXHXHV SDFNHWV FRPSUHVVHV KHDGHUV DQG XVHV D WXQQHO WR VHQG D
QXPEHURI SDFNHWVLQWRD PXOWLSOH[HGRQH 7KHEHKDYLRXURIWKH
V\VWHP KDV EHHQ VWXGLHG IRU ,3Y DQG ,3Y VKRZLQJ WKDW
VLJQLILFDQWEDQGZLGWKVDYLQJVFDQEHDFKLHYHG)RUFHUWDLQWLWOHV
XS WR RI WKH EDQGZLGWK FDQ EH VDYHG IRU ,3Y 7KLV
SHUFHQWDJH JURZV XS WR IRU ,3Y DV WKLV SURWRFRO KDV D
ELJJHU RYHUKHDG 7KH FRVW RI WKHVH EDQGZLGWK VDYLQJV LV WKH
DGGLWLRQ RI D QHZ GHOD\ZKLFK KDV DQ XSSHU ERXQG WKDW FDQ EH
PRGLILHG6RWKHUHLVDWUDGHRII WKHELJJHUWKHDGGHGGHOD\VWKH
ELJJHUWKHEDQGZLGWKVDYLQJV2QWKHRWKHUKDQGWKHWHVWVVKRZ
WKDWLIWKHQXPEHURISOD\HUVLVELJHQRXJKWKHDGGHGGHOD\VFDQ
EHDFFHSWDEOHLQWHUPVRIXVHU¶VH[SHULHQFH
.H\ZRUGVJDPLQJ GHOD\ PXOWLSOH[LQJ FRPSUHVVLQJ
PHDVXUHPHQW QHWZRUNJDPHV 4XDOLW\RI([SHULHQFH )LUVW3HUVRQ
6KRRWHU
,
,1752'8&7,21
2QOLQHJDPLQJYLD,QWHUQHWLVDVHUYLFHWKDWJURZVTXLFNO\
ZRUOGZLGH7KHUHDUHVRPHWLWOHVZKLFKKDYHPLOOLRQVRIXVHUV
VR WKH HQWHUSULVHV WKDW GHYHORS WKH JDPHV KDYH WR IDFH D
GLIILFXOW SUREOHP ZKHQHYHU D QHZ WLWOH LV UHOHDVHG WKH\ QHHG
KDUGZDUH DQG EDQGZLGWK UHVRXUFHV LQ RUGHU WR DYRLG WKH
VDWXUDWLRQRIWKHLULQIUDVWUXFWXUH$VWKHVXFFHVVRIDQHZWLWOHLV
QRW YHU\ SUHGLFWDEOH WKH\ PD\ KDYH WR RYHUSURYLVLRQ WKHVH
UHVRXUFHVEHFDXVHWKHXVHUVWKDWEX\WKHJDPHKDYHWRUHFHLYH
DJRRGVHUYLFH,Q>@DVWXG\RIWKHEHKDYLRURIWKHJDPHUVZDV
SUHVHQWHGDQGWKHDXWKRUVFRQFOXGHGWKDWWKH\DUHYHU\GLIILFXOW
WRVDWLVI\ LIWKH\KDYHFRQQHFWLRQSUREOHPVWKH\XVXDOO\OHDYH
DQGQHYHUUHWXUQDQGWKH\GRQRWWHQGWREHOR\DOWRDVHUYHU
7ZR RI WKH PRVW SRSXODU JHQUHV RI RQOLQH JDPHV DUH
00253*V 0DVVLYH 0XOWLSOD\HU 2QOLQH 5ROH 3OD\LQJ
*DPHV DQG)36 )LUVW3HUVRQ6KRRWHUV 5HIHUHQFH>@VWXGLHG
WKH WUDIILF RI 00253*V FRQFOXGLQJ WKDW WKH\ KDYH VRPH
7KLV ZRUN KDV EHHQ SDUWLDOO\ ILQDQFHG E\ &38)/,3, 3URMHFW 0,&,11
7,1 0%$&7R,3 3URMHFW RI $UDJRQ ,' $JHQF\ DQG ,EHUFDMD
2EUD 6RFLDO DQG 1'&,3,44R( 3URMHFW RI &DWHGUD 7HOHIRQLFD 8QLY RI
=DUDJR]D
SPECTS 2011
227
,Q)36WKHDFWLRQVRIWKHSOD\HUVKDYHWREHSURSDJDWHGWR
WKHVHUYHUDQGWRWKHUHVWRIWKHSOD\HUVLQDYHU\VKRUWWLPHVR
QHWZRUN GHOD\V DUH YHU\ FULWLFDO7KHVH JDPHV SURGXFH D KLJK
UDWHRIVPDOO8'3SDFNHWV W\SLFDOO\VRPHWHQVRIE\WHV IURP
WKH FOLHQW WR WKH VHUYHU VR WKH RYHUKHDG FDXVHG E\ ,38'3
KHDGHUV LV VLJQLILFDQW 6HUYHU WR FOLHQW SDFNHWV DUH W\SLFDOO\
ELJJHU
7KHUHDUHVRPHVFHQDULRVZKHUHPDQ\SOD\HUVRIWKHVDPH
JDPH VKDUH WKH SDWK IURP WKH DFFHVV QHWZRUN WR WKH JDPH
VHUYHU HJ ,QWHUQHW &DIpV ZKLFK DUH YHU\ SRSXODU LQ PDQ\
FRXQWULHVIUHTXHQWO\KDYHFRPSXWHUVDEOHWRUXQRQOLQHJDPHV
DQGJDPHUVXVXDOO\JRWKHUHWRSOD\LQJURXSV )LJDDQGE
7KH WUDIILF EHWZHHQ VHUYHUV RI WKH VDPH JDPH LV DQRWKHU
VFHQDULR ZKHUH WKH SDFNHWV RI PDQ\ SOD\HUV VKDUH WKH VDPH
SDWK )LJF
7KHWUDIILFRIWKHVHJURXSVRISOD\HUVFRXOGEHFRPSUHVVHG
DQG PXOWLSOH[HG LQ RUGHU WR VDYH EDQGZLGWK WDNLQJ LQWR
DFFRXQWWKDWWKHDFFHVVQHWZRUNLVXVXDOO\WKHERWWOHQHFN$QG
LQ FDVH RI '6/ WKH XSOLQN KDV QRUPDOO\ OHVV EDQGZLGWK WKDQ
WKH GRZQOLQN %\ WKH DGGLWLRQ RI D ORFDO DJHQW ZKLFK TXHXHV
SDFNHWVFRPSUHVVHVKHDGHUVDQGVHQGVPXOWLSOHSDFNHWVLQWRD
ELJJHU RQH VRPH EDQGZLGWK VDYLQJ FRXOG EH DFKLHYHG DW WKH
FRVWRIDGGLQJQHZGHOD\VPDLQO\FDXVHGE\WKHUHWHQWLRQWLPH
DWWKHTXHXH
,QRUGHUWRDYRLGZRUNORDGWRWKHFHQWUDOJDPHVHUYHUVRPH
SURSRVDOV>@>@LQFOXGHGQHWZRUNHOHPHQWV SUR[LHV QH[WWR
WKHDFFHVVQHWZRUN,QFRQWUDVWWKHORFDODJHQWSURSRVHGLQWKH
FXUUHQWZRUNFRXOGEHGLVWULEXWHGZLWKWKHJDPHDSSOLFDWLRQLQ
WKHVDPHZD\DVORFDOVHUYHUVDUHGLVWULEXWHGZLWKFHUWDLQWLWOHV
7KHWXQQHOIURPWKHFOLHQWVWRWKHVHUYHUFRXOGHLWKHUEHFUHDWHG
E\ D GHGLFDWHG PDFKLQH )LJ D RU E\ WKH FRPSXWHU RI D
SOD\HU )LJE WKXVDYRLGLQJWKHFRVWRIDQHZPDFKLQH
$W WKHRWKHU VLGH WKH VHUYHUZRXOG KDYHWR LPSOHPHQW WKH
GHPXOWLSOH[HU DQG GHFRPSUHVVRU ZKLFK ZRXOG LPSO\ VRPH
SURFHVVLQJ FDSDFLW\ DQG VSDFH WR VWRUH WKH FRQWH[W RI HDFK
IORZ LHWKH LQIRUPDWLRQ QHFHVVDU\WRUHEXLOG WKH FRPSUHVVHG
KHDGHUV VRPHWHQVRIE\WHVDVZHZLOOVHH>@ 7KLVZLOOQRW
LPSO\ D VFDODELOLW\ SUREOHP DV WKH VHUYHU DOUHDG\ VWRUHV WKH
VWDWH RI WKH JDPH IRU HDFK SOD\HU 2Q WKH RWKHU KDQG WKH
VDYLQJVLQWHUPVRIEDQGZLGWKDQGSDFNHWVSHUVHFRQGPD\DOVR
EHEHQHILFLDOIRUWKHVHUYHU
,IWKHQXPEHURISOD\HUVLVELJHQRXJKLWFDQEHH[SHFWHG
WKDWZKLOHDGGLQJVPDOOGHOD\VDELJQXPEHURISDFNHWVFRXOG
EH PXOWLSOH[HG LQWR D ELJJHU RQH %DQGZLGWK VDYLQJ QRW RQO\
DIIHFWVWKH JDPLQJWUDIILFEXWLWFDQDOVREHEHQHILFLDOIRUWKH
EDFNJURXQG WUDIILF ZKLFK VKDUHV WKH DFFHVV ZLWK LW
)XUWKHUPRUH PXOWLSOH[LQJ KDV DQRWKHU DGYDQWDJH WKH QXPEHU
RISDFNHWVSHUVHFRQGWKHURXWHUKDVWRPDQDJHZLOOEHUHGXFHG
7KHUH H[LVW RWKHU DSSOLFDWLRQV DQG VFHQDULRV ZKHUH PDQ\
UHDOWLPH IORZV VKDUH WKH VDPH SDWK HJ 9R,3 WUXQNLQJ DQG
WKH XVH RI PXOWLSOH[LQJ DQG FRPSUHVVLQJ WHFKQLTXHV KDV EHHQ
SURSRVHG DQG HYHQ VWDQGDUGL]HG >@ IRU WKHP 0DQ\ RQOLQH
JDPHVSUHVHQWVLPLODUWUDIILFSDWWHUQVJHQHUDWLQJDKLJKUDWHRI
WLQ\ SDFNHWV DQG WKXVSUHVHQWLQJ D ELJRYHUKHDG7KH QRYHOW\
RI WKH SUHVHQW ZRUN LV WKH XVH RI VLPLODU PXOWLSOH[LQJ
WHFKQLTXHV IRU WKHVH JDPHV¶ WUDIILF LQ ZKLFK VLJQLILFDQW JDLQV
FDQDOVREHREWDLQHGZLWKRXWORVLQJTXDOLW\
:HZLOOPDLQO\VWXG\WKHVFHQDULRVSUHVHQWHGLQ)LJDDQG
EEXWPRVWRIWKHFRQFOXVLRQVFDQDOVREHDSSOLHGWRWKHWKLUG
RQH )LJF 2QO\FOLHQWWRVHUYHUWUDIILFLVVWXGLHGDVELJJHU
VDYLQJVFDQEHREWDLQHGDQGLQPDQ\VFHQDULRV HJ'6/ LWLV
WUDQVPLWWHG YLD WKH PRVW UHVWULFWLYH OLQN :H KDYH WR PHDVXUH
WKH LPSDLUPHQWV RQ WKH SDUDPHWHUV WKDW GHWHUPLQH WKH TXDOLW\
H[SHULHQFHGE\XVHUVLQRUGHUWRSURSHUO\WXQHWKHSDUDPHWHUV
WKDWGHILQHWKHWUDGHRIIEHWZHHQEDQGZLGWKVDYLQJDQGTXDOLW\
$OWKRXJK WKLV WHFKQLTXH FRXOG EH DSSOLHG WR RWKHU JDPH
JHQUHV ZH ZLOO XVH )36 WUDIILF LQ WKLV ZRUN DV WKHVH JDPHV
KDYH YHU\ VWULQJHQW UHDOWLPH UHTXLUHPHQWV 7KH VXEMHFWLYH
TXDOLW\ PDLQO\ GHSHQGV RQ GHOD\ DQG SDFNHW ORVV >@ 7KH
6\VWHP 5HVSRQVH 7LPH 657 WKH WLPH WKH V\VWHP QHHGV WR
GHWHFWDXVHUHYHQWWRSURFHVVLWDQGWRVHQGWKHXSGDWHGJDPH
VWDWHWRWKHORFDORXWSXWGHYLFH KDVWREHPDLQWDLQHGXQGHUD
FHUWDLQYDOXH
7KHUHVWRIWKHZRUNLVRUJDQL]HGDVIROORZV 1H[WVHFWLRQ
SUHVHQWV WKH UHODWHG ZRUNV 6HFWLRQ ,,, H[SODLQV WKH SURSRVHG
WXQQHOLQJ FRPSUHVVLQJ DQG PXOWLSOH[LQJ PHWKRG 6HFWLRQ ,9
GHWDLOVWKHUHVXOWV7KHSDSHUHQGVZLWKWKHFRQFOXVLRQV
,,
/RFDO
DJHQW
$FFHVV
QHWZRUN
3OD\HUV
,QWHUQHW
3OD\HUV
$FFHVV
QHWZRUN
3OD\HUDQG
ORFDODJHQW
$ 2QOLQH*DPLQJ7UDIILF
7KHUHLVDVLJQLILFDQWDPRXQWRIOLWHUDWXUHUHJDUGLQJWRWKH
WUDIILFRIRQOLQHJDPHV:HZLOORQO\FRQVLGHUDFWLYHWUDIILFLH
WKH RQH JHQHUDWHG RQFH WKH JDPH KDV VWDUWHG 7KLV WUDIILF
SUHVHQWVWZRGLIIHUHQWEHKDYLRUV ILUVWWKHFOLHQWDSSOLFDWLRQLV
LQ FKDUJH RI FRPPXQLFDWLQJ WKH DFWLRQV RI WKH SOD\HUV WR WKH
VHUYHU XVLQJ VPDOO SDFNHWV ZLWK D VPDOO SHULRG 6HFRQG WKH
VHUYHUFDOFXODWHVWKHQHZVWDWHRIWKHJDPHDQGEURDGFDVWVLWWR
DOOWKHSOD\HUVXVLQJELJJHUSDFNHWVZKRVHVL]HGHSHQGVRQWKH
QXPEHURISOD\HUV5HI >@SUHVHQWHGDPHWKRGWRH[WUDSRODWH
VHUYHUWRFOLHQWWUDIILFREWDLQHGIURPHPSLULFDOPHDVXUHPHQWV
7KH\ REWDLQHG VL]H GLVWULEXWLRQV IRU DQ 1SOD\HU JDPH IURP
PHDVXUHGWUDIILFRIDQGSOD\HUV,QWKDWZRUNLWLVDOVRVDLG
WKDW WKH FOLHQW WR VHUYHU VL]H GLVWULEXWLRQLVLQGHSHQGHQWRI WKH
QXPEHURISOD\HUV
*DPH6HUYHU
D
,QWHUQHW
*DPH6HUYHU
,Q > @ D PLOOLRQ SDFNHW WUDFH RI &RXQWHU6WULNH ZDV
DQDO\]HG DQG D FRQFOXVLRQ ZDV WKDW WKH GHVLJQ RI WKH JDPH
WDUJHWV WKH VDWXUDWLRQ RI WKH ERWWOHQHFN ZKLFK LV WKH ODVWPLOH
OLQN $OVR LQ >@ WKH FKDUDFWHULVWLFV RI PDQ\ RQOLQH JDPHV
ZHUHDQDO\]HGLQWHUPVRISDFNHWVL]HDQGLQWHUSDFNHWWLPH,Q
>@DVXUYH\RIGLIIHUHQWWUDIILFPRGHOVIRUSRSXODUJDPHV
FDQEHIRXQG7KHVHVWXGLHVVKRZWKDWWKHVHJDPHVJHQHUDWHD
KLJK UDWH RI VPDOO SDFNHWV 7KLV EHKDYLRXU SURGXFHV D ELJ
RYHUKHDG VREDQGZLGWK VDYLQJV FDQEHDFKLHYHGE\ PHDQVRI
KHDGHUFRPSUHVVLQJDQGPXOWLSOH[LQJ
E
*DPH
3UR[\
&HQWUDO*DPH
6HUYHU
*DPH
3UR[\
,Q > @LWLV DOVR VDLG WKDW WKH PDLQ ERWWOHQHFN LV IUHTXHQWO\
WKHQXPEHURISDFNHWVSHUVHFRQGWKDWDURXWHUFDQPDQDJHDQG
QRW WKH EDQGZLGWK RI WKH DFFHVV OLQH 5RXWHUV DUH XVXDOO\
GHVLJQHG IRU ELJ SDFNHWV DQG FDQ H[SHULHQFH SUREOHPV ZKHQ
PDQDJLQJEXUVWVRIVPDOOSDFNHWV
*DPH
3UR[\
3OD\HUV
F
)LJXUH 6FHQDULRVZKHUHPDQ\SOD\HUVVKDUHWKHVDPHSDWK D SOD\HUV
VKDULQJDQDFFHVVQHWZRUNXVLQJDORFDODJHQWE SOD\HUVXVLQJWKHFRPSXWHU
RIDQRWKHURQHLQRUGHUWRFUHDWHWKHWXQQHOF 7UDIILFEHWZHHQSUR[\VHUYHUVRI
WKHVDPHJDPH7KLFNOLQHVUHSUHVHQWWKHWUDIILFRIDQXPEHURISOD\HUV
SPECTS 2011
5(/$7(':25.6
228
% ,QIUDVWUXFWXUHIRU6XSSRUWLQJ2QOLQH*DPHV
7KH SUREOHP RI WKH LQIUDVWUXFWXUH WKDW VXSSRUWV WKH JDPHV
KDVDOVREHHQVWXGLHGLQVRPHZRUNV)URPWKHSRLQWRIYLHZRI
WKHXVHU5HI>@SUHVHQWHGDQDOJRULWKPWRDOORZWKHFOLHQWWR
DGDSWLYHO\VHOHFWWKHEHVWVHUYHUIRUDFHUWDLQRQOLQHJDPH7KLV
FRXOGDOORZDJURXSRIXVHUVWRSOD\LQWKHVDPHVHUYHUDQGXVH
PXOWLSOH[LQJWHFKQLTXHV
PDNHV WKH LPSOHPHQWDWLRQ PRUH GLIILFXOW >@ DQG PD\ DGG
ELJJHUSURFHVVLQJGHOD\V
)URP WKH SRLQW RI YLHZ RI WKH VHUYHU WKHUH DUH WZR
DUFKLWHFWXUHV WR VXSSRUW WKLV VHUYLFH FHQWUDOL]HG DQG
GLVWULEXWHG,QWKHILUVWRQHWKHUHLVDVHUYHUWKDWPDLQWDLQVWKH
VWDWHRIWKHJDPHDQGGLVWULEXWHVLWWRWKHSOD\HUV7KHSUREOHP
LV WKDW WKH VHUYHU UHSUHVHQWV D ERWWOHQHFN ,Q GLVWULEXWHG
DUFKLWHFWXUHV >@ WKHUH LV QR QHHG IRU D FHQWUDO VHUYHU DV WKH
SOD\HUV H[FKDQJH WKH LQIRUPDWLRQ %XW WKLV DUFKLWHFWXUH LV
JHQHUDOO\QRWXVHGLQFRPPHUFLDOJDPHV
,Q WKLV VHFWLRQ ZH ZLOO H[SODLQ WKH SURSRVHG FRPSUHVVLQJ
DQGPXOWLSOH[LQJPHWKRG$VWXG\RIWKHEDQGZLGWKHIILFLHQF\
ZKLFKFDQEHDFKLHYHGLVDOVRSUHVHQWHG
7KHSUREOHPRIWKHVFDODELOLW\RIWKHUHTXLUHGLQIUDVWUXFWXUH
IRUWKHVHJDPHVZDVDOVRVWXGLHGE\0DXYHHWDO>@DQGWKH\
SURSRVHG WKH XVH RI SUR[LHV LQ RUGHU WR SURYLGH FRQJHVWLRQ
FRQWURO UREXVWQHVV UHGXFH GHOD\V DQG DYRLG FKHDWLQJ 6RPH
SUR[LHVFRXOGEHGLVWULEXWHGQH[WWRWKHSOD\HUVDYRLGLQJVRPH
ZRUNORDGWRWKHFHQWUDOVHUYHU5HI>@DOVRSURSRVHGWKHXVHRI
ERRVWHUER[HV ZKLFK ZRXOG EH QH[W WR WKH URXWHU DQG FRXOG
NQRZ WKH VWDWH RI WKH QHWZRUN EHLQJ DEOH WR JLYH QHWZRUN
VXSSRUW WR WKH DSSOLFDWLRQV $V VDLG LQ WKH LQWURGXFWLRQ WKH
VROXWLRQ SURSRVHG LQ WKH FXUUHQW ZRUN FRXOG HYHQ UXQ LQ WKH
PDFKLQHRIDSOD\HU
& &RPSUHVVLQJ$OJRULWKPV
6RPH ,(7) VWDQGDUGV WKDW FRPSUHVV KHDGHUV ZHUH
GHYHORSHG PDQ\ \HDUV DJR ILUVW 9-+& >@ SUHVHQWHG D
PHWKRG WR FRPSUHVV ,37&3 KHDGHUV 6RPH \HDUV ODWHU ,3+&
>@ ZDV DOVR DEOH WR FRPSUHVV 8'3 DQG ,3Y KHDGHUV $W WKH
VDPH PRPHQW &573 ZDV SUHVHQWHG LQ RUGHU WR FRPSUHVV
,38'3573 KHDGHUV DQG VRPH \HDUV ODWHU LW ZDV HQKDQFHG
DQGQDPHG(&573%XWWKHVHWZRSURWRFROVDUHQRWVXLWDEOHIRU
FRPSUHVVLQJ JDPLQJ WUDIILF DV LW LV QRW 573 7KHUH ZDV DQ
LQWHUHVWLQJSURSRVDO>@RIXVLQJDSURWRFROVLPLODUWR573IRU
RQOLQHJDPLQJ$QDGYDQWDJHRIWKLVSURSRVDOLVWKHSRVVLELOLW\
RIUHXVLQJJHQHULFVHUYLFHVDYRLGLQJWKHQHHGRILPSOHPHQWLQJ
WKHPIRUHYHU\JDPH%XWQRZDGD\VFRPPHUFLDOJDPHVPDLQO\
XVH,38'3SDFNHWV
7KHVH DOJRULWKPV FRPSUHVV KHDGHUV LQ D KRSE\KRS ZD\
XVLQJWKHKLJKUHGXQGDQF\RI,37&3DQG8'3KHDGHUILHOGVLQ
RUGHU WR DYRLG VHQGLQJ VRPH RI WKHP $ FRQWH[W LV GHILQHG
ZKLFKLVILUVWWUDQVPLWWHGIURPWKHVHQGHUWRGHGHVWLQDWLRQZLWK
WKHILUVWKHDGHUV7KHGLIIHUHQWKHDGHUILHOGVDUHFODVVLILHGLQWR
QRQFKDQJHUDQGRPGHOWDDQGLQIHUUHG7KHILUVWRQHVDUHRQO\
VHQW LQ IXOO KHDGHUV 5DQGRP KHDGHUV DUH VHQW ZLWKRXW
FRPSUHVVLRQ ZKLOH GHOWD RQHV DUH FRGLILHG XVLQJ OHVV E\WHV
WKDQWKHRULJLQDOVL]HRIWKHILHOG)LQDOO\LQIHUUHGKHDGHUVFDQ
EHREWDLQHGIURPWKHILHOGVRIRWKHUOD\HUVHJWKHOHQJWKRIWKH
SDFNHWFDQEHREWDLQHGIURPWKHOHYHOFRUUHVSRQGLQJILHOG
52+&Y>@LVDPRUHUHFHQWVWDQGDUGZKLFKLVDOVRDEOH
WRFRPSUHVV,38'3573KHDGHUVDQG,38'3RQHV,WUHGXFHV
WKH LPSDFW RI FRQWH[W GHV\QFKURQL]DWLRQ E\ SURYLGLQJ D
IHHGEDFNPHFKDQLVPIURPWKHGHFRPSUHVVRUWRWKHFRPSUHVVRU
,WXVHVWKUHHGLIIHUHQWFRPSUHVVLRQOHYHOVZKLFKFRUUHVSRQGWR
RSHUDWLRQ PRGHV ,QLWLDOL]DWLRQ DQG 5HIUHVK )LUVW 2UGHU DQG
6HFRQG2UGHU,QWKHODVWOHYHOWKHKHDGHUFDQEHFRPSUHVVHG
WR MXVW RQH E\WH >@ 7KH XVH RI WKHVH DGYDQFHG WHFKQLTXHV
SPECTS 2011
229
,,, &2035(66,1*$1'08/7,3/(;,1*0(7+2'
$ 7XQQHOLQJ&RPSUHVVLQJDQG0XOWLSOH[LQJ$OJRULWKP
,Q5)&>@WKH,(7)DSSURYHG7XQQHOHG&RPSUHVVHG
573 7&573 LQRUGHUWRFRPSUHVVDQGPXOWLSOH[573IORZV
)LUVW (&573 FRPSUHVVLQJ LV DSSOLHG DQG PDQ\ SDFNHWV DUH
LQFOXGHG LQWR WKH VDPH RQH XVLQJ 3330X[ )LQDOO\ D /73
WXQQHO LV XVHG LQ RUGHU WR VHQG WKH ZKROH PXOWLSOH[HG SDFNHW
HQGWRHQG
:HKDYHXVHGDVLPLODUVFKHPHEXWLQRXUFDVHWKHWUDIILFLV
QRW 573 VR ZH FDQ RQO\ FRPSUHVV ,38'3 KHDGHUV XVLQJ
,3+&RU52+&Y:HZLOOFDOOWKLVPHWKRG7XQQHO&RPSUHVV
0XOWLSOH[ IURP QRZ 7&0 )LJ VKRZV WKH SURWRFRO VWDFN
DQGWKH VWUXFWXUHRI D7&0 SDFNHW,W FDQ EH GLYLGHG LQWR WKH
QH[WSDUWV
x
x
x
x
Common Header (CH):&RUUHVSRQGVWRWKH,3/73
DQGWKH333KHDGHUV
PPPMux header (MH):,WLVLQFOXGHGDWWKHEHJLQQLQJ
RIHDFKFRPSUHVVHGSDFNHW
Reduced header (RH):,WFRUUHVSRQGVWRWKH,38'3
FRPSUHVVHGKHDGHURIHDFKRULJLQDOSDFNHW
Payload (P): ,W LV WKH 8'3 SD\ORDG RI WKH RULJLQDO
SDFNHWVJHQHUDWHGE\WKHDSSOLFDWLRQ
% 7KHRUHWLFDO$QDO\VLVRIWKH3URSRVHG0HWKRG
:H ZLOO QH[W PDNH DQ DQDO\VLV RI WKH EDQGZLGWK VDYLQJ
ZKLFKFDQEHDFKLHYHGE\WKHXVHRIWKLVWHFKQLTXH:HDVVXPH
WKDW WKH PXOWLSOH[HG SDFNHW VL]H ZLOO QHYHU EH DERYH
E\WHVZKLFKLVFHUWDLQIRUWKHWUDIILFVRIWKLVZRUN
$V VDLG LQ WKH LQWURGXFWLRQ SDFNHW GHOD\ KDV D YHU\ ELJ
LPSRUWDQFH IRU WKLV VHUYLFH 6R ZH KDYH XVHG D PXOWLSOH[LQJ
SROLF\WKDWPDLQWDLQVSDFNHWGHOD\XQGHUDQXSSHUERXQG,QWKH
PXOWLSOH[HULWLVGHILQHGDSHULRGQDPHG 7DQGDPXOWLSOH[HG
3D\ORDG
3D\ORDG
&RPSU+HDGHU
8'3
&RPSU+HDGHU
,3
3330X[
333
/73
,3
/73
KHDGHU
,3KHDGHU
&+
333
KHD
GHU
333
0X[
&RPSU
+HDGHU
3D\ORDG
0+
5+
3
333
0X[
&RPSU
+HDGHU
3D\ORDG
0+
5+
3
)LJXUH 7&0SURWRFROVWDFNDQGVFKHPHRIDPXOWLSOH[HGSDFNHW
1DWLYH
WUDIILF
SHULRG
SHULRG
SHULRG
SHULRG
0XOWLSOH[HG
WUDIILF
)LJXUH %HKDYLRURIWKHPXOWLSOH[LQJSROLF\
SDFNHW LV VHQW DW WKH HQG RI HDFK SHULRG LQFOXGLQJ DOO WKH
DUULYHGRQHV )LJ 7KHUH DUH WZR H[FHSWLRQV LI WKHUH LVQR
SDFNHW WR PXOWLSOH[ QRWKLQJ ZLOO EH VHQW DQG LI WKHUH LV RQO\
RQH SDFNHW LW ZLOO EH VHQW LQ LWV QDWLYH IRUP DV WKH XVH RI D
WXQQHOZRXOGPDNHLWEHELJJHU
:HZLOOUHIHUWRWKHSDFNHWVJHQHUDWHGE\WKHDSSOLFDWLRQDV
QDWLYHLQFRQWUDVWWRPXOWLSOH[HG PX[ RQHV:LWKWKLVSROLF\
WKH DYHUDJH UHWHQWLRQ GHOD\ ZLOO EH 7 DQG LWV XSSHU ERXQG
ZLOOEH7
$Q LQWHUHVWLQJ SDUDPHWHU LV WKH EDQGZLGWK UHODWLRQVKLS
%:5ZKLFKLVWKHGLYLVLRQRIPX[DQGQDWLYHEDQGZLGWKV:H
ZLOOGHQRWHWKHQXPEHURIDUULYHGSDFNHWVLQDSHULRGDVN1+
GHQRWHVWKHVL]HRIDQ,38'3KHDGHU,QRUGHUWRREWDLQ%:5
ZH ZLOO ILUVW FDOFXODWH WKH QXPEHU RI E\WHV VHQW LQ D SHULRG
ZKHQ PXOWLSOH[LQJ LV DSSOLHG VR ZH KDYH WR GLVWLQJXLVK WKH
FDVHRIKDYLQJRQHSDFNHW
VL]HPX[ 3U N 1+(>3@
3U N! >&+(>N_N!@ 0+(>5+@(>3@ @
1H[W WKH H[SHFWHG YDOXH RI WKH VL]H RI WKH QDWLYH SDFNHWV
DUULYHGLV
VL]HQDWLYH (>N@ 1+(>3@
%:5D
2Q EHKDOI RI FODULW\ ZH ZLOO QRW LQFOXGH KHUH WKH
FDOFXODWLRQ RI (>N_N!@ 3U N DQG 3U N! 7KHVH
FDOFXODWLRQV DUH LQFOXGHG LQ WKH $SSHQGL[ $V VKRZQ WKHUH
WKH\PD\YDU\GHSHQGLQJRQWKHEHKDYLRURIHDFKJDPH
,QRUGHUWRJHWQXPHULFDODQGJUDSKLFDOUHVXOWVZHZLOOQRZ
XVH WKH UHDO SDUDPHWHUV RI VRPH FRPPHUFLDO JDPHV DQG WKH
RQHVXVHGLQWKHSURSRVHGSURWRFROV
x
1+ E\WHV IRU ,3Y8'3 DQG E\WHV IRU
,3Y8'3
x
&+ E\WHVIRU,3Y FRUUHVSRQGWR,3WR/73
DQGWR333KHDGHU)RU,3Y&+ E\WHV
x
0+ E\WHVFRUUHVSRQGLQJWR3330X[
x
(>3@ 7KH YDOXH RI WKH 8'3 SD\ORDG GHSHQGV RQ WKH
DSSOLFDWLRQXVHG
x
(>N@ 7KHQXPEHURISDFNHWVSHUVHFRQGJHQHUDWHGE\
WKH1SOD\HUVRIWKHJDPH
x
(>5+@ ,Q WKLV H[DPSOH WR EH LQ WKH ZRUVW FDVH ZH
KDYHFRQVLGHUHG,3+&FRPSUHVVLQJ8'3KHDGHUVWR
E\WHV E\ XVLQJ RQO\ ELWV IRU WKH &,' ILHOG DQG
DYRLGLQJ WKH RSWLRQDO FKHFNVXP ,3Y DQG ,3Y
KHDGHUVFDQDOVREHFRPSUHVVHGWRE\WHV6RZHZLOO
FRQVLGHU E\WHV DYHUDJH IRU FRPSUHVVHG KHDGHUV DQG
RUE\WHVIRUIXOOKHDGHUVZKLFKDUHVHQWHYHU\
VHFRQGV WKH GHIDXOW )B0$;B7,0( SDUDPHWHU RI
,3+&
&+
3U N
3U N!
(>N @
(>N @ 1+ (> 3@
3U N!
(>N _ N ! @ 0+ (> 5+ @ (> 3@
(>N @
1+ (> 3@
7KHILUVWWHUPLVFDXVHGE\WKHGHFLVLRQRIQRWPXOWLSOH[LQJ
ZKHQ KDYLQJ RQO\RQHSDFNHW 7KH VHFRQGRQHH[SUHVVHV KRZ
WKHFRPPRQKHDGHULVVKDUHGE\WKHZKROHSDFNHW,WEHFRPHV
VPDOOHU DV WKH QXPEHU RI PXOWLSOH[HG SDFNHWV LQFUHDVHV 7KH
WKLUG WHUP GHSHQGV RQ WKH FRPSUHVVLQJ DOJRULWKP DQG LQ WKH
DYHUDJHSDFNHWVL]HJHQHUDWHGE\WKHDSSOLFDWLRQ
6RLI ZH KDYHDELJ QXPEHURI XVHUVRUDELJ SHULRG WKH
QXPEHURISDFNHWV ZLOO EHELJ DQG WKH ILUVW DQG VHFRQG WHUPV
ZLOO EHFRPH QHJOLJLEOH 5HJDUGLQJ WR WKH WKLUG RQH 3U N!
ZLOO DOPRVWEH DQG WKH VDPH ZLOO KDSSHQ WR (>N_N!@(>N@
6RZHFDQREWDLQWKHH[SUHVVLRQIRUDQDV\PSWRWHIRU%:5
SPECTS 2011
230
:HREVHUYHWKDWWKHVPDOOHUWKHYDOXHRI(>3@WKHVPDOOHU
WKHYDOXHRIWKHDV\PSWRWH6RWKHSUHVHQWHGWHFKQLTXHVKRXOG
KDYH DJRRGEHKDYLRULQDSSOLFDWLRQVWKDWJHQHUDWHD KLJKUDWH
RI VPDOO SDFNHWV DV )36 JDPHV GR /RJLFDOO\ LW LV H[SHFWHG
WKDW WKHELJJHU WKH QXPEHURISOD\HUV WKHEHWWHUWKH EHKDYLRU
DV WKH VDPH QXPEHU RI SDFNHWV FDQ EH PXOWLSOH[HG ZLWK OHVV
DGGHGGHOD\V$QGWKHLQFUHDVHRI7ZLOODOVREHEHQHILFLDOIRU
%:5 EXW ZH FDQ QRW LQFUHDVH LW LQGHILQLWHO\ DV SOD\HUV DUH
YHU\VHQVLWLYHWRGHOD\
$QGGLYLGLQJ DQG ZHREWDLQ%:5
%:5
0+ (> 5+ @ (> 3@
1+ (> 3@
8VLQJWKHVHYDOXHVZHREWDLQWKHYDOXHVVKRZQLQ7DEOH
7KH\DUHWKHYDOXHVRIWKHDV\PSWRWHLHWKHEHVW%:5WKDWFDQ
EH DFKLHYHG LI WKH QXPEHU RI XVHUV DQG WKH SHULRG DUH ELJ
7$%/(,
*DPH
%:5$6@ >@ ,Q RXU FDVH WKH
WUDFHVKDYHEHHQREWDLQHGZLWK2SHQ*/UHQGHULQJZKLFKLVWKH
PRVWFRPPRQRQHDQGKDVLQWHUSDFNHWWLPHVRIPVDQG
PVZLWKDRISUREDELOLW\HDFK7KLVPDNHVWKHYDOXHRI O
EHSDFNHWVSHUVHFRQG7KHDQDO\VLVRIWKHSUREDELOLWLHVIRU
WKLVWUDIILFKDVEHHQLQFOXGHGLQWKH$SSHQGL[VXEVHFWLRQ%
0XOWLSOH[HG
FRPSUHVVHG
DQGWXQQHOHG
3OD\HU
3OD\HUWR1
3OD\HU
SHULRG
3OD\HU1
3OD\HU1
)LJXUH 0HWKRGXVHGWREXLOGWKHWUDFHV
%DQGZLGWK5HODWLRQVKLS%:5
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
SOD\HUVVLPXODWLRQ
SOD\HUVWKHRUHWLFDO
%:5
SHULRG PV
232
,QWHUSDFNHWWLPHKLVWRJUDP
LQWHUSDFNHWWLPH PV
)LJXUH +LVWRJUDPRILQWHUSDFNHWWLPHLQPV
SPECTS 2011
)LJXUH &RPSDUDWLYHRIWKHWKHRUHWLFDODQGWKHVLPXODWLRQUHVXOWVRI%:5
QXPEHURISDFNHWV
$VLPXODWLRQKDVEHHQFRQGXFWHGXVLQJ0DWODELQRUGHUWR
REWDLQWKHFRPSUHVVHGDQGPXOWLSOH[HGWUDIILFWUDFHVDVVKRZQ
LQ)LJ)LUVWWKHWUDFHLVVHSDUDWHGLQWRWKHLQGLYLGXDOWUDFHV
RI WKH GLIIHUHQW SOD\HUV DQG WKH VHUYHU WR FOLHQW WUDIILF LV
HOLPLQDWHG )RU JHQHUDWLQJ WKH WUDIILF IRU WKH WHVWV ZH H[WUDFW
WKHJHQHUDWLRQWLPHWKHXVHUDQGWKHVL]HRIWKHSDFNHWIURPWKH
UHDOWUDFHV1H[W,38'3FRPSUHVVLQJLVDSSOLHGWRHDFKIORZ
)LQDOO\ XVLQJ WKH SHULRG 7 WKH VL]HV DQG WLPHV RI WKH
PXOWLSOH[HGSDFNHWVDUHFDOFXODWHG
3OD\HU
,38'3
KHDGHUV
FRPSUHVVHG
1RWXVHG
,Q RUGHU WR FRPSDUH WKH VLPXODWLRQ UHVXOWV ZLWK WKH
WKHRUHWLFDORQHV ZH KDYH XVHG WKH VDPH JDPH LQWKLV VHFWLRQ
+DOI /LIH &RXQWHU 6WULNH 7KH WUDIILF WUDFHV KDYH EHHQ
REWDLQHG IURP &$,$ SURMHFW HJ WKH WUDFH IRU SOD\HUVLVLQ
>@ 7KHUH DUH DYDLODEOH WUDFHV IURP WR SOD\HUV7KHUH LV
DQ RIIVHW RI WKH ILUVW SDFNHWV DQG RQO\ WKH QH[W
QXPEHUBRIBSOD\HUV SDFNHWV DUHLQFOXGHG WR HQVXUH WKDW
DOOWKHSDFNHWVFRUUHVSRQGWRDFWLYHJDPHWUDIILFZKLFKLVWKH
RQHZHDUHVWXG\LQJ
,Q RUGHU WR REWDLQ WUDFHV IRU PRUH SOD\HUV ZH KDYH DGGHG
VRPH RI WKHP HJ ZH KDYH REWDLQHG D WUDFH RI SOD\HUV LQ
GHGXVW VFHQDULR E\ WKH DGGLWLRQ RI WKH WUDFHV RI DQG
SOD\HUV LQ WKH VDPH VFHQDULR 7KLV FDQ EH GRQH GXH WR D
SURSHUW\ RI WKH FOLHQW WR VHUYHU WUDIILF ZKRVH GLVWULEXWLRQ LV
LQGHSHQGHQW RI WKH QXPEHU RI SOD\HUV >@ >@ WKH FOLHQW WR
VHUYHUWUDIILFRIDSOD\HUJDPHZLOOEHVLPLODUWRWKHDGGLWLRQ
RIWKUHHJDPHVRI DQGSOD\HUV/RJLFDOO\ZHKDYHFXWWKH
WLPH RI WKH WUDFHV WR WKH VKRUWHVW RQH REWDLQLQJ WUDFHV RI
VHFRQGV
3OD\HU
3OD\HUWR1
&OLHQWWRVHUYHU
7TXHXH
6HUYHUWRFOLHQW
7UHWHQWLRQ 7SURFHVV
3DFNHWVSHUVHFRQG
7KHPHWKRGKDVEHHQWHVWHGZLWKWKHWUDIILFRI)36JDPHV
EHFDXVH WKHVH DSSOLFDWLRQV KDYH YHU\ VWULQJHQW WHPSRUDO
FRQVWUDLQWVDVSOD\HUVGHPDQGDKLJKLQWHUDFWLYLW\6LPXODWLRQV
KDYHEHHQFRQGXFWHGLQRUGHUWRVWXG\WKHEDQGZLGWKVDYLQJV
DQG WKHUHVXOWV VKRZ WKDW WKHEDQGZLGWK FDQEHUHGXFHG XS WR
IRU ,3Y DQG RYHU IRU ,3Y 7KH DGGHG GHOD\V FDQ
UHPDLQVPDOOLIWKHQXPEHURISOD\HUVVKDULQJWKHVDPHSDWKLV
ELJHQRXJK$VDIXWXUHOLQHZHFRQVLGHUWKHGHSOR\PHQWRIDQ
DOJRULWKPWKDWG\QDPLFDOO\DGMXVWVWKHPXOWLSOH[LQJSDUDPHWHUV
GHSHQGLQJRQWKHQXPEHURISOD\HUVDQGWKHQHWZRUNVWDWLVWLFV
DVGHOD\DQGSDFNHWORVV
SOD\HUV
SOD\HUV
SOD\HUV
SOD\HUV
SSV
$33(1',;
QDWLYH
3HULRGLQPV
)LJXUH 3DFNHWVSHUVHFRQGPDQDJHGE\WKHDFFHVVURXWHU
+HUH ZH SUHVHQW WKH FDOFXODWLRQV QHFHVVDU\ WR REWDLQ DQ
DQDO\WLFDO H[SUHVVLRQ RI (>N_N!@ ZKLFK LV UHTXLUHG WR EXLOG
WKH JUDSKV RI %:5 SUHVHQWHG LQ VHFWLRQ ,,, )LUVW ZH REWDLQ
(>N@DV
SOD\HUV
3DFNHWVL]HLQE\WHV
SOD\HUV
(>N@ 3U N (>N_N @3U N (>N_N @
SOD\HUV
SOD\HUV
E\WHV
3U N! (>N_N!@
$QGWDNLQJLQWRDFFRXQWWKDW(>N_N @ DQG(>N_N @
ZHREWDLQ
(>N_N!@
QDWLYH
3HULRGLQPV
)LJXUH6L]HRIPX[SDFNHWV
)LJ SUHVHQWVWKHQXPEHURISDFNHWVSHUVHFRQGPDQDJHG
E\WKHDFFHVVURXWHU$VH[SODLQHGLQVHFWLRQ,,$DUHGXFWLRQ
RI WKLVSDUDPHWHUFDQDOVREHLQWHUHVWLQJ:HREVHUYHWKDW WKH
ELJJHU WKH SHULRG WKH VPDOOHU WKH DPRXQW RI SDFNHWV SHU
VHFRQGZKLFKWHQGVWREHWKHLQYHUVHRIWKHSHULRGGHVSLWHWKH
QXPEHU RI SOD\HUV )LJ SUHVHQWV WKH SDFNHW VL]H ZKLFK
JURZVOLQHDUO\ZLWKWKHSHULRG
9
&21&/86,216
7KLV ZRUN KDV SUHVHQWHG D WXQQHOLQJ FRPSUHVVLQJ DQG
PXOWLSOH[LQJPHWKRGZKLFKFDQEHXVHGWRDFKLHYHEDQGZLGWK
VDYLQJV E\ FRPSUHVVLQJ KHDGHUV DQG JURXSLQJ SDFNHWV LQWR
ELJJHURQHV,WFDQEHXVHIXOLQRUGHUWRUHGXFHWKHRYHUKHDGRI
RQOLQH JDPLQJ WUDIILF DV WKHVH DSSOLFDWLRQV XVXDOO\ JHQHUDWH D
KLJK UDWH RI VPDOO SDFNHWV 7KH PHWKRG XVHV DQ ,38'3
FRPSUHVVLQJSURWRFROPXOWLSOH[LQJZLWK3330X[DQGD/73
WXQQHOLQRUGHUWRZRUNHQGWRHQG
7KH HQWHUSULVHV ZKLFK GHYHORS JDPHV FRXOG EH LQWHUHVWHG
RQUHGXFLQJWKHEDQGZLGWKDQGDOVRWKHQXPEHURISDFNHWVSHU
VHFRQG WKH\ KDYH WR PDQDJH7KH EDQGZLGWK VDYLQJVFDQ DOVR
EH LQWHUHVWLQJ LQ RUGHU WR REWDLQ D EHWWHU EHKDYLRU LQ DFFHVV
QHWZRUNVZLWKOLPLWHGEDQGZLGWK
233
6RZHQHHGWRREWDLQWKHH[SUHVVLRQVIRU3U N 3U N
DQG3U N! ,QWKHSUHYLRXVDQDO\VLVZHKDYHGHILQHGNDVWKH
WRWDOQXPEHURISDFNHWVDUULYHGWRWKHPXOWLSOH[HULHWKHVXP
RI WKH SDFNHWV IURP HDFK SOD\HU 1RZ ZH GHILQH O DV WKH
QXPEHU RI SDFNHWV RI D VLQJOH SOD\HU :H FRQVLGHU WKDW WKH 1
GLIIHUHQW SOD\HUV¶ SDFNHW DUULYDOV DUH LQGHSHQGHQW VR (>N@ 1
(>O@ 1O7
$ &RQVWDQWSDFNHWUDWH
7KH GLIIHUHQW SUREDELOLWLHV GHSHQG RQ WKH VWDWLVWLFDO
GLVWULEXWLRQRIWKH LQWHUSDFNHWGHOD\RIWKH VWXGLHGJDPH:H
ZLOOFRQVLGHUDFRQVWDQWSDFNHWUDWHDVLWRFFXUVLQPDQ\JDPHV
>@/HWWEHWKHLQWHUSDFNHWWLPH:HZLOOFRQVLGHU7 WLQ
RUGHUWRDYRLGELJDGGHGGHOD\VVRWKHPD[LPXPYDOXHRIOLV
DQGFRQVHTXHQWO\
(>O@ O7 3U O 3U O
,IZHKDYH7WWKHQ3U O VRXVLQJ
3U O (>O@ O7
3U O 3U O O7
$QGLIZHKDYH7!WWKHQ3U O VRNQRZLQJWKDWWKH
VXPRIWKHSUREDELOLWLHVLVDQGXVLQJ ZHREWDLQ
SPECTS 2011
(>N @ 3U N
3U N !
3U O (>N@ ±O7
3U O 3U O (>N@± O7
>@
$QGQRZZHFDQILQG3U N
3U N >3U O @ 1
>@
%XW3U N LVQXOOLIWKHUHLVPRUHWKDQRQHSOD\HUDQG7!W
DV HYHU\ SOD\HU ZLOO KDYH VHQW DW OHDVW RQH SDFNHW GXULQJ WKH
SHULRG6RWKHH[SUHVVLRQIRU3U N IRU7WLV
§1·
3U N _7W ¨¨ ¸¸ 3U O >3U O @ 1
©¹
>@
>@
>@
% 7ZRSRVVLEOHLQWHUSDFNHWWLPHV
,Q WKLV VXEVHFWLRQ ZH FRQVLGHU WKH FDVH RI D JDPH WKDW
JHQHUDWHVSDFNHWVXVLQJWZRGLIIHUHQWLQWHUSDFNHWWLPHV/HWW
EH WKH VPDOOHVW RQH DQG W WKH ELJJHVW RQH DQG S DQG S WKH
UHVSHFWLYHSUREDELOLWLHVRIKDYLQJWDQGW:HZLOOFRQVLGHUDV
KDSSHQVLQWKHJDPHFRQVLGHUHGLQWKLVZRUNWKDW7 WDQG
W W,QWKLVFDVHZHKDYHWKHQH[WYDOXHIRUO
O
SW S W
>@
> @
>@
>@
>@
:HZLOOQRZGLVWLQJXLVKWZRFDVHV)LUVWLIZHKDYH7 W
WKHQZHKDYHWKHVDPHFDVHDVLQ DQG DV3U O
,Q WKH FDVH W 7 W ZH KDYH WR ILQG 3U O LH WKH
SUREDELOLW\ RI KDYLQJ QR SDFNHWV LQ D SHULRG 7 ZKLFK ZLOO EH
WKH SUREDELOLW\ RI WKH SHULRG EHJLQQLQJ GXULQJ WKH ILUVW W7
VHFRQGVRIDQ LQWHUSDFNHW WLPH RIGXUDWLRQ W VR FRQVLGHULQJ
WKDWWKHFRQVHFXWLYHLQWHUSDFNHWWLPHVDUHLQGHSHQGHQW
3U O S
W 7
SW S W
SO W7
>@
>@
>@
>@
$QG QRZ XVLQJ DQG NQRZLQJ WKDW WKH VXP RI WKH
SUREDELOLWLHVKDVWREHZHZLOOEHDEOHWRREWDLQ
3U O O>7S 7W @
3U O SO 7W
>@
>@
> @
)LQDOO\ DQG FDQ EH XVHG LQ RUGHU WR REWDLQ WKH
SUREDELOLWLHVRIWKHGLIIHUHQWYDOXHVRIN
>@
5()(5(1&(6
>@
>@ & &KDPEHUV : )HQJ 6 6DKX ' 6DKD 0HDVXUHPHQWEDVHG
&KDUDFWHUL]DWLRQRID&ROOHFWLRQRI2QOLQH*DPHV,Q3URFHHGLQJVRIWKH
WK $&0 6,*&20 FRQIHUHQFH RQ ,QWHUQHW 0HDVXUHPHQW ,0&¶
86(1,;$VVRFLDWLRQ%HUNHOH\
>@ . &KHQ 3 +XDQJ & /HL *DPH WUDIILF DQDO\VLV $Q 00253*
SHUVSHFWLYH ,Q 3URFHHGLQJV RI WKH LQWHUQDWLRQDO ZRUNVKRS RQ 1HWZRUN
>@
SPECTS 2011
234
DQG RSHUDWLQJ V\VWHPV VXSSRUW IRU GLJLWDO DXGLR DQG YLGHR
1266'$9¶ SS $&01HZ