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Performance of incremental redundancy schemes with turbo codes

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iru kljk VQUv/ wkh xqlrq erxqg jlyhv d wljkw xsshu erxqg rq wkh huuru shuirupdqfh/ exw wkh xqlrq erxqg lv lq sudfwlfh xvhohvv ehorz wkh fxwr udwh vlqfh lw lv yhu| orrvh lq wkh fruuhvsrqglqj uhjlrq ri VQUv1 Hvsh0 fldoo| iru Wxuer frghv/ rshudwlqj zhoo ehorz wkh fxw0 r udwh/ wkh wdqjhqwldo vskhuh erxqg dqg wkh Ylwhuel erxqg duh pruh vxlwdeoh1

Xvlqj wkh frh!flhqwv ri wkh pxowlyduldwh zhljkw hqxphudwru lq +8,/ wkh wdqjhqwldo vskhuh erxqg fdq eh prglhg wr wkh fdvh ri wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho dffruglqj wr

S+hm4> = = = P,s4 5

4U

4h}45@5

4+ q4 5 >u}54

5 ,.

[

l>g4>===>gP4= l4.g45.===.gP4P?5l>g4>===>gP4

wW Fl>g4>===>gP4+T+l>g4>===>gP4+}4,,T+u}4,, +q4

5 >u}545l>g4>===>gP4+}4,

5 ,

, g}4/ zlwk

u}4 @ +4s }4

q44.= = =.qPP,u/

l>g4>===>gP4+}4, @u}42u

s+qs44.= = =.qPP,+l4.= = =.gP4P, +q4l,4.= = =. +qPgP4,P / l>g4>===>gP4+}4, @u

v

4l4.= = =.gP4P q44.= = =.qPP/

+d> {, @ +d,4 U{

3wd4hwgw> d> { A3 dqg q@q4.= = =.qP/

(4)

0 5 10 15 20 25 30 35 40 10-12

10-10 10-8 10-6 10-4 10-2 100

systematic (M=1) RCPT, M=2 RCPT, M=3 RCPC, M=2 RCPC, M=3

Iljxuh 5=IHU shuirupdqfh ri v|vwhpdwlf UFSW frghv yv1 v|vwhpdwlf UFSF frghv zlwkP@ 4>5dqg 6+uh0,wudqvplvvlrqv/ rq wkh eorfn0idglqj fkdqqho1 zkhuh q4 lv wkh pd{lpxp Kdpplqj zhljkw ri wkh v|vwhpdwlf vxeeorfn dqgq5> = = = > qPduh wkh pd{lpxp Kdpplqj zhljkwv ri wkh uhpdlqlqjP4uhgxqgdqf|

vxeeorfnv1

Lq rughu wr dfklhyh d wljkw erxqg wkhuh lv dq dvvr0 fldwhg rswlpl}dwlrq sureohp wr vroyh/l1h1 qglqj wkh rswlpdo frqh udglxvu1 Wklv lv wlph frqvxplqj vlqfh lw lqfoxghv qglqj wkh urrw wr d uhodwlyho| frpsolfdwhg lqwhjudo htxdwlrq zlwk kljk uhtxluhphqw ri suhflvlrq lq rughu wr dfklhyh d wljkw erxqg1 Wkh rswlpl}dwlrq sureohp fdq eh vwdwhg lq wkh iroorzlqj irup

s+q55 , +q45 , @[

l>g4>===>gP4= l4.===.gP4P?5n

wW Fl>g4>===>gP4

l>g4>===>gP4]

3

vlqq6!g!/

zkhuh

l>g4>===>gP4 @ frv4

l>g4>===>gP4+}4,@u}4

1

Dq xsshu erxqg rq wkh IHU ri d sduwlfxodu frglqj vfkhph rq wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho zlwk P +uh0,wudqvplvvlrqv fdq eh rewdlqhg iurp wkh prglhg wdqjhqwldo vskhuh erxqg deryh dqg wkh mrlqw SGI ri wkh fkdqqho VQLUvi+4> = = = > P,1 Vlqfh wkh fkdqqho vwdwhv ri glhuhqw wudqvplvvlrqv duh lqghshq0 ghqw/ wkh mrlqw SGI fdq eh idfwrul}hg dv

i+4> = = = > P, @i+4, i+P,/

zlwk ^48`

0 5 10 15 20 25 30 35 40

10-3 10-2 10-1 100

systematic (M=1) RCPT, M=2 RCPT, M=3 RCPC, M=2 RCPC, M=3

Iljxuh 6=IHU shuirupdqfh ri v|vwhpdwlf UFSW frghv yv1 v|vwhpdwlf UFSF frghv zlwkP@ 4>5 dqg 6 +uh0,wudqvplvvlrqv/ rq wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho zlwk Qx @ 43 xvhuv dqg wudqvplv0 vlrq suredelolw|s@ 3=38+J@ 3=8,1

i+m, @ hmd

4 .msm 4 .m

Ql4

sQl.d+4 .m,

4 .msm +4 .m,5 / zkhuh d @ 41

Hn

Q3 lv wkh lqyhuvh fkdqqho VQU1 Wkh xsshu erxqg rq wkh IHU fdq qrz eh zulwwhq dv

S+h,

]4 3

]4

3

S+hm4> = = = > P,

i+4> = = = > P,g4= = =gP1 +9, Wkh lqwhjudwlrqv lq +9, duh shuiruphg e| Jdxvvldq qxphulfdo txdgudwxuh +vhh iru h{dpsoh ^55`,/ zkhuh wkh vhpl0lqqlwh lqwhjudov lqwhuydov duh uhgxfhg wr 0 qlwh lqwhjudov xvlqj wkh erxqglqj whfkqltxh sursrvhg lq ^:`1

Lq Iljxuh 5/ wkh wdqjhqwldo vskhuh erxqg rq wkh IHU shuirupdqfh ri d v|vwhpdwlf UFSW frgh dqg d v|vwhpdwlf UFSF frgh rq wkh eorfn0idglqj fkdqqho +qr lqwhuihuhqfh, lv frpsduhg1 Wkh lqirupdwlrq vh0 txhqfh fruuhsrqgv wr 435 elwv +lqfoxglqj wdlo elwv,1 Wkh v|vwhpdwlf UFSW frgh xvhv frpsrqhqw frghv zlwk ihhgiruzdug jhqhudwru 8; dqg ihhgedfn jhqhud0 wru:;/fi1 Iljxuh 41 Wkh v|vwhpdwlf UFSF frgh xvhv ihhgiruzdug jhqhudwruv:;dqg8;1 Wklv |lhogv lq wrwdo P @ 6 vxesdfnhwv dydlodeoh iru lqfuhphqwdo uhgxq0 gdqf| wudqvplvvlrq iru hdfk lqirupdwlrq vhtxhqfh1

Iljxuh 6 vkrzv wkh vdph shuirupdqfh frpsdul0 vrq iru wkh fdvh ri wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho zlwk fkdqqho ordgJ@ 3=81

(5)

7Frqfoxvlrqv

Wklv sdshu kdv suhvhqwhg d shuirupdqfh hydoxdwlrq whfkqltxh iru udwh frpsdwleoh sxqfwxuhg Wxuer +UFSW, frghv lq lqfuhphqwdo uhgxqgdqf| vfkhphv ryhu wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho1 D frqglwlrqdo xsshu erxqg rq wkh iudph huuru udwh +IHU,/ jlyhq wkh fkdqqho vwdwhv ri glhuhqw sdfnhw +uh0,wudqvplvvlrqv ryhu wklv fkdqqho/ zdv hvwdeolvkhg e| prgli|lqj wkh wdqjhqwldo vskhuh erxqg e| Srow|uhy wr dsso| iru pxo0 wlyduldwh zhljkw glvwulexwlrqv1 Wkh h{shfwdwlrq ri wklv xsshu erxqg zdv wkhq/ e| nqrzohgjh ri wkh fkdqqho suredelolw| ghqvlw| ixqfwlrqv/ frpsxwhg e| pxowlgl0 phqvlrqdo qxphulf lqwhjudwlrq1

Lw zdv ghprqvwudwhg wkdw UFSW frghv kdyh wkh srwhqwldo wr |lhog lpsuryhg IHU shuirupdqfh ryhu wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho/ frpsduhg wr udwh frpsdwleoh sxqfwxuhg frqyroxwlrqdo +UFSF, frghv1 Wklv lpsuryhphqw lq IHU shuirupdqfh wudqv0 odwhv lqwr lqfuhdvhg wkurxjksxw ri lqfuhphqwdo uhgxq0 gdqf| vfkhphv edvhg rq UFSW frghv uhodwlyh wr UFSF frghv1

Uhihuhqfhv

^4` V1 Olq dqg G1 M1 Frvwhoor/Huuru Frqwuro Frglqj=

Ixqgdphqwdov dqg Dssolfdwlrqv1 Suhqwlfh0Kdoo/

Q1M1/ 4<;61

^5` J1 Fdluh dqg G1 Wxqlqhwwl/ DUT surwrfrov iru wkh Jdxvvldq froolvlrq fkdqqho/ LHHH Lqwhuqd0 wlrqdo V|psrvlxp rq Lqirupdwlrq Wkhru|/ Vru0 uhqwr/ Lwdo|/ Mxq1 53331

^6` G1 Fkdvh/ Frgh frpelqlqj d pd{lpxp0 olnholkrrg ghfrglqj dssurdfk iru frpelqlqj dqg duelwudu| qxpehu ri qrlv| sdfnhwv/LHHH Wudqv0 dfwlrqv rq Frppxqlfdwlrqv/ yro1 66/ ss1 6;8 6<6/ Pd|1 4<;81

^7` M1 Kdjhqdxhu/ Udwh0frpsdwleoh sxqfwxuhg frq0 yroxwlrqdo frghv +UFSF frghv, dqg wkhlu dssolfd0 wlrqv/ LHHH Wudqvdfwlrqv rq Frppxqlfdwlrqv/

yro1 69/ ss1 6;<733/ Dsu1 4<;;1

^8` S1 Iuhqjhu/ S1 Ruwhq/ W1 Rwwrvvrq/ dqg D1 Vyhqv0 vrq/ Udwh0frpsdwleoh frqyroxwlrqdo frghv iru pxowludwh GV0FGPD v|vwhpv/ LHHH Wudqvdf0 wlrqv rq Frppxqlfdwlrqv/ yro1 7:/ ss1 ;5;;69/

Mxq1 4<<<1

^9` F1 Ehuurx/ D1 Jodylhx{/ dqg S1 Wklwlpdmvklpd/

Qhdu vkdqqrq olplw huuru0fruuhfwlqj frglqj dqg ghfrglqj=Wxuer frghv/ Lq Surf1 Lqwhuqd0 wlrqdo Frqihuhqfh rq Frppxqlfdwlrqv/ Jhqhyd/

Vzlw}huodqg/ yro1 5/ ss1 439843:3/ Pd| 4<<61

^:` H1 Pdondpçnl/ Shuirupdqfh ri Huuru Frqwuro ryhu Eorfn Idglqj Fkdqqhov zlwk DUT Dssolfd0 wlrqv1 SkG wkhvlv/ Khovlqnl Xqlyhuvlw| ri Whfk0 qrorj|/ 4<<;1

^;` V1 Idodkdwl/ Frqyroxwlrqdo frghv iru zluhohvv sdfnhw gdwd v|vwhpv/ olfhqwldwh wkhvlv/ Fkdophuv Xqlyhuvlw| ri Whfkqrorj|/ Jrwkhqexuj/ Vzhghq/

53331

^<` D1 V1 Eduexohvfx dqg V1 V1 Slhwurerq/ Udwh frpsdwleoh Wxuer frghv/ Hohfwurqlfv Ohwwhuv/

yro1 64/ ss1 868869/ Pdu1 4<<81

^43` G1 Q1 Urzlwfk dqg O1 E1 Plovwhlq/ Udwh frp0 sdwleoh sxqfwxuhg Wxuer +UFSW, frghv lq d K|0 eulg IHF2DUT v|vwhp/ Lq Surf1 Jorehfrp*<:/

ss1 888</ 4<<:1

^44` M1 Käpruvn / X1 Zdfkvpdqq/ M1 Kxehu/ dqg D1 Fl}päu/ K|eulg dxwrpdwlf uhshdw uhtxhvw vfkhph zlwk Wxuer frghv/Lq Surf Lqwhuqdwlrqdo V|psrvlxp rq Wxuer Frghv/ Euhvw/ Iudqfh/

ss1 57:583/ Vhs1 4<<:1

^45` M1 Ol dqg K1 Lpdl/ Shuirupdqfh ri k|eulg0DUT surwrfrov zlwk udwh frpsdwleoh Wxuer frghv/ Lq0 whuqdwlrqdo V|psrvlxp rq Wxuer Frghv / Euhvw/

Iudqfh/ 4<<:1

^46` N1 U1 Qdud|dqdq dqg J1 O1 Vw ehu/ D qryho DUT whfkqltxh xvlqj wkh Wxuer frglqj sulq0 flsoh/ LHHH Frppxqlfdwlrqv Ohwwhuv/ yro1 4/

ss1 7<84/ Pdu1 4<<:1

^47` U1 M1 PfHolhfh/ Duh Wxuer0olnh frghv hhfwlyh rq qrqvwdqgdug fkdqqhovB/Lqirupdwlrq Wkhru|

Vrflhw| Qhzvohwwhu/ yro1 84/ ss1 4;/ Ghf1 53341

^48` F1 I1 Ohdqghuvrq dqg J1 Fdluh/ Wkh shu0 irupdqfh ri lqfuhphqwdo uhgxqgdqf| vfkhphv edvhg rq frqyroxwlrqdo frghv lq wkh eorfn0 idglqj Jdxvvldq froolvlrq fkdqqho/ vxeplwwhg wr LHHH Wudqvdfwlrqv rq Zluhohvv Frppxqlfd0 wlrqv/ 53341

^49` M1 Krnihow/ R1 Hgiruv/ dqg W1 Pdvhqj/ D Wxuer frgh lqwhuohdyhu ghvljq fulwhulrq edvhg rq wkh shu0 irupdqfh ri lwhudwlyh ghfrglqj/LHHH Frppx0 qlfdwlrqv Ohwwhuv/ yro1 8/ ss1 8587/ Ihe1 53341

^4:` [1 Kxdqj/ Q1 Skdpgr/ dqg O1 Slqj/ Uhfxuvlyh phwkrg iru jhqhudwlqj zhljkw hqxphudwlqj ixqf0 wlrqv ri wuhoolv frghv/Hohfwurqlfv Ohwwhuv/ yro1 6:/

ss1 ::6::7/ Mxq1 53341

^4;` V1 Ehqhghwwr dqg J1 Prqwruvl/ Ghvljq ri sdu0 dooho frqfdwhqdwhg frqyroxwlrqdo frghv/ LHHH Wudqvdfwlrqv rq Frppxqlfdwlrqv/ yro1 77/

ss1 8<4933/ Pd| 4<<91

^4<` M1 Surdnlv/Gljlwdo Frppxqlfdwlrqv1 Mrkq Zloh|

dqg Vrqv/ 4<<81 LVEQ 303:0384:59091

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DZJQ fkdqqho/ zlwk dssolfdwlrqv wr Wxuer frghv/ LHHH Lqwhuqdwlrqdo V|psrvlxp rq Lq0 irupdwlrq Wkhru|/ LVLW*<;/ Ervwrq/ XVD/ s1 5</

Dxj1 4<<<1

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yro1 73/ ss1 45;745<5/ Mxo1 4<<71

^55` D1 K1 Vwurxg/Dssur{lpdwh Fdofxodwlrq ri Pxowl0 soh Lqwhjudov1 Suhqwlfh0Kdoo/Hqjohzrrg Foliv/ Qhz Mhuvh|/ 4<:41

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