The Performance of Incremental Redundancy

4 downloads 0 Views 368KB Size Report
formance with random binary and Gaussian coding in the limit of large block lengths, ... random coding may provide significantly better throughput performance, ...


Ai ihuLh4@?Ui Lu W?Uhi4i?|@* +i_?_@?U) 5Ui4it M@ti_ L? L?L*|L?@* L_it ? |i *LU!6@_?} B@tt@? L**tL? @??i*

@h* 6hi_h! wi@?_ihtL?4 @?_ BtiTTi @hi5 4

+@_L L44?U@|L?t BhLTc w?_ N?iht|)  L Hc 5,22 ffc 5i_i?

L?iG neS Ef e S222 f2c 6@ G neS Ef e S222 e.Hc ,4@*G @h* 6hi_h!wi@?_ihtL?9it*|ti 5

LM*i L44?U@|L?t BhLTc W?t||| ,hiUL4c

 L b c fSbfec 5LT@?|TL*t ,#,jc 6h@?Ui L?iG n Ef e b ff 2bfec 6@ G n Ef e b ff 2S2.c ,4@*G BtiTTi@hi9ihiUL4uh

6iMh@h) fc 2ff

#+6A

2

Devwudfw Wkh wkurxjksxw shuirupdqfh ri lqfuhphqwdo uhgxqgdqf| +LQU, vfkhphv/ edvhg rq vkruw frqvwudlqw ohqjwk frqyroxwlrqdo frghv/ lv hydoxdwhg iru wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho1 Uhvxowv edvhg rq vlpxodwlrqv dqg xqlrq erxqg frpsxwdwlrqv duh frpsduhg wr hvwlpdwhv ri wkh dfklhydeoh wkurxjksxw shu0 irupdqfh zlwk udqgrp elqdu| dqg Jdxvvldq frglqj lq wkh olplw ri odujh eorfn ohqjwkv/ rewdlqhg wkurxjk lqirupdwlrq rxwdjh frqvlghudwlrqv1 Iru orz fkdqqho ordgv/ lw lv revhuyhg wkdw LQU vfkhphv zlwk elqdu| frqyroxwlrqdo frghv dqg olplwhg eorfn ohqjwk pd| surylgh wkurxjksxw forvh wr wkh dfklhydeoh shuirupdqfh iru elqdu| udqgrp frglqj1 Krzhyhu/ iru wkhvh orz ordgv/ frpsduhg wr elqdu| udqgrp frglqj/ Jdxvvldq udqgrp frglqj pd| surylgh vljqlfdqwo| ehwwhu wkurxjksxw shuirupdqfh/ zklfk surpswv wr wkh xvh ri odujhu prgxodwlrq frqvwhoodwlrqv1 Iru kljk fkdqqho ordgv/ d uhodwlyho| odujh jds lq wkurxjksxw shuirupdqfh ehwzhhq elqdu| frqyroxwlrqdo frghv dqg elqdu| udqgrp frghv lqglfdwhv d srwhqwldo iru h{whqvlyh shuiru0 pdqfh lpsuryhphqw e| dowhuqdwlyh frglqj vwudwhjlhv1 Rqo| vpdoo lpsuryhphqwv ri wkh wkurxjksxw kdyh ehhq revhuyhg e| lqfuhdvlqj wkh frpsoh{lw| wkurxjk lqfuhdvhg vwdwh frqyroxwlrqdo frglqj1 Nh|zrugv Wkurxjksxw/ frqyroxwlrqdo frghv/ lqfuhphqwdo uhgxqgdqf|/ k|eulg dxwrpdwlf uhshdw uhtxhvw1

Y YA|iNaW|NA W?Uhi4i?|@* hi_?_@?U) EW+ |iU?^it @hi tMiU| |L @? ?Uhi@t?} ?|ihit| ? Lh_ih |L @Uii |h@?t4ttL? | *L ihhLh ThLM@M*|) ? T@U!i|Lhi?|i_ }tTii_ hi*itt *?!t W? |t T@Tihc ULihi?| T@U!i|Lhi?|i_ |h@?t4ttL? ? @ u@_?} 4*|T*i@UUitt i?hL?4i?| t 4L_i*i_ M) @ M*LU!u@_?} B@tt@? UL**tL? U@??i* @?_ |i |hL}T| @Uii_ | W+ tUi4it M@ti_ L? UL?L*|L?@* UL_it t t|_i_ Ai @Ui@M*i Tih uLh4@?Uic ? |ih4t Lu |hL}T| ? M|t%t%O3c uLh _gihi?| 4*|T*i@UUitt ThL|LUL*t Lih |t U@??i* @t hiUi?|*) Mii? ?it|}@|i_ ? do W? |i U@ti ihi |i hiUiih @t Tih uiU| !?L*i_}i @ML| |i U@??i* t|@|i @?_ t?}*itih _i|iU|L? t TihuLh4i_c ?uLh4@|L? |iLhi|U UL?t_ih@|L?t uLh B@tt@? h@?_L4 UL_itc M@ti_ L? |i UL?UiT| Lu ?uLh4@|L? L|@}i ThLM@M*|) d2c oc ?_U@|i |@| W+ tUi4it _L @i |i TL|i?|@* |L )i*_ t4T*i @?_ iUi?| ihhLh ULhhiU|L? uLh t*L||i_ B@tt@? 4*|T*i@UUitt U@??i*t #i |L |i t|LU@t|U ?@|hi Lu |i U@??i* T@h@4i|iht Lu |i M*LU!u@_?} B@tt@? UL**tL? U@??i*c U@T@U|) ihtt ?uLh4@|L? L|@}i ThLM@M*|) t @ 4Lhi ti?tM*i Tih uLh4@?Ui ?_U@|Lh |@? @ih@}i U@T@U|) ? |i U@ti Lu T@U!i|Lhi?|i_c _iUL_?}_i*@) UL?t|h@?i_ t)t|i4tc i} 4LM*iUi***@h h@_L decDo Lh ?_LLh *LU@* @hi@ ?i|Lh!t 5?Ui uLh 6iMh@h) .

#+6A



@?) |h@?t4ttL? h@|ic |ihi t @ ?L?3ihL ThLM@M*|) Lu LTih@|L? Mi*L |i ?t|@?|@?iLt U@??i* U@T@U|)c |i U@??i* U@T@U|)c ? |i t|hU| ti?tic t i^@* |L 3ihL 6h|ih4Lhic |i @ih@}i U@??i* U@T@U|) U@??L| Mi @Uii_ _i |L |i €?|i UL_i *i?}| UL?t|h@?| 4TLti_ M) |i hi^hi4i?| uLh *4|i_ _iUL_?} _i*@) OLiihc ? |i U@ti Lu @ t)t|i4 | *@h}i M@?__||4i ThL_U|c i ` A

c | U@? Mi @h}i_ |@| h|@**) ihhLhuhii

_iUL_?} U@? Mi @Uii_ @t *L?} @t |i |h@?t4ttL? h@|i t *itt |@? |i ?t|@?|@?iLt U@T@U|) hit*|?} uhL4 iih) ?t|@?Ui Lu |i U@??i* T@h@4i|iht tL4i|?} |@| L*_ t|u) @? ihhLhTihuLh4@?Ui i@*@|L? M@ti_ L? ?uLh4@|L? L|@}i ThLM@M*|) d o W| t UL44L? |L hit|hU| |i @?@*)tt Lu 4*|T*i@UUitt t)t|i4t |L |i ?L?u@_?} U@ti Ai @Ui@M*i TihuLh4@?Ui uLh ?L?u@_?} ?|ihuihi?Ui U@??i*t @i Mii? t|_i_ ? dSo @?_ _gihi?| UL_i_ 4L_*@|L? @?_ ?|ih*i@?} t|h@|i}it uLh tU U@??i*t @i Mii? ?it|}@|i_ ? d.o W? d.oc | @t @h}i_ |@| U@??i* UL_it | } _iht|) @?_ }LL_ TihuLh4@?Ui L? u@_?} U@??i*t L*_ Mi hitt|@?| @*tL |L 4*|T*i@UUitt ?|ihuihi?Uic hit*|?} uhL4 tiih@* tiht t4*|@?iLt*) |h)?} |L @**LU@|i |i t@4i |h@?t4ttL? t*L| Ai h@|L?@*i uLh |t t |@| i@)c ?t|@?|@?iLtc ?|ihuihi?Ui UL*_ Mi tii? @t @ !?_ Lu i |hi4i u@_?} _T W? |t T@Tihc i Thiti?| tL4i tTTLh|?} hit*|tc M@ti_ L? Lht|U@ti T@hti ihhLh ii?| ThLM@M*|) E,c ?_U@|?} |@| |i ThL_U| _t|@?Ui 4i@thic ti_ |L @ttitt |i TihuLh4@?Ui Lu UL_i_ t)t|i4t Lih M*LU!u@_?} U@??i*t ? dHoc 4@) Mi ti_ |L €?_ }LL_ UL_it @*tL uLh |i M*LU!u@_?} B@tt@? UL**tL? U@??i* OLiihc _it}? Lu Th@U|U@* *LUL4T*i |) UL_it | } TihuLh4@?Ui L? 4*|T*i @UUitt U@??i*t ? |i Thiti?Ui Lu u@_?}c t t|** @ U@**i?}?} tti @?_ | t ?L| U*i@h i|ih ?Uhi@ti_ UL4T*i |) UL_?} tUi4it tU @t *L?} UL?t|h@?| *i?}| UL?L*|L?@* UL_it Lh |ih@|i _iUL_?} tUi4it tU @t AhML UL_it dbo Lh *L_i?t|) T@h|)UiU! UL_it dfo t |i @) |L }L ? Lh_ih |L ?Uhi@ti |i |hL}T| Lih tU U@??i*t W?tThi_ M) |t U@**i?}ic i t|_) |i |hL}T| TihuLh4@?Ui Lu W+ tUi4it M@ti_ L? @ ti*iU|L? Lu *LUL4T*i |) M?@h) UL?L*|L?@* UL_it @?_ i UL4T@hi | |i *4|?} TihuLh4@?Ui Lu ih) *L?} M?@h) @?_ B@tt@? h@?_L4 UL_it W| t LMtihi_ |@| W+ tUi4it | M?@h) UL?L*|L?@* UL_it Lu *4|i_ M*LU! *i?}|t 4@) ThL_i |hL}T| U*Lti |L |i @Ui@M*i TihuLh4@?Ui uLh M?@h) t}?@*?} @| *L U@??i* *L@_t OLiihc uLh |iti *L *L@_tc B@tt@? h@?_L4 UL_?} ThL_it t}?€U@?|*)

6iMh@h) .

#+6A

e

Mi||ih |hL}T| TihuLh4@?Uic U ThL4T|t |L |i ti Lu *@h}ih 4L_*@|L? UL?t|i* *@|L?t 6Lh } U@??i* *L@_tc |ihi t TL|i?|@* uLh *@h}i 4ThLi4i?| M) @*|ih?@|i UL_?} t|h@|i}itc L|ih |@? UL?L*|L?@* UL_?}c t?Ui L?*) ih) t4@** 4ThLi4i?|t @i Mii? LMtihi_ M) ?Uhi@t?} |i UL4T*i |) |hL} ?Uhi@ti_ t|@|i UL?L*|L?@* UL_?} YY 7+t|j6 $jtWiV|NA  t*L||i_ 4*|T*i@UUitt UL44?U@|L? t)t|i4 t UL?t_ihi_ Aihi @hic ? |L|@*c  tiht ? |i t)t|i4c @U|i @UULh_?} |L @ ih?L** _t|hM|L? | ThLM@M*|) R ? iih) |4i t*L| r `i UL?t_ih @ t|@|U ThL|LUL* ihi |i |h@?t4ttL? ThLM@M*|it Lu |i ?__@* tiht @hi UL?t|@?| ? |4i @?_ |i *L@_ Lu |i t)t|i4 t C ' R    Ai |h@?t4ttL? ThLM@M*|it Lu ?__@* tiht @hi |t ?L| @giU|i_ M) |i @4L?| Lu _iUL_?} u@*hit uLh |ih ThiLt*) |h@?t4||i_ T@U!i|t  tMti| Lu ?|ihuihiht NEr L| Lu @ |L|@* Lu  '    TL|i?|@* ?|ihuihiht @hi t4*|@?iLt*) @U|i ? |4i t*L| r @UULh_?} |L @ M?L4@* _t|hM|L? | T@h@4i|iht E c R Ai |h@?t4||i_ t}?@* Lu @ tihc @t i** @t |i ?|ihuih?} t}?@*tc @hi tMiU| |L M*LU!?_iTi?_i?| +@)*i} u@_?} | UL4T*i i?i*LTi S&cr uLh i@U @U|i tih & W? |i t)t|i4 4L_i*c |ihi t @*tL @ ?Lti UL?|hM|L? &crc, _i |L |ih4@* ?Lti @?_ ?|ihuihi?Uic ?_iTi?_i?| uLh i@U t)4ML* TLt|L? , Ai _iUL_ih Lu @ T@h|U*@h tih & TihuLh4t t?}*itih _i|iU|L? @?_ |hi@|t |t ?Ltic @t i** @t |i ?|ihuihi?Ui uhL4 |i L|ih tiht Lu |i t@4i |4i t*L|c @t @__|i |i B@tt@? ?Lti E`B @?_ tiit @ U@??i* @UULh_?} |L +&crc, ' S&cr %&crc, n &crc, 

E

Ai |h@?t4||i_ U@??i* t)4ML*t %&crc, uhL4 tih & ? |4i t*L| r @hi @tt4i_ hi@* @*i_ @?_ |i @?@*)tt t hit|hU|i_ |L M?@h) @?|TL_@* 4L_*@|L? Ai t}?@*|L?Lti@?_?|ihuihi?Ui h@|L E5W+ Lu |i t}?@* ? E ULhhitTL?_?} |L tih & '  @| |h@?t4ttL? t*L|  U@? Mi h||i? @t q c '

f %2 n

S2c . S

2

&MdE  S&c .&

c

E2

ihi . @?_ .& @hi |i U@??i* t)4ML* i?ih}it Lu |i _ithi_ tih @?_ |i ?|ihuih?} tihtc hitTiU|i*)c @?_ f t |i t?}*it_i_ ?Lti TLih tTiU|h@* _i?t|) 6Lh i@ti Lu 6iMh@h) .

#+6A

D

i TLt|L? @?_ | ?L *Ltt Lu }i?ih@*|)c t?Ui |i t)t|i4 t t)44i|hUc | t tUi?| |L UL?t_ih L?*) L?i T@h|U*@h tih & '  @?_ L?*) |Lti |4i t*L|t r ihi |t tih @U|@**) |h@?t4| Ai }*LM@* |4i t*L| ?_i r U@? |ihiuLhi Mi hiT*@Ui_ M) |i ?_i  ULhhitTL?_?} |L |i | |h@?t4ttL? Lu @ M*LU! uhL4 tih & '  Ai tih ?_i ? E2 ** ? |i ti^i* Mi L4||i_c *i||?} q  ' q c  ,@U |h@?t4||ihhiUiih T@h i4T*L)t @? W+ tUi4i uLh |h@?t4ttL? Lih |i U@??i* Ai |h@?t4||iht @hi @tt4i_ |L @i ?L U@??i* t|@|i ?uLh4@|L? E5W OLiihc TihuiU| 5W t @tt4i_ @@*@M*i @| |i hiUiiht Ntiht @i @? ?€?|i Mgih Lu ?uLh4@|L? T@U!i|t @@*@M*i uLh |h@?t4ttL? @?_ ?L @hh@* ThLUitt t UL?t_ihi_ Oi?Uic i @hi ?L| UL?Uih?i_ | ?t|@M*|) @?_ Mgih LihL ThLM*i4t @t ? U*@ttU@* @?@*)tt Lu *L@ ThL|LUL*t Etii uLh i @4T*i do | |i hiUiih t_ic 4@ 44 *!i*LL_ Ew _i|iU|L? t TihuLh4i_ | |i V|ihM @*}Lh|4 W? |i W+ tUi4i ?_ih UL?t_ih@|L?c TihuiU| E}i?i@ttt|i_ T@U!i| ihhLh _i|iU|L? t @tt4i_ ,hhLh _i|iU|L? U@? Mi @UUL4T*ti_ | } hi*@M*|) |L |i ThUi Lu @ t*}| h@|i *Ltt M) t?} U)U*U hi_?_@?U) UiU! E+ UL_it d2c o *|ih?@|i*)c M) i T*L|?} t|@|t|Ut Lu |i 4i|hUt UL4T|i_ M) |i _iUL_ih Lh hi_?_@?U) ?|hL_Ui_ M) TTih *@)ih ThL|LUL*t Lh @TT*U@|L?tc ihhLh _i|iU|L? 4@) Mi @Uii_ |L| ?|hL_U|L? Lu @__|L?@* hi_?_@?U) t)4ML*t deo OLiihc |i uLh4ih @TThL@U @t Mii? LMtihi_ |L )i*_ Mi||ih |hL}T| |@? |i *@||ih ? hi|h@?t4ttL? tUi4it t4*@h |L |Lti t|_i_ ? |t T@Tih dDo Wu |i hiUiih u@*t |L tUUittu**) _iUL_i @ T@U!i|c @ ?i}@|i @U!?L*i_}4i?| Ek t UL44?U@|i_ |hL} @ _t|Lh|L?*itt M@U!@h_ U@??i* |L |i |h@?t4||ih Ai hiUiT|L? Lu |i k 4itt@}i @| |i |h@?t4||ih hit*|t ? |h@?t4ttL? Lu ?i hi_?_@?U) t)4ML*tc U @hi @UU4*@|i_ @?_ ThLUitti_ M) |i hiUiih W? Lh_ih |L ThL_i @ tihit Lu tU ?Uhi4i?|@* hi_?_@?U) T@U!i|tc i UL?t_ih t)t|i4@|U hiUhti h@|i  % h@|iUL4T@|M*i dSo UL?L*|L?@* UL_itc ihi |i L|T| Lu i@U }i?ih@|Lh 4@!it T L?i Lu  tMT@U!i|t @?_ |i €ht| tMT@U!i| ULhhitTL?_t |L |i ?UL_i_ 4itt@}i Ai UL?L*|L?@* UL_it ?_ih UL?t_ih@|L? @hi 4@ 4@* 4?44 _t|@?Ui ThL_U| UL_it ?_ih |i UL?t|h@?| Lu h@|iUL4T@|M*|) W? tL4i U@titc |iti UL_it _L ?L| UL?U_i | 4@ 4@* 4?44 _t|@?Ui ThL_U| UL_it t?Ui |i *@||ih _L ?L| @*@)t ThL_i h@|iUL4T@|M*|) OLiihc |i _gihi?Uit ? |i _t|@?Ui ThL_U|

6iMh@h) .

#+6A

S

tTiU|h@ @hi }i?ih@**) t4@** 6Lh i@U ?uLh4@|L? T@U!i|c @ tih @t  tMT@U!i|t Lu T@h|) t)4ML*t @@*@M*i uLh |h@?t4ttL? Wu @ k t hiUii_ TL? |h@?t4ttL? Lu |i €ht| tMT@U!i|c |h@?t4ttL? Lu |i ?i | tMT@U!i| t ?|@|i_ Ai |h@?t4ttL?t t|LT u i|ih |i |h@?t4||i_ ?uLh4@ |L? T@U!i| t @U!?L*i_}i_ @t ULhhiU| Lh u ?L 4Lhi tMT@U!i|t @hi @@*@M*i W? |i *@||ih U@tic |i ?uLh4@|L? T@U!i| t UL?t_ihi_ @t *Lt| @?_ |h@?t4ttL? Lu |i ?i | ?uLh4@|L? T@U!i| t ?|@|i_ ? |i t@4i @) @t ThiLt T@U!i|t W? Lh @?@*)tt Lu |i |hL}T| TihuLh4@?Uic i @_LT| @? i ThittL? Lu |i |hL}T|c M@ti_ L? hi?i@*hi@h_ |iLh)c _ihi_ ? do Ai 4@ 44 ?4Mih Lu Ehi|h@?t4||i_ T@U!i|t t UL?t|h@?i_ |L   OLiihc |ihi t ?L _i*@) UL?t|h@?| @?_ tUUitti Ehi|h@?t4ttL?t 4@) |t LUUh | *@h}i tiT@h@|L? ? |4i Ai ?4Mih Lu tMT@U!i|t @@*@M*i uLh W+ |h@?t4ttL? t UL?t|h@?i_ M) |i UL_i h@|i Lu |i UL_i ti_ uLh ihhLh ULhhiU|L?  *Lh@|i 4L|ih UL_i t ti_ |L ThL_i @ 4@ 44 Lu  tMT@U!i|t Lu UL_i_ t)4ML*t ULhhitTL?_?} |L @ T@U!i| Lu K ?uLh4@|L? M|t ,@U Lu |i tMT@U!i|t |h@?t4||i_ Lih |i U@??i* UL?tt|t Lu u UL_i_ t)4ML*t LM|@?i_ uhL4 }h@|i UL_it | h@|i - ' K*u Ai UL_i h@|i Lu |i ULhhitTL?_?} *Lh@|i 4L|ih UL_i t |t -*  6Lh UL?L*|L?@* UL_itc |@*M|t @hi ti_ |L uLhUi |i i?UL_ih M@U! |L |i 3ihL t|@|i ? Lh_ih |L |ih4?@|i |i |hi**t ? @ !?L? t|@|ic U )i*_t @ t4@** h@|i*Ltt W? Lh UL4T|@|L?t @?_ t4*@|L?t |t t hiiU|i_ ? @ _iUhi@ti Lu |i i?ih}) Lu |i |h@?t4||i_ t)4ML*t `i UL?Ui?|h@|i L? |i U@ti ihi @ t)t|i4@|U M?@h) UL?L*|L?@* UL_i t ti_ |L}i|ih | M?@h) 4L_*@|L? Ai |h@?t4ttL? h@|i - Lu |i t)t|i4 t |t *itt |@? Lh i^@* |L L?i YYY Naj $jt}A NAtajiB|NAt UULh_?} |L Lh !?L*i_}ic *||*i igLh| @t Mii? 4@_i |L _it}? iUi?| UL_it i  T*U|*) uLh |i M*LU!u@_?} B@tt@? UL**tL? U@??i* OLiihc UL_i _it}? Uh|ih@ uLh @ M*LU!u@_?} +@)*i} i?hL?4i?| @i ThiLt*) Mii? @__hitti_ ? dHc .o W? dHoc | @t t}}it|i_ |@|c uLh i@U UL4TLt|i ihhLh ii?|c €ht|*)c |i _iht|) Lh_ihc i |i ?4Mih Lu ?L?3ihL UL_i UL4TL?i?| EtMT@U!i| _t|@?Uit @?_c tiUL?_@h*)c |i UL4TL ?i?| _t|@?Ui ThL_U| tL*_ Mi 4@ 43i_ Ai _iht|) Lh_ih ? tU @ M*LU!u@_?} i?hL?4i?| U@? Mi _i€?i_ @t |i *L}*L} _L4@? t*LTi Lu |i M*LU! ihhLh ThLM@M*|) ? 6iMh@h) .

#+6A

.

|i @t)4T|L|U hi}L? Lu |i t}?@*|L?Lti h@|L E5+ Ai _it}? Uh|ih@ ? dHo ihi ?uihhi_ M) t|_)?} |i i TiU|i_ , Mi|ii? UL_iLh_tc ihi |i i TiU|@|L? @t |@!i? Lih |i ThLM@M*|) _i?t|) u?U|L? E#6 Lu |i M*LU!u@_?} U@??i* W? |t tiU|L? i |@!i |i t@4i @TThL@Uc | |i 4L_€U@|L? |@| |i |h@?t4ttL? ?_ih UL?t_ih@|L? 4@) Mi tMiU| |L M*LU!?|ihuihi?Ui ? @__|L? |L M*LU!u@_?} `i UL? t_ih L?*) *Lh@|i 4L|ih UL_it | -   % c U 4T*it |@|  t |i 4@ 44 @Ui@M*i _iht|) Lh_ih d.o `i _i€?i |i , UL?_|L?i_ L? |i U@??i* 5W+t q  c    c q  @t 3y 4 x [ x   D  EU $ U mq  c    c q   ' ' Cw q  _M  EU c U  c

E 

 '

  ihi _M  EU cU  t |i O@44?} _t|@?Ui Mi|ii? |i | UL_i UL4TL?i?|t Lu |i UL_i

Lh_ T@h EU cU   t4T*i TTih ML?_ L? E c i@t) |L u@U|Lh3ic U@? Mi LM|@?i_ M) i T*L|?} |i uL**L?} TTih ML?_ L? |i 'u?U|L? dHo  2 'E%  e3% *2 c %  f 2

Ee

`| E  @?_ Eec @? TTih ML?_ L? |i , uL**Lt @t

S   3'q  _M EU cU %2  \ 3q  _M EU cU %2  EU $ U mq  c    c q    e ' e c 2 2  ' 





@?_ |i i TiU|i_ ,c Lih @ T@h|U*@h _iht|) U@??i*c U@? Mi UL4T|i_ @t 



]"

 EU $ U  '

]" 

f

 EU $ U mq  c    c q  s Eq  c    c q  _q     _q  c

ED

f

ihi s Eq  c    c q   t |i L?| #6 Lu |i U@??i* 5W+t ULhhitTL?_?} |L _gihi?| UL_i UL4TL?i?|t 5?Ui |i u@_?} @?_ ?|ihuihi?Ui t|@|it @hi @tt4i_ |L Mi ?_iTi?_i?| uLh _gihi?| UL_i UL4TL?i?|tc ED U@? Mi u@U|Lhi_ @t "  ]  \  \ 3 q  _M EU cU %2     EU $ U  ' e sEq  _q  ' U  2  ' 2  ' f

6iMh@h) .

ES

#+6A

H

6Lh *L t)t|i4 *L@_tc i i TiU| |i _it}? Uh|ih@ uLh |i M*LU!u@_?} U@??i* |L L*_ @*tL uLh |i M*LU!u@_?} B@tt@? UL**tL? U@??i* OLiihc uLh } *L@_t i ?ii_ |L UL?t_ih |i , ED ? 4Lhi _i|@* Ai #6 Lu |i 5W+ Lu |i M*LU!u@_?} B@tt@? UL**tL? U@??i* uL**Lt uhL4 dT Ti?_ o sq E5 ' e35@  ihi @ ' 

1

2.



 n 5  R5 n5

 3



R   n @  E n 5 E n 5  R5 c E n 52

E.

&  W? @Mti?Ui Lu ?|ihuihi?Uic i  ' fc E. hi_Uit |L |i #6 Lu |i

f

5+ Lu |i M*LU!u@_?} U@??i* sq E5 ' @e35@ d.o W? |t U@tic U ? ES t }i? M) ]" U ' @

M EU cU %2 n@o

e3q  d_

f

 c _q  ' M   _ EU c U .& *f n 

U *i@_t |L |i ThiLt*) 4i?|L?i_ _t|@?Ui ThL_U| Uh|ih@ uLh UL_i _it}? uLh |i M*LU!u@_?} U@??i* W? UL?|h@t| |L |i M*LU!u@_?} U@??i*c h|@**) ?L 4ThLi4i?| Lu |i , t i TiU|i_ ? |i M*LU!u@_?} B@tt@? UL**tL? U@??i* i? |i U@??i* 5+ .& *f MiUL4it tUi?|*) *@h}i At t _i |L |@| @** tiht ? |i t)t|i4 @hi @tt4i_ |L |h@?t4| | |i t@4ic }c U@??i* 5+ @?_ |t |i ?|ihuihi?Ui TLih ?Uhi@tit ULhhitTL?_?}*) 6Lh |i t@!i Lu 4@|i4@|U@* |h@U|@M*|)c i uLUt L? |i , ? |i *4| Lu } U@??i* 5+tc i @ $ f ? E. `| |t @tt4T|L?c |i #6 E. Lu |i 5W+ t4T*€it |L dTTi?_ o  sq E5 '

 n 5  R5 n5

 3



R   c E n 52

@?_ i U@? i Thitt |i , @UULh_?} |L "    ]  n q   Rq   3 _q  ER    \ 3q  _M EU cU %2  EU $ U  ' e    2  n q E n q  2  ' 



f

5?Ui f  R   @?_ q   fc |i , U@? Mi TTih ML?_i_ uLh    @t "  2  ]  ER    \ 3q  _M EU cU %2  ER    \  EU $ U   e  _q  ' a E2c ihi 2  n q 2  '  ' 



f

6iMh@h) .

EH #+6A

b

]" a E`  '

M   e3q  _ EU cU %2 

f



`  _q    n q

W| t TLttM*i |L hih|i a E`  @UULh_?} |L

a E`  '

; A ?



*%

`S 32 E3% ` 32 A &-  E% 3& = E`3- %  e%  . E%  n &'f



` 'f `  c

  ihi % ' _M  EU cU  %2 @?_ . E% t |i i TL?i?|@* ?|i}h@* dbo

]" 3%| e .? E% ' _|c |? 

| ? '  5?Ui ` ' 2c i ?L @i a E2 ' %  e%  . E%  n c @?_ t?} |i ?i^@*|) dbo  e%  % n  i LM|@? a E2

]" 3% | e _|c | 

  % n 

Eb

L?t_ih?} EH @?_ Ebc ? @UULh_@?Ui | UL?iU|hit 4@_i ? d.oc | @TTi@ht hi@ tL?@M*i |L @tt4i |@| _it}? Uh|ih@ _ihi_ uLh |i M*LU!u@_?} U@??i* L*_ )i*_ }LL_ UL_it @*tL uLh |i M*LU!u@_?} B@tt@? UL**tL? U@??i*c ii? |L} UL_it | }ih 4?44 _t|@?Ui ThL_U| 4@) ?L| tL _h@4@|U TihuLh4@?Ui 4ThLi4i?|t @t t}}it|i_ M) |i h@|ih @| Mi@Lh Lu |i TTih ML?_ Eb W? L|ih |ih4tc t?Ui |ihi t @ hi*@|i*) t*L _iU@) Lu |i , @*L?} | ?Uhi@t?} 5+c |ihi t @ t}?€U@?| UL?|hM|L? |L |i ihhLh TihuLh4@?Ui uhL4 ihhLh ii?|t ULhhitTL?_?} |L }ih _t|@?Ui ThL_U| 4i@thit @?_ |ihiuLhi @ Lht|U@ti , @?@*)tt 4@) Mi Lu *4|i_ @*i uLh Thi_U|L? Lu |i @U|@* TihuLh4@?Ui OLiihc | 4@) t|** Mi ?uihhi_ |@| *4|@|L? Lu |i 4*|T*U|) Lu UL_iLh_t | t4@** _t|@?Ui ThL_U| 4i@thit t @? 4TLh|@?| LMiU|i ? @__|L? |L 4@ 43@|L? Lu |i 4?44 _t|@?Ui ThL_U| +iU@** |@| |i ?Lh4@*3i_ t^@hi_ ,U*_i@? _t|@?Ui Lu |i | UL_i UL4TL?i?| uL**Lt

6iMh@h) .

#+6A

f

  uhL4 |i O@44?} _t|@?Ui @t _2 EU cU  ' e_M  EU cU  W? dHoc |i }iL4i|hU 4i@? # $* \ 2 EU c U  ' _2 EU c U  Ef  '

@t ti_ @t @ 4i@thi Lu |i UL4TL?i?| _t|@?Ui ThL_U| Mi|ii? _gihi?| UL_iLh_t @?_ i @i @_LT|i_ |i t@4i @TThL@U OLiihc 4L|@|i_ M) |i *@h}i @?|UT@|i_ 4T@U| Lu }ih Lh_ih _t|@?Ui ThL_U|tc i i |i?_ |i @?@*)tt Lu |i _t|@?Ui ThL_U| tTiU|h@ |L ?ULhTLh@|i 4Lhi UL_iLh_t |@? |Lti ULhhitTL?_?} |L |i 4?44 _t|@?Ui ThL_U| 6Lh *?i@h UL_itc | ?L *Ltt Lu }i?ih@*|)c |i ?L|@|L? ? Ef U@? Mi t4T*€i_ |L L?*) UL?t_ih |i UL4TL?i?| i}| ThL_U| 2 EU Lu _gihi?| UL_iLh_t Uc _i€?i_ M) 2 EU ' 2 EUcfc ihi f _i?L|it |i @**3ihLt UL_iLh_ Ai h@|i  % UL?L*|L?@* UL_it ti_ ? |t t|_) @i Mii? _i|ih4?i_ M) 4@  43@|L? Lu |i M*LU! _iht|) Lh_ih @?_ |i UL4TL?i?| i}| ThL_U| #gihi?| UL_it @i Mii? h@?!i_ L? M@tt Lu |ih UL4TL?i?| i}| ThL_U| tTiU|h@c _i€?i_ M) |i 4@} ?|_i Lu |i UL4TL?i?| i}| ThL_U|t Lu |i UL_iLh_t @?_ |i ULhhitTL?_?} 4*| T*U|it Ai i}| ThL_U|t @?_ |ih hitTiU|i 4*|T*U|it @i Mii? UL4T@hi_ uLh t?}*iihhLh ii?|t | |L|@* O@44?} i}| ELih @** UL_i UL4TL?i?|t tU |@|  [ _M _ EUc f '  EUc f  gc M

 '

ihi |i @_LU ULUi Lu g ' 2_soee @t Mii? 4@_i ? Lh_ih |L *4| |i UL4T*i |) Lu |i UL_i ti@hU ,hhLh ii?|t | }ih |L|@* O@44?} i}|t @hi @tt4i_ |L )i*_ ?i}*}M*i UL?|hM|L?t |L |i ,  4L_€i_ ihtL? Lu |i 65A @*}Lh|4 d2fo @t ti_ |L UL4T@hi |i i}| ThL_U| tTiU|h@ Lu _gihi?| UL_it W? |i U@ti Lu i^@* 4?44 UL4TL?i?| i}| ThL_U|tc |i UL_i | |i *Lit| 4*|T*U|) Lu |i 4?44 UL4TL?i?| i}| ThL_U| t ULti?c Lh u @*tL |i 4*|T*U|it @hi i^@*c |i UL_i | |i }it| tiUL?_ 4?44 UL4TL?i?| i}| ThL_U| t ULti?c i|U Ai W+ t)t|i4t ?_ih UL?t_ih@|L?t ti t)t|i4@|U UL_?} At 4@) Mi @Uii_ M) t)t|i4@|U hiUhti UL?L*|L?@* i?UL_ihtc LM|@?i_ M) ULLt?} @ uii_M@U! }i?ih@|Lh TL*)?L4@* _i?|U@* |L @?) Lu |i T@h|) }i?ih@|Lh TL*)?L4@*t Aiti i?UL_iht )i*_ UL_it | uh@4i ihhLh TihuLh4@?Ui _i?|U@* |L |Lti Lu |ih ?L?t)t|i4@|U UL?|ihT@h|t 6iMh@h) .

#+6A



W? Lh_ih |L LM|@? |i W+ ThLTih|)c h@|iUL4T@|M*i UL_it @hi hi^hi_ +@|iUL4T@|M*i UL?L*|L?@* UL_it U@? Mi _ihi_ ? |L @)tG i|ih M) ?it|i_ UL_i ti@hUit M@ti_ L? }LL_ }h@|i UL_it dSc 2oc Lh T?U|h?} Lu *Lh@|i i?UL_iht !?L? |L Mi }LL_ uhL4 ThiLt }*LM@* UL_i ti@hUit W? |t t|_)c ML| 4i|L_t @i Mii? ?it|}@|i_ @?_ @TT*i_ |L UL_it | UL_i h@|it ? |i ?|ih@* *S |L *2 Ai T?U|h?} tc Liihc *4|i_ |L @ t4T*i uLh4c ihi |i UL_i h@|i t ?Uhi@ti_ M) T?U|h?} Lu |i i?|hi t|hi@4 Lu T@h|) M|t uhL4 L?i }i?ih@|Lh @| i@U *ii* Lu |i UL_i h@|i Ai }i?ih@|Lh TL*)?L4@*t Lu |i i?UL_iht uL?_ | |i €ht| 4i|L_ @hi Thiti?|i_ ? A@M*i W 6Lh UL_it | 4i4Lh) v i^@* |L 2 @?_ ML| 4i|L_t )i*_ |i t@4i i?UL_ihtc Liihc uLh UL_it | 4i4Lh) e @?_ D |i hit*|t @hi _gihi?| Aihi @hi ?_ii_ 4Lhi i*@MLh@|i tUi4it Lu T?U|h?} |@| 4@) )i*_ 4Lhi iUi?| UL_itc Liihc tU ?it|}@|L?t @hi UL?t_ihi_ |L Mi Mi)L?_ |i tULTi Lu |t T@Tih Ai h@|iUL4T@|M*|) UL?t|h@?| 4TLtit tL4i *4|@|L? L? |i ThL_U| i}| tTiU|h@ |@| U@? Mi @Uii_ 6Lh W+ t)t|i4tc | @TTi@ht hi@tL?@M*i |L h@?! u@4*it Lu h@|i UL4T@|M*i UL_it @UULh_?} |L |i TihuLh4@?Ui Lu |ih }h@|i 4i4Miht E€ht| 4i|L_c t?Ui |t U@h@U|iht|U ** _L4?@|i |i Lih@** |hL}T| AihiuLhic ? Lh t|_)c i uLUt L? h@|iUL4T@|M*i UL_it _ihi_ uhL4 ?it|i_ UL_i ti@hUit M@ti_ L? }LL_ }h@|i UL_itc ? @ i}| ThL_U| tTiU|h4 ti?ti YX CiN}V| AB,+tt uNi Y- | NAN,|NAB, Najt W? |t tiU|L?c |i |hL}T| TihuLh4@?Ui Lu W+ tUi4it | UL?L*|L?@* UL_it t UL?t_ihi_ Ai hit*|?} TihuLh4@?Ui ML?_t @hi @*@M*i 4@?*) ? |i hi}L? Lu } 5+tc ihi UL4T|ih t4*@|L?t @hi 4Lt| |i_Lt |L U@hh) L| Ai |hL}T| TihuLh4@?Ui Lu @? W+ tUi4i t @ u?U|L? Lu |i ThLM@M*|) Lu ihhL ?iLt _iUL_?} @u|ih @?} hiUii_ 6 T@U!i|t | ?L tUUittu* _iUL_?} @@*@M*i uhL4 ThiUi_?} tMti|t Lu T@U!i|t At ThLM@M*|) t hiuihhi_ |L @t |i t4*|@?iLt uh@4i ih hLh h@|i E6,+ @?_ t _i?L|i_ M) hEe6 c ihi |i ii?| e6 ULhhitTL?_t |L t4*|@?iLt _iUL_?} u@*hit @u|ih @?} hiUii_ tMT@U!i|t  ' c    c 6 #i |L |i U*Lti hi*@|L? Mi|ii? |i t4*|@?iLt 6,+ @?_ |i |hL}T| TihuLh4@?Uic |i Ui?|h@* TL?| Lu |t tiU|L? t Thi_U|L? Lu |i t4*|@?iLt 6,+ uLh tTiU€U UL?L*|L?@* UL_it UULh_?} |L |i hit*|t ? doc |i |hL}T| uLh @ t)t|i4 | ?L _i*@) UL?t|h@?|c 6iMh@h) .

#+6A

2

M| @ h@|i UL?t|h@?| _i|ih4?i_ M) |i ?4Mih Lu @@*@M*i tMT@U!i|t c uL**Lt uhL4   hEe  M|t%t%O3 # ' -C  3 S hEe6 

E

6'f

W? doc |i @Ui@M*i |hL}T| ? |i *4| Lu *@h}i M*LU! *i?}|t @t ?it|}@|i_ i? B@tt@? h@?_L4 UL_it ihi ti_ |L }i?ih@|i |i W+ T@U!i|t W? |t U@tic |i t4* |@?iLt 6,+ U@? Mi _i|ih4?i_ M) ?uLh4@|L? L|@}i UL?t_ih@|L?tc U )i*_t |i |hL}T| | i^@*|) @UULh_?} |L E At t _i |L |i u@U| |@| hEe6  t _iUhi@t ?} | 6c t?Ui |i 4|@* ?uLh4@|L? UL?i)i_ Lih |i U@??i* ?Uhi@tit | |i ?4Mih Lu hiUii_ T@U!i|t 6 6Lh |i @?@*)tt Lu |i |hL}T| TihuLh4@?Ui Lu Th@U|U@* UL_it | 4t| Mi |@!i? ?|L @UUL?| |@| @? ihhL?iLt _iUL_?} @||i4T| @u|ih 6 hiUii_ tMT@U!i|t 4@) LUUh TL? @ ThiUi_?} tUUittu* _iUL_?} @||i4T| @u|ih tMT@U!i| c ihi    6 6h|ih4Lhic |i ThLM@M*|) hEe6  t ?L| @@*@M*i uhL4 ?L? ML?_ UL?t_ih@|L?tc @*|L} | 4@) Mi UL4T|i_ M) t4*@|L?t W? Lh_ih |L @?_*i |t *4|@|L?c | t tiu* |L _i€?i @? ii?| e6 c _gihi?| uhL4 |i ii?| e6  wi| e6 _i€?i |i ii?| Lu _iUL_?} u@*hi @u|ih 6 hiUii_ tMT@U!i|t Lu |i t@4i UL_iLh_c | ?L hi}@h_ |L |i _iUL_?} t|@|t @u|ih @?) ThiLt _iUL_?} @||i4T|t 6Lh ?t|@?Uic @?) UL4M?@|L? Lu ULhhiU| @?_ ?ULhhiU| _iUL_?}t 4@) @i LUUhhi_ @| |i hiUiT|L? Lu |i  ThiUi_?} tMT@U!i|t Ai ThLM@M*|) Lu |i ii?| e6 c |@| ULhhitTL?_t |L t4*|@?iLt _iUL_?} u@*hit @u|ih i@U hiUii_ tMT@U!i|  ' c    c 6c U@? ?L Mi i Thitti_ @t |i ?|ihtiU|L? Lu |i ThLM@M*|it Lu e c    c e6 @t hEe6  ' hE e _    _ e6  @?_ i @i hEe6   hE e6 

E2

5?Ui |i |hL}T| t @ _iUhi@t?} u?U|L? Lu |i ThLM@M*|it hEe6 c | t ?L TLttM*i |L ti E @?_ t|@|i @ *Lih ML?_ L? |i @Ui@M*i t)t|i4 |hL}T| uLh @? W+ tUi4i M@ti_ L? @ Th@U|U@* UL_ic i Thitti_ ? |ih4t Lu |i TTih ML?_ L? |i t4*|@?iLt 6,+ it|@M*ti_ ? E2 W? Lh_ih |L i@*@|i |i *Lih ML?_ L? |i |hL}T|c i uLUt L? |i UL4T|@|L? Lu hE e6  uLh Th@U|U@* UL_it

6iMh@h) .

#+6A



W?L!?} |i ?L? ML?_c hE e6  U@? Mi TTih ML?_i_ @t % #v $& 6 S S  hE e6   . ' q  _M c  EU c f U

 McU 'f

E 

 '

  ihi _M  EU cf t |i O@44?} i}| Lu tMT@U!i|  Lu UL_iLh_ U ? |i UL_i c @?_

|i i TiU|@|L? t |@!i? Lih |i U@??i* 5W+t q   6L**L?} d22oc |i u?U|L? 'E% U@? Mi hih||i? ? |i Thiuihhi_ uLh4  'E% ' Z

Z* ]2

 i T 

f

 %2 _c %  fc 2 t?2 

Ee

Uc M) i |h@U|L? Lu |i tMT@U!i| O@44?} i}|t @t i TL?i?|t |L |i u@U|Lht Lu @? 6 u@U|Lh ThL_U|c i?@M*it hih|?} Lu E  @t 5 Z*2 6 ] 6 \ M     S  _ EU cf i T q  E2 t?2   _8  hE e6   . 7 Z U McU 'f '

ED

f

Ai i@*@|L? Lu |i ?L? ML?_ ? ED hi^hit |i !?L*i_}i Lu |i  @h@|i O@4 4?} i}| i?4ih@|Lh Lu |i UL_ic U _itUhMit |i T@h||L??} Lu UL_iLh_t ?|L |i tMT@U!i|t |h@?t4||i_ ? i@U |4i t*L| Ai @h@|i i}| i?4ih@|Lh @t |i uLh4 A E` c    c `  '

[ 



 \  |E c    c   `  c

[ 

ES

 '

ihi  t |i O@44?} i}| Lu |i t)4ML*t ULhhitTL?_?} |L tMT@U!i| c |E c    c   t |i 4*|T*U|) Lu UL_iLh_t @?}  |T*i  c    c  c @?_ ` @hi _44) @h@M*it uLh |i O@44?} i}| Lu i@U tMT@U!i| Ai TTih ML?_ L? |i t4*|@?iLt 6,+ ? ED U@? ?L Mi i Thitti_ @t @ u?U|L? Lu |i i}| i?4ih@|Lh A E` c    c ` c U U@? Mi i@*@|i_ M) t|@?_@h_ t)4ML*U UL4T|@|L? Lu |i |h@?tuih u?U|L? Lu |i i?UL_ih t|@|i _@}h@4 dTTi?_ o 5Mt|||?} |i t4 Lih @** UL_iLh_t ? ED |  t4t Lih @** UL4M?@|L?t Lu  tMT@U!i| O@44?} i}|t  c _M  EU cf U@? Mi hiT*@Ui_ M)  ? |i i TL?i?|t @?_ i

LM|@?

5 hE e   . 7

Z* ] 2\ 

[ [  |E c    c   Z   

6iMh@h) .



f  '

 i T 

q 2 t?2 



6 _8 

E.

#+6A

e

) |i _i€?|L? Lu |i 4*|@h@|i i}| i?4ih@|Lhc E. U@? Mi i Thitti_ @t @ u?U|L? Lu A E` c    c `  _hiU|*) @t 5 Z*2 6     ]   q q A i T  c    c i T  2 _8  hE e   . 7 2 Z 2 t?  2 t? 

EH

f

W? u@U|c |i t4*|@?iLt 6,+ uLh @?) 6 ' c    c  U@? Mi TTih ML?_i_ t?} |i t@4i i}| i?4ih@|Lh A E` c    c `  M) *i||?} ` '  uLh  ' 6 n c    c  tL |@| |i O@44?} i}|t  ULhhitTL?_?} |L |i tMT@U!i|t  ' 6 n c    c  @i ?L ?i?Ui L? |i t4*|@?iLt 6,+ 5?Uic ? Lh U@tic |i i}| i?4ih@|Lh t hit|hU|i_ |L ?U*_i L?*) t?}*i ihhLh ii?|tc | t ?L| TLttM*i |L @TT*) EH _hiU|*) OLiihc @? TTih ML?_ L? |i t4*|@?iLt 6,+c @ih@}i_ Lih |i L?| U@??i* t|@|t|Ut q  c    c q  U@? Mi LM|@?i_c t?} |i hit*|t ? d.o @?_ d2 oc @UULh_?} |L hE e   .dE  E   n oc ihi

; ? c f     E ' = fc i*tiihi

Eb

E2f

@?_ ihi  Eq  c    c q   ' Z

Z* ]2

  A i T 

f

   q q cci T  _c 2 t?2  2 t?2 

ihi  '   u 6Lh ?L|@|L?@* UL?i?i?Uic i @i h||i?  ?t|i@_ Lu Eq  c    c q   ? Eb @?_ E2f Ai ti Lu |i ?_U@|Lh u?U|L? E2f ? |i TTih ML?_ Eb t i T*@?i_ @t uL**Lt Wuc uLh tL4i q  c    c q  c |i u?U|L?  |@!it L? @*it *@h}ih |@? c |i ?L? ML?_ t ti*itt @?_ U@? Mi |h@**) |}|i?i_ M) t?}  ?t|i@_ Wuc uLh tL4i q  c    c q  c |i u?U|L?  |@!it L? ?i}@|i @*itc | 4i@?t |@| |i ULhhitTL?_?} h@|L?@* u?U|L? A E` c    c `  t i@*@|i_ uLh @h}4i?|t L|t_i |t hi}L? Lu UL?ih}i?Ui EhiU@** |@| A t LM|@?i_ @t |i t4 Lu @? ?€?|i TLih tihit L|Ui |@|  t @? TTih ML?_ L? hE e6  L?*) u |i ULhhitTL?_?} A t i@*@|i_ ?t_i |t hi}L? Lu UL?ih}i?Uic L|ihti  t 4i@??}*itt AihiuLhic ? Lh_ih |L t|** LM|@? @? TTih ML?_c i hiT*@Ui  M)  uLh |Lti q  c    c q  )i*_?}  f 6iMh@h) .

#+6A

D

W? Lh_ih |L UL4T|i |i i TiU|@|L? ? Ebc i|ih L?|i@h*L t4*@|L? Lh ?4ih U@* ^@_h@|hi t @| @?_c t?Ui @?@*)|U@* ?|i}h@|L? @TTi@ht |L Mi |LL ?L*i_ W? i|ih U@tic |i i}| i?4ih@|Lh uLh @ T@h|U*@h UL?L*|L?@* UL_ic }i? @t @ h@|L?@* i ThittL?c t U@*U*@|i_ | hi@*@*i_ T@h@4i|iht ? Lh_ih |L UL4T|i |i i TiU|@|L? 6Lh ?t|@?Uic |i UL?L*|L?@* UL_i | 4i4Lh) 2 @?_ }i?ih@|Lh TL*)?L4@*t .H @?_ DH @t |i t?}*iihhLh ii?| i}| i?4ih@|Lh A E` c `2  '

` `22  `e `22 n `2 `2e    2` n `2  `22

E2

| |i TLt|L?t Lu |i _44) @h@M*it ` @?_ `2 c ?4ihU@* @*it @hi ?tih|i_ ? @*|ih?@|i UL4T|@|L?c |@| 4}| Mi 4Lhi UL?i?i?|c t LM|@?i_ u i i T@?_ |i i}| i?4ih@|Lh ? E2 @?_ |h?U@|i 6Lh |i U@ti Lu |i M*LU!u@_?} U@??i*c tU @ UL4T|@|L? U@? UL4i U*Ltih |L |i @*it LM|@?i_ uhL4 UL4T|ih t4*@|L?t d.o OLiihc | _Lit ?L| hit*| ? @ |hi TTih ML?_ L?*) @? @TThL 4@|L? Lu @? TTih ML?_ 6h|ih4Lhic |i ?4Mih Lu |ih4t |L ?U*_i ? tU @ |h?U@|i_ ML?_ 4t| Mi _i|ih4?i_ 6Lh |i M*LU!u@_?} B@tt@? UL**tL? U@??i*c |t _iTi?_t L? ML| |i 5+ @?_ |i U@??i* *L@_ W?t|i@_c i |@!i |i h@|L?@* uLh4 Lu |i 4*|@h@|i i}| i?4ih@|Lh ? E2 @?_ ti |i #6 Lu |i q  @*it |L U@*U*@|i |i i TiU|@|L? ? 44i_@|i UL4T*U@|L? | |i i TiU|@|L? ? Eb tc Liihc |i ?L?*?i@h|) ?|hL_Ui_ M) |i u?U|L? Ai i}|i_ ?|i}h@|L? Lih |i 4*|_4i?tL?@* #6 ]" hE e6  

]" 

f

Eq  c    c q 6   iE  E   n j  _q     _q 6

E22

f

4t| |ihiuLhi Mi _L?i @u|ih |i ?4ihU@* ?|i}h@|L? Lih  dTTi?_ o X CiN}V| AB,+tt uNi Y- | wNA} -BAaN6 Najt W? 5iU|L? WVc |i ii?| e6 @t _i€?i_ @t |i ThLM@M*|) Lu _iUL_?} u@*hi LUUhh?} @u|ih 6 hiUii_ tMT@U!i|t Lu |i t@4i UL_iLh_ }i? |@| ?L tUUittu* _iUL_?} Thi Lt*) LUUhhi_ t tL? ? doc | h@?_L4 UL_?}c ? |i *4| uLh *@h}i tMT@U!i| *i?}|tc |i ThLM@M*|) Lu e6 t }i? M) hEe6  ' h 6iMh@h) .

#6 [  '

$ UEq    - c

E2  #+6A

S

ihi UEq   t |i 4|@* ?uLh4@|L? Lu @ t)44i|hU M?@h)?T| `B U@??i* | 5W+ q  c @?_ - t |i |h@?t4ttL? h@|i Lu |i t)t|i4 Ai 4|@* ?uLh4@|L? Lu @ t)44i|hU M?@h)?T| U@??i* U@? Mi U@*U*@|i_ @t d2eo ] "  s I s   2 2 q  E5 23 q   s e35 _5 M|t%t)4ML* UEq   '   *L}2  n e Z 3"

E2e

W? |i U@ti Lu @ U@??i* | hi@*@*i_ B@tt@? _t|hM|i_ ?T|tc |i 4|@* ?uLh 4@|L? uL**Lt uhL4 d2Do UEq   '

 *L}2 E n q   M|t%t)4ML* 2

5?Ui |i 5W+t q  @hi ?_iTi?_i?| _i?|U@**) _t|hM|i_ E_ h@?_L4 @h@M*it E+Vtc @*tL |i 4|@* ?uLh4@|L? UEq   t @? _ +V Atc ? Lh_ih |L UL4T|i E2 c S |i U4*@|i _t|hM|L? u?U|L? E#6 Lu 6  ' UEq   U@? Mi i@*@|i_ M) 6 |4it UL?L*|L? Lu |i #6t Lu UEq   @?_ tMti^i?| ?|i}h@|L? W? Lh_ih |L hi_Ui |i UL4 T|@|L? UL4T*i |) uLh *@h}i 6c i? UL?L*|L? 4}| )i*_ |LL |i_Lt UL4T|@|L?tc | t TLttM*i |L ?L!i |i Ui?|h@* *4| |iLhi4 |L @TThL 4@|i |i t4*|@?iLt 6,+ @t    7 c hEe6     ' s E-  6U E2D 6jU     ihi U7 ' . UEq   @?_ j 2U ' V@h UEq    Ai @Ui@M*i t)t|i4 |hL}T| ? M|t%t%O3c ? |i *4| Lu *L?} tMT@U!i| *i?}|tc uL**Lt uhL4 E XY 6jiWB, -jt,|t ? i @4T*i Lu |i 6,+ TihuLh4@?Ui uLh |i M*LU!u@_?} U@??i* E?L ?|ihuihi?Ui t tL? ? 6}hi c ihi |i @Ui@M*i TihuLh4@?Uit hEe6  uLh M?@h) @?_ B@tt@? h@?_L4 UL_it @hi UL4T@hi_ |L hE e6  uLh M?@h) UL?L*|L?@* UL_it 54*@|L?t @?_ TTih ML?_t @}hii i** @?_ |i ?uLh4@|L? L|@}i ThLM@M*|it Lu M?@h) @?_ B@tt@? h@?_L4 UL_?} @hi tii? |L Mi hi*@|i*) U*Lti uLh 6 :  L|ic Liihc |@| |i ?uLh 4@|L? L|@}i ThLM@M*|) | M?@h) h@?_L4 UL_?} t i^@* |L L?ic hi}@h_*itt Lu |i 5+c uLh |i U@ti Lu L?i t?}*i |h@?t4ttL? E6 '  At t _i |L |@| |i 4|@* ?uLh4@|L? ? E2e U@??L| i Uii_ - '  ? |t U@ti L4T@h?} |i @Ui@M*i TihuLh4@?Uit uLh M?@h) @?_ B@tt@? h@?_L4 UL_it |L |i TihuLh4@?Uit Lu M?@h) UL?L*|L?@* UL_it ? |i Thiti?Ui Lu ?|ihuihi?Uic 6}hi 2 tLt 6iMh@h) .

#+6A

.

|@| |i 6,+ Uhit @||i? L| uLh @** UL_it @| } U@??i* |h@?t4| 5+t At t hi@tL?@M*i t?Ui |i ?|ihuihi?Ui T@h| Lu |i ?Lti _L4?@|it uLh tUi?|*) } 5+t 6Lh *L U@??i* *L@_tc M?@h) UL?L*|L?@* UL_it | *L UL4T*i |)c i ui t|@|itc @hi LMtihi_ |L UL4i hi*@|i*) U*Lti |L |i TihuLh4@?Uit @Ui@M*i | M?@h) h@?_L4 UL_it 6Lh } *L@_tc Liihc |ihi t @ *@h}i }@T Mi|ii? |i TihuLh4@?Ui Lu *L UL4T*i |) UL?L*|L?@* UL_it @?_ |i @Ui@M*i TihuLh4@?Ui 6h|ih4Lhic uLh } *L@_tc UL?L*|L?@* UL_it | @? ?Uhi@ti_ ?4Mih Lu t|@|it @i Mii? LMtihi_ |L )i*_ L?*) 4L_it| TihuLh4@?Ui 4ThLi4i?|t 6}hi tLt |i 6,+ LM|@?i_ M) t4*@|L?t Lu M?@h) UL?L*|L?@* UL_it | _gihi?| UL4T*i |)c ? hi*@|L? |L |i TihuLh4@?Ui @Ui@M*i | M?@h) h@?_L4 UL_itc @| |i hi*@|i*) *L t)t|i4 *L@_ C ' f2D Ai ?it|}@|i_ UL?L*|L?@* UL_it @i @** 4@ 44 4?44 i}| ThL_U| @?_ M*LU! _iht|)  ' e EUu 5iU|L? WWW Ai ULhhitTL?_?} i?UL_iht @i ec 2 @?_ 2DS t|@|it @?_ }i?ih@|Lh TL*)?L4@*t dDH c.H c.H cDH oc dD.H cSDH c.H c. H oc @?_ dDD.H c.DH cD2 H c. H o 6hL4 A@M*i Wc | t U*i@h |@| UL_it | }ih ?4Mih Lu t|@|it U@? @Uii *@h}ih 4?44 i}| ThL_U|c @?_c @UULh_?}*)c |i 6,+ TihuLh4@?Ui t tii? |L 4ThLi | }ih UL4T*i |) ? 6}hi  6}hi e **t|h@|it |i TihuLh4@?Uit Lu |i t@4i UL_it @| @ }ih *L@_c C ' Df W? |t U@tic | t tii? |@| | t 4Lhi _U*| |L @TThL@U |i @Ui@M*i TihuLh4@?Ui Lu M?@h) h@?_L4 UL_it |hL} UL?L*|L?@* UL_it | }ih UL4T*i |) #i |L |t @||h@U|i TihuLh4@?Ui UL4T*i |) |h@_iLgc i uLUt L? |i H t|@|i UL_i | }i?ih@|Lht d H cDH c.H cDH o @t @ iU*i uLh uh|ih |hL}T| UL?t_ih@|L?t W? |t T@Tihc |i _tUttL? t uLUti_ L? UL?L*|L?@* UL_it ihi K ' u At 4T*it @ hit|hU|L? |L tMT@U!i|t ULhhitTL?_?} |L |h@?t4ttL? h@|i - '  OLiihc @ }i?ih@* LMtih@|L? uhL4 |i @?@*)tt Lu |i @Ui@M*i |hL}T| TihuLh4@?Ui uLh |i h@?_L4 UL_it t |@| LT|43@|L? Lu |i |h@?t4ttL? h@|i - tL*_ Mi 4@_i ? Lh_ih |L 4@ 43i |i |hL}T| uLh @ }i? h@|i UL?t|h@?| c *L@_ C @?_ U@??i* 5+ .& *f  W? 6}hi Dc |i |hL}T| TihuLh4@?Ui uLh h@?_L4 UL_it ? |i *4| Lu *@h}i M*LU! *i?}| t }i? uLh _gihi?| |h@?t4ttL? h@|it W? |i hi}L? Lu *L *L@_tc }ih h@|i t tii? |L )i*_ }ih |hL}T| OLiihc uLh }ih *L@_tc |i h@|i tL*_ Mi _iUhi@ti_ ? Lh_ih |L @Uii |i 4@ 44 |hL}T| 6h|ih4Lhic uLh *L *L@_tc ihi -  c B@tt@? h@?_L4 UL_?} _Lit ?L| ThL_i 4U }ih |hL}T| |@? M?@h) h@?_L4 UL_?}

6iMh@h) .

#+6A

H

Bi? |@| |i 5+ t tUi?|*) }c B@tt@? h@?_L4 UL_?} tL*_ Mi @ttLU@|i_ | }ih |h@?t4ttL? h@|it E- :  ? Lh_ih |L u**) i T*L| |i |hL}T| TL|i?|@* Lu |iti UL_it Ai Mi@Lht **t|h@|i_ ? 6}hi D @hi |)TU@* uLh |i L*i h@?}i Lu 5+t Ef |L ef_ t|_i_ ? |t T@Tih W? 6}hi Sc |i |hL}T| ? |i @hi@ Lu *L *L@_tc t tii? |L Mi t}?€U@?|*) ?Uhi@ti_ i? B@tt@? h@?_L4 UL_it | }ih |h@?t4ttL? h@|it @hi i4T*L)i_ ? |i W+ tUi4i ? |i L|ih @?_c *Lih |h@?t4ttL? h@|it 4T*) }ih |hL}T| uLh } *L@_t W? |t i @4T*ic |h@?t4ttL? h@|i - '  )i*_t 4@ 44 |hL}T| @MLi U@??i* *L@_ C ' D OLiihc uLh *L@_t Mi*L C ' Dc |i |hL}T| U@? Mi ?Uhi@ti_ u }ih |h@?t4ttL? h@|it @hi ti_ 6}hi . tLt |i |hL}T| TihuLh4@?Ui uLh M?@h) UL?L*|L?@* UL_it E?L? ML?_ @?_ t4*@|L?t UL4T@hi_ |L |i @Ui@M*i |hL}T| TihuLh4@?Ui uLh M?@h) @?_ B@t t@? h@?_L4 UL_it E|h@?t4ttL? h@|i - '  Ai 6,+ UL4T|i_ | |i ?L? ML?_ ThL_it ?_ii_ @ *Lih ML?_ L? |i |hL}T| TihuLh4@?Ui @Uii_ | UL?L*|L?@* UL_it 6Lh *L U@??i* *L@_tc |i |hL}T| TihuLh4@?Ui uLh UL?L*|L?@* UL_it UL4it ih) U*Lti |L |@| Lu M?@h) @?_ B@tt@? h@?_L4 UL_it @?_ hi*@|i*) t4@** TihuLh4@?Ui 4ThLi4i?|t @hi |t i TiU|i_ M) |h??} |L 4Lhi tLTt|U@|i_ UL_it t @ 4@||ih Lu u@U|c |i |hL}T| TihuLh4@?Ui Lu M?@h) h@?_L4 UL_it @TTi@ht |L Mi Lhti |@? |@| Lu |i M?@h) UL?L*|L?@* UL_it At t _i |L |i UhU4t|@?Ui |@| |i |hL}T| TihuLh4@?Ui uLh M?@h) h@?_L4 UL_it t UL4T|i_ ? |i *4| Lu ih) *L?} tMT@U!i|tc *ic uLh |i UL?L*|L?@* UL_i i UL?t_ih |i tMT@U!i|t @i @ €?|i *i?}| Lu f M|t E?U*_?} |@*M|t 6Lh UL?L*|L?@* UL_itc ?Uhi@ti_ M*LU! *i?}| t i TiU|i_ |L Lhti? |i 6,+ TihuLh4@?Ui OLiihc uLh AhML UL_it Lh *L_i?t|) T@h|)UiU! UL_it |i 6,+ TihuLh4@?Ui 4ThLit | |i M*LU! *i?}|c @| *i@t| ? |i `B U@??i* At 4@) 4T*) @ TLt|i 4T@U| L? |i |hL}T| TihuLh4@?Ui @*tL uLh |i M*LU!u@_?} B@tt@? UL**tL? U@??i*c T@h|U*@h*) @| } *L@_t XYY NAW,tNAt Ai ?it|}@|L?t Thiti?|i_ ThL_i 4Lhi ?t}| ?|L |i |hL}T| TihuLh4@?Ui Lu Th@U|U@* UL_it ? hi*@|L? |L |iLhi|U@* *4|t uLh |i M*LU!u@_?} B@tt@? UL**tL? U@??i* ? TTih ML?_ L? |i ihhLh h@|ic }i? @ Uih|@? ?4Mih Lu Ehi|h@?t4||i_ 6iMh@h) .

#+6A

b

M*LU!tc @t Mii? it|@M*ti_ @?_ @ *Lih ML?_ L? |i |hL}T| uL**Lt uhL4 |t TTih ML?_ Ai TTih ML?_ L? |i ihhLh h@|i t LM|@?i_ M) UL4T|?} |i i TiU|@|L? Lu |i ?L? ML?_ Lih |i L?| U@??i* t}?@*|L?Lti@?_?|ihuihi?Ui h@|Lt E5W+t Lu 4*|T*i |h@?t4ttL?t t @ M)ThL_U|c |i _t|hM|L? Lu |i 5W+ uLh @ M*LU!u@_?} B@tt@? UL**tL? U@??i* | M?L4@**) _t|hM|i_ ?|ihuihi?Ui @U||) t _ihi_ @ti_ L? ?uLh4@|L? L|@}i UL?t_ih@|L?tc | t LMtihi_ |@| |i t)t|i4 |hL}T| uLh t4T*i M?@h) UL?L*|L?@* UL_it | w _iUL_?} t U*Lti |L |i @Ui@M*i TihuLh4@?Ui uLh M?@h) h@?_L4 UL_it ? |i *4| Lu *L?} tMT@U!i|t uLh *L U@??i* *L@_t OLiihc uLh |iti *L *L@_tc B@tt@? h@?_L4 UL_?} ThL_it t}?€U@?|*) Mi||ih |hL}T| TihuLh4@?Uic U ThL4T|t |L |i ti Lu *@h}ih 4L_*@|L? UL?t|i**@|L?t 6Lh } U@??i* *L@_tc |ihi t TL|i?|@* uLh *@h}i 4ThLi4i?| M) @*|ih?@|i UL_?} t|h@|i}itc L|ih |@? UL?L*|L?@* UL_?}c t?Ui L?*) t4@** 4ThLi4i?|t @i Mii? LMtihi_ M) ?Uhi@ti_t|@|i UL?L*|L?@* UL_?} At @?@*)tt uLUti_ L? M?@h) UL?L*|L?@* UL_itc M| |ihi @hi ?_U@|L?t |@| @_@T |@|L? Lu |i |h@?t4ttL? h@|i tL*_ Mi i4T*L)i_ ? Lh_ih |L 4@ 43i |i |hL}T| @| _gihi?| t)t|i4 *L@_t @?_ U@??i* 5+t Ai TihuLh4@?Ui Lu W+ tUi4it | h@|i @_@T|@|L? @?_ @_@T|i 4L_*@|L? ** Mi tMiU| |L u|hi hiti@hU VVjAa!   iNOBO,|+ $jAt|+ 8AW|NAt Ai U@??i* 5W+ @UULh_?} |L E2 t @ +V |@| t @ u?U|L? Lu |L L|ih +Vt 6Lh @ € i_ ?4Mih Lu ?|ihuihihtc |i #6 Lu |i U@??i* 5W+ t _i?L|i_ M) st E+c ihi t ' f @nf2

@?_ f @?_ f2 @hi ?_iTi?_i?|c i TL?i?|@* @?_ }@44@ _t|hM|i_c hitTiU|i*)

Ai i TL?i?|@* _t|hM|L? @?_ }@44@ _t|hM|L? ML| @i |i t@4i T@h@4i|ih b 1 @?_ @ '  2.f&  ? i TL?i?|@* _t|hM|L? t i^@*i?| |L @ KEc b _t|hM|L? `i |t @i f  KE? ' c b @?_ f2  KE?2 c bc U )i*_t |i #6 Lu |i 5W+ @t do 8t E+ '  

e3b+@  E n +?2

Ai ULhhitTL?_?} #6 t hi@_*) LM|@?i_ @t st E+ '

6iMh@h) .

b@E n + n ?2 3b+@ e c E n +?2 n

#+6A

2f

U t @*_ uLh @ _i|ih4?t|U ?4Mih Lu ?|ihuihiht ?2  OLiihc ? Lh t)t|i4 4L_i*c i @tt4i |@| |i tiht @hi @U|i @UULh_?} |L @ M?L4@* _t|hM|L? 6Lh i@ti Lu i TLt|L?c i €ht| _ihi |i _t|hM|L? uLh |i t4T*€i_ U@ti i? .& *f }Lit |L ?€?|) W? |t U@tic |i 5W+ t |i uh@U|L? Lu |L }@44@ _t|hM|i_ +Vt W| t TLttM*i |L tL |@|c |i #6 Lu |i hit*|?} +Vc ` ' f %f2 c U@? Mi h||i? @t d2So KE? n ?2  s` E ' KE? KE?2 



? 3  ?2 n   c n n

E2S

ihi ? @?_ ?2 @hi UL?t_ihi_ @t _i|ih4?t|U @*it L *i| ? '  @?_ *i| 2 Mi @ t|LU@t|U +V Ai UL?_|L?@* #6 }i? |i ?4Mih Lu @U|i ?|ihuihiht ?2 ?L uL**Lt uhL4 E2S @t  s` ƒ2 Em?2  ' ?2

 n

?2n



Ai ?4Mih Lu @U|i ?|ihuihiht t @ M?L4@**) _t|hM|i_ +V @?_ |i L?| #6 Lu ` @?_ 2 t LM|@?i_ @t s`c2 Ec ?2  ' s` ƒ2 Em?2   s2 E?2  ,*4?@|?} |i _iTi?_i?Ui L? 2 M) t44?} Lih @** TLttM*i @*it Lu 2 )i*_t s` E '

 [

s`c2 Ec ?2  '

?2 'f

R   '  E n 2



 [

 ?2

?2 'f

 n   R n

 n

 3

?2 n    ?2 R E  R 3?2 ?2



E2.

W? |i }i?ih@* U@ti Lu @hM|h@h) .& *f c i U@? ti E2. |L LM|@? |i #6 Lu |i 5W+ @t s~ E5 '

 [ ?2 'f

s~c2 E5c ?2  '

' e3b5@ 



  [ b@E n 5 n ?2 ?2 'f  3

 n 5  R5 n5

E n 5?2 n



 e3b5@

   ?2 R E  R 3?2 ?2

R   n b@  E n 5 E n 5  R5  E n 52

VVjAa!   6jiWB, #BaiB|ij Ai ?|i}h@|L? Lih c ?|hL_Ui_ M) |i Thiuihhi_ uLh4 Lu |i 'u?U|L?c t @?_*i_ 2 2 | B@ttiM)ti ^@_h@|hi wi||?} }Er?2  ' A Ee3q  %E2 t?  c    c e3q  %E2 t?   6iMh@h) .

#+6A



@?_ r?E ' %c i LM|@?  Z

Z* ]2 f

 }Er? _ ' Z 2

] f

_%  }E%  s ' 2Z   %2 2

t?Ui  ' @hUt?E% )i*_t _ %_% ' 

s



_% c   %2

}E%2  s



E2H

  %2  Lc _i?|u)?} | |i B@tt

iM)ti uLh4*@ Lu |i €ht| !?_ d2.o ]



 2 E&32*2

  +&

? [ s E+& _+&  &c sE+&c c 2

'



ihi



2   Z & ' c +c ' ULt 2?

 @?_ c '

Z c ?

E2H U@? Mi @TThL 4@|i_ @t  2Z

     E?3*23  ? _%  [Z ? L__  [ 2 2   2 2 n  }E%  s  } ULt Z ' } ULt Z  2Z ' ? 2? ? 'f 2?   %2 3



2

W? Lh_ih |L Mh?} |i ?4ihU@* ?|i}h@|L? *4|t ? E22 _L? |L @ €?|i )TihUMi uhL4 @ ti4?€?|i )TihUMic i @_LT| |i ML?_?} |iU?^it ThLTLti_ ? d.o @?_ |i €?|i ?|ih@* ?|i}h@|L? t TihuLh4i_ | B@ttwi}i?_hi ^@_h@|hi 6Lh |i ?€?|i ?|ih@* ?|i}h@|L? ? E2ec B@ttOih4|i ^@_h@|hi t ti_ VVjAa!   .A6jiB|NA Nu |j bj}| DjAjiB|A} 8AW|NA Ai 4*|@h@|i i}| _t|hM|L? ? E2 ULhhitTL?_t |L @ h@|i  %2 UL?L*|L?@* UL_ic }i?ih@|i_ M) @ e t|@|i i?UL_ih | }i?ih@|Lh TL*)?L4@*t .H @?_ DH  Ai ULhhi tTL?_?} }i?ih@*3i_ t|@|i _@}h@4 d2Ho t hiThiti?|i_ 5  ` `2 5 6 9 9 9 f , 6 f 7 8'9 9 9 ` `2  B O 7 f f

M) @ 4@|h L? |i uLh4 6 f f : : ` `2 : :c : : f f 8 `2 `

@?_ |i 4*|@h@|i i}| _t|hM|L? t LM|@?i_ M) A E` c `2  ' 6EW  O3 Bc 6iMh@h) .

E2b #+6A

22

t?Ui , '  L|i |@| |t i}| _t|hM|L? L?*) t @*_ uLh |i t?}*iihhLh ii?|t Ai 4*|@h@|i i}| _t|hM|L? ? E2b 4@) ? }i?ih@* Mi t|@|i_ @t @ h@|L?@* i ThittL? E2 Lh @t @ 4*|T*i t4 ES -jujijAWjt do

B @hi @?_ # A??i||c RAi |hL}T| Lu )Mh_+" ThL|LUL*t uLh |i B@tt@? UL**tL? U@??i*c W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* e.c TT b. bHHc a* 2ff

d2o

B k@T*@? @?_ 5 5@4@c R,hhLh i TL?i?|t @?_ L|@}i ThLM@M*|it uLh |i M*LU!u@_?} B@tt@? U@??i*c ? hLU W?|ih?@|L?@* 5)4TLt4 L? ihtL?@*c W?_LLh @?_ LM*i +@_L L44?U@|L?tc wL?_L?c Nkc TT 2b ec 5iT bb

d o

w O 3@hLc 5 5@4@c @?_  # `)?ihc RW?uLh4@|L?|iLhi|U UL?t_ih@|L?t uLh Ui***@h 4LM*i h@_Lc W,,, Ah@?t@U|L?t L? ViU*@h AiU?L*L})c L* e c TT Db .Hc @) bbe

deo

5 5@4@ @?_  # `)?ihc RW?uLh4@|L?|iLhi|U UL?t_ih@|L?t uLh t)44i|hUc Ui***@hc 4*|T*i@UUitt u@_?} U@??i*t T@h| Wc W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* e c TT H.. Hbec L bb.

dDo

5 5@4@ @?_  # `)?ihc RW?uLh4@|L?|iLhi|U UL?t_ih@|L?t uLh t)44i|hUc Ui***@hc 4*|T*i@UUitt u@_?} U@??i*t T@h| WWc W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* e c TT HbD bc L bb.

dSo

+ U,*iUi @?_ ` 5|@h!c R@??i*t | M*LU! ?|ihuihi?Uic W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* fc TT ee D c a@? bHe

d.o

B @hic , wiL?@h_c @?_ , V|ihMLc RL_*@|L? @?_ UL_?} uLh |i B@tt@? UL**tL? U@??i*c W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* eSc TT 2ff. 2f2Sc 5iT 2fff

dHo

+ k?LTT @?_  O4M*i|c R? UL_?} uLh M*LU! u@_?} U@??i*tc W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* eSc TT Hb 2fDc a@? 2fff

dbo

 ihhLc  B*@i c @?_  A|4@t4@c Ri@h 5@??L? *4| ihhLhULhhiU|?} UL_?} @?_ _iUL_?}G AhML UL_itc ? hLU W,,, W?|ih?@|L?@* L?uihi?Ui L? L44?U@|L?tc Bi?i@c 5|3ih*@?_c L* 2c TT fSD f.fc @) bb 

dfo + B@**@}ihc wL#i?t|) @h|)iU! L_it # |ittc @tt@Uti||t W?t|||i Lu AiU?L*L})c @4Mh_}ic @tt@Uti||tc N5c bS  do # ih|ti!@t @?_ + B@**@}ihc #@|@ i|Lh!t hi?|UiO@**c bH. d2o 5 w? @?_ # a Lt|i**Lc ,hhLh L?|hL* L_?}G 6?_@4i?|@*t @?_ TT*U@|L?t hi?|UiO@**c bH  d o + O #i?} @?_ # a Lt|i**Lc R+i*@M*|) @?_ |hL}T| @?@*)tt Lu @ UL?U@|i?@|i_ UL_?} tUi4ic W,,, Ah@?t@U|L?t L? L44?U@|L?tc L* Dc TT SbH .fDc a* bH. deo O v@4@4L|L @?_ k W|Lc RV|ihM _iUL_?} @*}Lh|4 uLh UL?L*|L?@* UL_it | hiTi@| hi^it|c W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* 2Sc TT Def De.c 5iT bHf dDo w k +@t4tti? @?_ 5  `U!ihc R TihuLh4@?Ui @?@*)tt Lu |hi**t UL_i_ )Mh_+" ThL|LUL*t M@ti_ L? + ihhLh_i|iU|?} UL_itc ? hLU L44?U@|L?t AiLh) ?L?uihi?Uic W,,, B*LM@* Ai*iUL44? U@|L?t L?uihi?Uic OLt|L?c Ai @tc N5c L* c TT HS bfc #iU bb  dSo a O@}i?@ihc R+@|iUL4T@|M*i T?U|hi_ UL?L*|L?@* UL_it E+ UL_it @?_ |ih @TT*U@|L?tc W,,, Ah@?t@U|L?t L? L44?U@|L?tc L* Sc TT Hb effc Th bHH d.o , @*!@4 @!c ihuLh4@?Ui Lu ,hhLh L?|hL* Lih *LU! 6@_?} @??i*t | +" TT*U@|L?t # |ittc Oi*t?! N?iht|) Lu AiU?L*L})c Oi*t?!c 6?*@?_c bbH dHo a  `L3i?Uh@u| @?_ W  a@ULMtc h?UT*it Lu L44?U@|L?t ,?}?iih?} aL? `*i) @?_ 5L?tc bSD

6iMh@h) .

#+6A

2

dbo  Mh@4L|3 @?_ W 5|i}?c O@?_MLL! Lu @|i4@|U@* 6?U|L?t #Lih M*U@|L?tc bSD d2fo  i_ih@** @?_ + aL@??ittL?c R u@t| @*}Lh|4 uLh UL4T|?} |i _t|@?Ui tTiU|h4 Lu UL?L*|L?@* UL_itc W,,, Ah@?t@U|L?t L? W?uLh4@|L? AiLh)c L* Dc TT eS Dbc L bHb d2o  6hi?}ihc  h|i?c A ||LttL?c @?_  5i?ttL?c R+@|iUL4T@|M*i UL?L*|L?@* UL_it uLh 4*|h@|i #5# t)t|i4tc W,,, Ah@?t@U|L?t L? L44?U@|L?tc L* e.c TT H2H H Sc a? bbb d22o  k 54L? @?_ 5 *L?c R ?€i_ @TThL@U |L |i TihuLh4@?Ui @?@*)tt Lu _}|@* UL44?U@|L? Lih }i?ih@*3i_ u@_?} U@??i*tc hLUii_?}t Lu |i W,,,c L* HSc TT HSf H..c 5iT bbH d2 o B @hi @?_ , V|ihMLc RNTTih ML?_ L? |i uh@4i ihhLh ThLM@M*|) Lu |ih4?@|i_ |hi**t UL_itc W,,, L44?U@|L?t wi||ihtc L* 2c TT 2 ec a@? bbH d2eo + a U,*iUic Ai AiLh) Lu W?uLh4@|L? @?_ L_?} __tL? `it*i)c b.. d2Do A Lih @?_ a AL4@tc ,*i4i?|t Lu W?uLh4@|L? AiLh) aL? `*i) @?_ 5L?tc bb d2So  B|c ? W?|ih4i_@|i Lhti ? hLM@M*|) 5Th?}ih Vih*@}c bbD d2.o  O 5|hL_c TThL 4@|i @*U*@|L? Lu *|T*i W?|i}h@*t hi?|UiO@**c b. d2Ho  V|ihM @?_ a 4h@c h?UT*it Lu #}|@* L44?U@|L? @?_ L_?} UBh@O**c b.b

6iMh@h) .

#+6A

2e

10

0

CONV. CODE (BOUND) CONV. CODE (SIM.) BINARY (LIMIT.) GAUSSIAN (LIMIT.)

M=1

10

M=2

M=3

-4

FER

10

-2

10

-6

M=4

10

10

-8

-10

0

5

10

15

20 E /N [dB] k

25

30

35

40

0

Ilj1 41 IHU shuirupdqfhv ri elqdu| frqyroxwlrqdo frghv dqg elqdu| dqg Jdxvvldq udqgrp frghv lq wkh eorfn0idglqj fkdqqho +qr lqwhuihuhqfh,1 Wkh frqyroxwlrqdo frghv kdyh vxesdfnhw ohqjwk O @ 436 elwv dqg jhqhudwru sro|qrpldov ^46; /48; /4:; /48; `1 Wkh shuirupdqfhv diwhu wudqvplvvlrq ri 4/ 5/ 6 dqg 7 vxesdfnhwv duh looxvwudwhg1

6iMh@h) .

#+6A

2D

10

CONV. CODE (BOUND) CONV. CODE (SIM.) BINARY (LIMIT.) GAUSSIAN (LIMIT.)

0

M=1

FER

10

10

10

10

-1

M=2

-2

M=3

M=4

-3

-4

0

5

10

15

20 E /N [dB] k

25

30

35

40

0

Ilj1 51 IHU shuirupdqfhv ri elqdu| frqyroxwlrqdo frghv dqg elqdu| dqg Jdxvvldq udqgrp frghv lq wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho zlwk 83 xvhuv dqg wudqvplvvlrq suredelolw| 3=338 fruuhvsrqglqj wr fkdqqho ordg J @ 3=581 Wkh frqyroxwlrqdo frgh kdyh vxesdfnhw ohqjwk O @ 436 elwv dqg jhqhudwru sro|qrpldov ^46; /48; /4:; /48; `1 Wkh shuirupdqfhv diwhu wudqvplvvlrq ri 4/ 5/ 6 dqg 7 vxesdfnhwv duh looxvwudwhg1

6iMh@h) .

#+6A

2S

10

ν

0

2 =4 ν

2 = 32

M=1

FER

10

10

10

10

ν

2 = 256 BINARY (LIMIT.)

-1

M=2

-2

M=3

M=4

-3

-4

0

5

10

15

20 E /N [dB] k

Ilj1 61

25

30

35

40

0

IHU shuirupdqfhv ri elqdu| udqgrp frghv dqg frqyroxwlrqdo frghv zlwk 7/ 65 dqg 589 vwdwhv

iru wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho1 Wkh fkdqqho krvwv 83 xvhuv zlwk wudqvplvvlrq sure0 delolw| 3=338 fruuhvsrqglqj wr fkdqqho ordg J @ 3=581 Wkh frqyroxwlrqdo frghv kdyh vxesdfnhw ohqjwk O @ 433 elwv +h{foxglqj wdloelwv, dqg jhqhudwru sro|qrpldov ^8; /:; /:; /8; `/ ^8:; /98; /:4; /:6; ` dqg ^88:; /:84; /856; /:64; `1 Wkh shuirupdqfhv diwhu wudqvplvvlrq ri 4/ 5/ 6 dqg 7 vxesdfnhwv duh looxvwudwhg1

6iMh@h) .

#+6A

2.

ν

2 =4 10

2 = 256 BINARY (LIMIT.)

-0.1

FER

10

ν

0

10

10

-0.2

-0.3

0

5

10

15

20 E /N [dB] k

Ilj1 71

25

30

35

40

0

IHU shuirupdqfhv ri elqdu| udqgrp frghv dqg frqyroxwlrqdo frghv zlwk 7 dqg 589 vwdwhv iru

wkh eorfn0idglqj Jdxvvldq froolvlrq fkdqqho1 Wkh fkdqqho krvwv 83 xvhuv zlwk wudqvplvvlrq suredelolw| 3=4 fruuhvsrqglqj wr fkdqqho ordg J @ 8=31 Wkh frqyroxwlrqdo frghv kdyh vxesdfnhw ohqjwk O @ 433 elwv +h{foxglqj wdloelwv, dqg jhqhudwru sro|qrpldov ^8; /:; /:; /8; ` dqg ^88:; /:84; /856; /:64; `1 Wkh shuirupdqfhv diwhu wudqvplvvlrq ri 4 +vrolg,/ 5 +gdvkhg,/ 6 +gdvk0grwwhg, dqg 7 +grwwhg, vxesdfnhwv duh looxvwudwhg1

6iMh@h) .

#+6A

2H

0.5 GAUSSIAN (LIMIT.) BINARY (LIMIT.)

0.45 R=2.0

0.4 0.35

E /N = 15 dB

η [bits/s/Hz]

k

0.3

0

R=0.6

0.25 0.2 R=1.0

0.15 0.1

R=0.8

0.05 0 0

2

4

6

8

10

G Ilj1 81 Dfklhydeoh wkurxjksxw yv1 ordg iru orqj vxesdfnhw Jdxvvldq +vrolg, dqg elqdu| +gdvkhg, udqgrp frghv zlwk wudqvplvvlrq udwhv U @ 3=9/ 3=;/ dqg 4=3 dw Hn @Q3 @ 48 gE iru d pd{lpxp ri P @ 7 +uh0,wudqvplvvlrqv1

6iMh@h) .

#+6A

2b

1 R=1 R=2 R=4 R=6 R=8

0.9 0.8 0.7 η [bits/s/Hz]

0.6 0.5 E /N = 15 dB k

0.4

0

0.3 0.2 0.1 0 0

2

4

6

8

10

G Ilj1 91

Dfklhydeoh wkurxjksxw yv1 ordg iru orqj vxesdfnhw Jdxvvldq udqgrp frghv zlwk wudqvplvvlrq

udwhv U @ 4> 5> 7> 9 dqg ; dw Hn @Q3 @ 48 gE iru d pd{lpxp ri P @ 7 +uh0,wudqvplvvlrqv1

6iMh@h) .

#+6A

f

0.4 GAUSSIAN (LIMIT.) BINARY (LIMIT.) CONV. CODE (SIM.) CONV. CODE (BOUND)

0.35 0.3

η [bits/s/Hz]

0.25 E /N = 15 dB

0.2

k

0

0.15 0.1 0.05 0 0

2

4

6

8

10

G Ilj1 :1 Wkurxjksxw yv1 ordg zlwk elqdu| dqg Jdxvvldq udqgrp frghv frpsduhg wr frqyroxwlrqdo frghv zlwk jhqhudwru sro|qrpldov ^46; /48; /4:; /48; ` dqg vxesdfnhw ohqjwk O @ 436 elwv1 Doo vxesdfnhw frghv kdyh udwh U @ 4 dqg d pd{lpxp ri P @ 7 +uh0,wudqvplvvlrqv lv shuiruphg1

6iMh@h) .

#+6A





2D

24?

d} c}2 cc} o ELU|@*

2

e

bHf

Dc .



e

ffH Dc .c .

e

e

bHf

D

e

f2f Dc .c .c Dc .

S

e

ffH Dc .c .c Dc .c .

2

H

2ff  c D



H

2.f  c Dc .

e

H

2bf  c Dc .c D

D

H

2.  c Dc .c Dc 

S

H

2.f  c Dc .c Dc  c .

2

S 2SD 2.c 



S eDe 2.c c D

e

S e2 2.c c Dc

D

S eDS 2.c c Dc c 2.

S

S e.b 2.c c Dc c 2.c D

2

2 Sff D.c SD



2 .2e D.c SDc .

e

2 .e2 D.c SDc .c .

D

2 . D D.c SDc .c . c .D

S

2 .DH D.c SDc .c . c .Dc DD

Dc .c .c D

WDEOH L DjAjiB|Ni VN,+AN6B,t uNi WNAN,|NAB, WNajt | |j ,Bi}jt| 6A66 j}| ViNaW| 6jBtij BAa P ajit|+ Cj }jAjiB|Ni VN,+AN6B,t WNiijtVNAa |N iB|jWN6VB|O,j WNajt ajija O+ Ajt|ja WNaj tjBiW OBtja NA iB|j 4 25 WNajt

6iMh@h) .

#+6A