• No results found

Information Theory and coding

N/A
N/A
Protected

Academic year: 2021

Share "Information Theory and coding"

Copied!
28
0
0

Loading.... (view fulltext now)

Full text

(1)

C@"oJ

6d"u

r-lt-.-..

Tr:- Joteft J"odI

-*-hit'Tm\

-ffi

Ja,Lk\k- b;:Tca''[ L;^u

z'

il'

@

tffi-c'odt*

WWW;r")o)Jvw'

I .^ lt ^or,!at rv^rt)ta-brhfnTtx

:

rfn-"rAilt

ry,!X^,Y

'ilo

ffiaffi-bur

oJ/s v

cI'r-"---'*Jfi 'ujE'^ r.E il

a '^it\fvllr ffi t

h

t"fet*

%rr3"

i

Jr^r

d---4'{M

[d-#r

cr-ddqAa-r..orhrr Wo% W

oT\

*"

ffi;41

#,

Y\ '*Y JtJrfrt-@' -t*Vla! . o r ,,rr . *

*u

o[r

qdl-.ff

tftrr[--o''

f:'M'Lr\? q^r,oc.t,^- -ery+{* \^* rr- &t/s

(

enn bj.r,'-'*1., O^,Lti.ttt I I A

.p,

ffi#{.#a-M-qAC,Sd.-ar\ E\lt-k--

M

*1^4

T+'ftfr

(2)

y",h;trbffiry

q

13

tfu

'ryy'rt'

or.. '

hnyfu) tuL Jrb +rL

t

ftt 5, if $LLA nt

*ile

, a' A;cu- ;

ttr-

: ft (

t

t (1t

, 1 |

r

dL o 'ds

t

*fu1

fu1tu

l,l :t'-t frT\l

,

Tlloil

I

l"flhl

I

l+il@+

I ',,Wk ,QtqY rrnYrEnt

IolIFl

,'m

(3)

arr

ffit1

.;1;'*

iri,ryy,

ffi

'h"flfJ"

*J

lr,t'

^?;'fi'=

I

r^uv;rJ[--r $ -,fu ;ilL

Aaflvafu-5;#*ffi"

%

*,t{cstr

c.

,,r\ta

-lt\

^s +^ft

-A"Jt'4ff

T

'

.il*

r.ie

"rf

'ffiWJhto

uJu^ rth:*;n+ ,sh *hr-

^ffi#rf;

i io,^o

I

'Jru,-ffi

tr^ffi"

pr*,tu^? tlf

\

H;"

$f,ilf

.nAoqr,,

JJ,\ ctt-tr.r-l4k

rk 4rrf {t-

;

firffi;:

,1

,T-#

t'

il f@ 4r.,

wz Lt,

r

s

#ffi*4n

y:y^ffrr-ba

l" $. o(t -fWL*Dsrnill

@:

\=L

E .,0., K-3

o

f't, 1O qti

(4)

) ff -l itr

W%

t{"e

-

,w -a"'d'd-LA * oli

P01h''

.,,r1 )e-htworvw ol\-a-

W

n^\i*

@

,LU1

TltL #rY\,L dfirnctuk h-oJ\aw;u,tA f,I'ffi*

"trffi4tl vggd/.z nyvtuu* )oa., W' J&1 fu'n\)

) D l- fY1 tYr U ? -,,, ,/\, , I tuo Y\01A*lT*,(

^ rL

,L$-tr|-

*rWWeru

i4

A,l1:,, t-eon i= o)l)L-\

\

;?=

\tr!

ffii-L

ftov

'iri,tui rh obsw t'fr'

##

"0

W\^'tL:

"#Xui;

. **tut4e 3'w?vYLw q t

r

,Ut3;

tF^,

$l'',

- ,-, 1o C')) roe*

#'r-@ry

i

**y*:

o,d*"k:'-qrtHP,#,-

--,f?.]:^X-f^tp hi \4k \)it o) o -o ,L / * t _to d*onlr"e-t Lr)

(5)

y$,

vFL=

0

+C

ilt

lzfr,,r,

ilrctx

rfuIl"uB

W

Jrg

^W

a'n o'^fP*-f

u*ffi

qtr-

iuj

/'vh,sv6Y)

%*

fx;l

=

lC'.,#,*l'l "fl

f'l

"3

frr\"A-

--l

'ThA /WqI ry"tr 'l..p 11"' 'f--'

dl&'

flr

t-"L rh'ao fuJ.DtD

@

'{\rrajbut* : '/ A o '"J- t

^1 r A'tD otD oct) oLD

I- o tD q!2)

Ito

do I

g=l

c

o I

lcc

I lr

l"

I

t_i

rd \d. sD?

^d/.u

q

tf),

?,t'l

XY:-;}","

*

HWffiL#;i;u'd

[e

Y.r CL+rO

uoo q alrou,td. Jo-a* L7 n[ L+'tD

.rb

Ye-t

q rU c-8 |X''un bile'n H ?l''?,t' ro tD o-''q_ (c (o CO I tt I (D f2)

fl;1;

un otDocr) _ dt dt ocDot2) (o do

?ll?P

oo

--q

#fi:],

x'k;"'[

ll'l

J{HI

)

(6)

[' tr d,fhA Wr\^/ 01rtry4 ^

YM^

/W W,

h,iiw

MEb

wvi(m,:m,w

7t\Nn

L*,

t

) t

l

ono *lD

Ki1

v.tD

charu[ oLD (m qcD {rn Cr--J. ,at\d

ffi?

sto

n$\

=

L

d''

hnr-{ {=o v f=o

1o'-=

?:'

'*o

+

?iw''*?l''

#

AS')= ro t

:l

*f

')=

?Sn-r+ ?ln'nAe' n!:n

"{:

n,tO=

l'o

+

f

'l+O s

I

1"=

?SDn,

>+

?f'-,r?:'

(Tr o

dn=

O'l

+

I'otl'l

=

l

t''=

7jn

ry

*3','' wz org'vn) q,jn=

l'

t

t l'0 t

l'

o .4!D =t t

--4

H,-", 1

"l

n8

(7)

,L,n= ?!trnLr + ?i"rl,

+X[?-'?

]

"S,

,t*',=

['l

o

+

l'r

*

l"o u*,'

:?:''d"?f''*

+t

7t'rn3

*t'=

o)r

l'ttl'

,U'20

D

-o o{n= ?$n

"fr+f,'f;*#

*\

*l' )=

^:tc+

('l 6 *fn= \

Tt..-e J,o.u.

flr-

e.*_*=ne

rrn^|.ffi

N'!-w-Miffi,H,Wtu

bb%

t*

yorll'il:

'\',fLt

tt\\oot]

a-

U)

t,rutr

niLD=

kti,t)

f*eLsro 'JtcL/^'u- absl^l- (*cil"1,ll)

LU

V%qiG)=

I

ovg{, \[=

f

&o

(ottll

Cr) Cz) 'ltD 76 r * tD tr) ?f1 "lt )

(8)

*elu..llo-Eu\mffiYnry Lx u

i'e

u=e

(*0^W:

?r,'I r r ii";

V

==

;f;

c5+

D)

lpl',o,rJ

,-S,

&,*"1

q-00 o0 OD o0

tl

A/eLd N= v-- D'cl h(L+rn) hA" ' )i : tl 00 D0 0o 00

I0 lt

0o o0 00

tl t0 tl

o0 0D 00

tt lD lt

00 oo

0o

tt

to

tt 00

o0

0o

tt

tD L to0

rf

tn

fo I oo {r I oo 0o

I

oo oo Loo oo ri t wut

lo0

ID t t ll tD 0o t t oo 00 OO OO 00 00 r

r

oo

r0

t t t I (0 ool oo I oo I

ril

{H

C -' ' Ct L tc )(r t Ctl c{CD >_o Ctl

c^z

ofurutfi

+

c I () r -- /no ,, ^ Ar, l+

ti't

f.?

.-u,,.p,tL+< .f, lftYY,

(9)

T;:-,1-C2) ^()) ID ?8"', Xi-t, ^-

?X

il"t .^l,wwlR-I u-l ----lu-P ta| ,tXrsgtd-. yon"

rrrt

nn^,lg ?Wrrta-L

*

rrrCD )= frio +m ,D **'f* ,.t?D)

=

fb,

rn(D)

,,t'cr)

=

f'(D)l,',crD

rrrht

"[?ol

=

t'r*

Yncu)

#?o)=

r+D'+#; o*+f"d=(,or

rl(,

olf

-dt-orj 6. \

**1

ooo

/?rr

=

tZP) .'- (D)

=

tir+f)

-Lt+#:q

=

r+

*+{+

D+X"&

h;V

"{,{

fi

l;,,;

,'}

,,hn:

r, corr) (t a r .,Cl)^^'- I+D

+*

1 CD ) = | I -'/ | t'/ F (,

ot?o)=

A^+

L+ D' rrn}) = t-t D'+D' xtoco) = PAna-r +o * ,)#+'oe=6t t ttour)

*,o

y=

C',rla,l

(10)

M

)

f,A.e-!J3e-lr oLiaerronY\a F. fu,ci'L 'bek d

#

(J

\-,

,\.\_/-s fo,\.\_/-s

sJ7xlz J'n&)a-

ztwr@

-f s-t0,[-[ So .>lA Sz 53

Va]-tA-0- 00 t0 0t tt

s

€-

stuE

Affi

f^ilila-3p,po^fu[t

"l]:

?ccrr) a rcth- D +rt tn -z) 12) , bs,ttsttrr %f

u'-

zCn)i-? Cr *D t)\.-;d/ L 6l f'/ ,o ())

)v

ooD

PffiI

vdeu' rlr Y*"1

*rr-

f r,^, r c n-Dtcn-z)

I "tt, $' .So I 0o

s1

I

,o I

s2 I

ol I

s3 |

rl c I O I o I 0 t 9o Sr S2 s3 So S1 Sz_ S3 OD to ol tt oo t0 ot ll

f c o

o

lr o

o

lcto

Itto

looti II

lr

o ti

0o

ll lo ol II OO DI

lo

rill{D

(11)

,o. --.LO (Fi-*CDd-e- *'t\.tt- * *lb IJ So Io Io

I-ll

vr tf rl (l tl

il

t r_ l--l t1 I lo' il -f I t S2 !s3 -t7 sz ,r -) S1 0l z *a-il- D) z6a h,i6

cL\o-ad{'kA

to"th'a-ryY\\fiw

(12)

.tC "rnl1=

Cto0tr)

,il

,lr

=

(::,'orll

'rt'r

orrots")f

-ttu

*4.'4M

W

;*r

Mk-.*.*Uffibj,fi

^!0,,1

"*#ffiffi."rr

"C "&' -

t to^n e on[ tl,.'u

0€

z$,DIl f

-ffi0-*'

*u{.id, J'fi*

t, o'* t) e'

h)er.ll c^A tbljlt ji^r -/

"Sl So SL s3 {=o oo oo \a, I \ ---- t0

z3

L 56+ zu'D Uib

*.W;

-{'ffi1d

ry

(13)

P-rdo,tun;

r. Fo\

#\!-

l,.rvl;i^z_

Tf.i;;

;" W

h-u,l,Dt^-l-d) 4fu4 l}rc ,cnctr y.tnf-r-6,r4L Cfft'rte)ilt

(b

t

trffi

r\Ao

,Mq

ild,tb

.T,,,*-,

d\i)

\-

tr,ri,np #.lla-

.:

I}-otkr *n:ttrn ,{rud,L

-t7,.lu t.M?

/li' n

,,

(l 0

o'll)

tft

,lr ( toYn)

G""Iq-

to) uc;neLY ,-i* a L-' B{i DE,c

d

wl+,^ Fd\ o-- Llr li D ?o)= ,ro

)

f'=

lo t ,C,trrrrr&Uffi*n

,f>

rr '

Gi) fjrve q^lu-\Afe{ .ancdffx

r?iir { cod-u ,-'*trr& ,<fr\)'rAfon&tnV

u t')

I;^Y**f?',7

5 "^"d",'

-idw

( a***;n

P v

f\-@

A*'v,Lb *ftry1g'.. t1 u r'( l{-t'l) [r.rr 01) ?t'': r r o

lo'-

tc I

!t":

rr\

(14)

t?r@WW

tr=b ) K=l > "ryl

=2-I

(z^> l .t')

l-1.-;

*'t1*=r--

fU-T,I

)

\

!,*.:P

L\

I

liri

gx#|

g=:ili,c,+z)

I I

I-ttt Iot oti o0ooooco'oo"l

I

Iooottltotottoo0ooolJ;ll

looo

ooo

ttl

tot

otrooo ooo

t

I

(4--

\:3:;3i

#

jJ;

IIJ

[1

li:

\

I ' IOOO OOO0t;t" l)Ltt-t l'tt \L'/r - i I

t_

57L'

I 6tflil Yn = Ct t to D a ae ^,^^ r.r o I -dJ^^i-do11^oril

q+'""0^J13-

\

I

i,)=

d''

;+

rn

=

tlto) x(t ll o

iJ

I

jr..ljH*

tilot

) 'Ldy-/\d ,1 rt) ) ,) C) @ln 3 t')

(15)

c2) C= = J2-) = L (D f ':x m Derc_.. ( tot) >+ ftorr\J trot) >+CurDl)

tt\ ol

^(z) t- = ClllJO)l)o,,Orf) C

rtr)

x(ruDr)

I ll ol Ll

)o)l-,oro;l)r)

( t, I )of or cot) lic, tpc)lOl) cll

I o I c3i) \-. ...-I I I _c5) _ (--I J o\f= cs

*\n

J{T-

d-vt^^au>',:-co

vtP=

tt"

|'-tD

u rr..)

=

l+ D z ff'"(D)

=

l+o*D 5 [''Cr;

=

fDr,

x

'nn cD)

t''(r)

=

(r+o)' ( | +D*

**tD

ocil =

i+\t{+f*b,1$+#"f

L

rr')ro)

=

I-t

o3u",t+

f

)

r

(16)

-cr)_

tf

oaltro)

^rC

tlr%

c%o)=

f'*

'Yrl cED

=

[r+D')'(t+D**+D+)

.

=

1+e+Xs&;t* tlnX**"

2

t+ D+D5+# on.

*D* Ll totoor)

C5)(,D= 7cg:CO rn('D) L LL,,)- 0 \---_2_1 rri 2,rg

--

Li*D+f)

Cr-D+D-+

-*

l*\

"A{+ff+e6

+fuJt*\+o\+X*'q

='

t+ u2+ Y5+De

."

ccL= ClDloclD

,,0 \/=.tl l) oto )oolrl' o)loollol''ott)'

I i ! -r 3.

s

alfl,

/*eir- -9'-b+, n?^6dasl\-ai'

l'-1B*-I-(ra

W

Wear"xo,r.l f:-aukm

rr

g,{nfo- s'GJa

frilz}e--rtCrr) + otCn-t) .I_C111 +rtcn-z)

=

t

tn) +?ttn-t

l

L+ +D ct) A v --? (2) , Lb tb) L f D

jft@

+1t0.-,

(17)

-fiIlutt;p,64 vafuir tlr LrgI+ V t_,;,te.. ...1....r.r. I cr) ( 2-) Ca) tt$r) x.[n -r)'rto 4)l e c c 0oo

tg?

olo

tlo

ooo

ttl

10t

ctc

So 00 O I =St6 s\ 00to S1 to 0 t se-33 ol ll '-32 ol o i So S1 oo lo o I ot ot ollI oo s3 II o { S2 S3 ol tl

o It

I

ti

lle

0 cl

t loro

't,l

6l to ?To-2

(18)

'n cca) COd! Ett- 1

*7=(

ttrlt}

sg }C

rl

CI lc

tt

co

Ic

CI

000

,f

It\ 0t O 0t o -tfl \^^^a=[trtottr)al ,,t >D S> otl Ito ot o r{= oJ loo) r) ll t) \{= [r u r o Io roo lT ll o-' [D O, tol rolt)

,r

(rrt, D to) oo l, ot0t0o ll,ora tr (, f oo So .t"1 .n^^tr =(L

rtpf

9?Jo tl^ -lr- ) O s3 US t0l ooil o I

z

ttb t00 Sg 001 , OtO 00, CCt Sj

(19)

gg&-So ooo Sr t t).. I,i \ rtt\ \ 'r\ z\ oto\ \ /r .r ' o(o\ o/ *,/ \ 8z $Yt or0 \ i"; ) - -o-[ \ ----S3 o { 'b.fi

*? W'*t

tttot)

6,da^uo@ = (Ltt)0tD,0olr ttor t0o, \DlI

ou)

r

r-6t t-. u, tol / \

(20)

4*

r**

I I ollt 00 ro

Il

0l

lt 00 1o

t(

0t oc o0 t0 t t 00 Ccl Do tD t to 1 O tl] ) rn=_]

alvMulM

td#fl*-V

K=l

sl

pnF,Oohr- 11 =L )

<_^

l) cr . ol f .@ €z *r^ LXl1 P+rn) "is+fi=;a16 q-lo o0 0() CC CC 00 00 0D 00 ll 00 0f tl t1 0f o0 oo oo 00 u r. ',.I. ,;,

(21)

Ngoo

f:

Dq C/oo {(J 00 00 00

tl

oo oo

ol ll

oo

ll o/

tt (D

tt

ot

Iro

/J;

l0o

fo"

il or

l/

lo lr

0r 00 f0 U oo 00 to o0 00 00 [o+otD

(= L'?:1,11,

l;1

Hil[]:'):

*)

(= tlDl

t.l rQt, o ttotrlot)

ot l]

f=

Llo, ilr ottstt olr tas lat ,,).

r

tt) c t) L: *titl'T^CcD o(D1.- t*r*,3n-'LD)= lt D+ tr

u

-L.# Prn

-

e+

o'-o

rn[o)

=

t+

u3+D-.tD=

[ \tD+o) [t+#-tDD

=

t +

X*{-

D + X--t dt. X*#+ o? 4o

--

l+D

t

':Toe*Du

(22)

;.

D;-l oo oD I )o oo I f r oD

l;

ttlt

I

l

t

l,)

,-_

7(4_fi.m(o)

t')--o 1,.n,#al) Cr+ o3t'6O

.---*-'

-t o+*

Xi

d

-t&\

*'fu X*

#

atD

=

P+*+d+ok+o+ '" .. ,

to=

'q,*rH:)*SUf?r"

'Cr) rttooolll) ooo 'r*= 6tottitoot)

.

c--

c,o, ll)oltot.,ol)to'

t'"')

r

G ' jA ^t'*un n'*'

r

Fc

in-

ct;#;lrff#

q0^e4jre,\L!4

$x'

4"il

fr!

Si, '

"'o

7Lt)-- Ct o t) dL+ (t t a)

tir

'ftrnr

i-;"f"

E'P'rDa h

ttb

,-""^tM

an'i'n

q'f'r"oo^A

'

ft or'.') Lr) C 4 rj) C A(2)

(23)

E|" uPu/r tleAtuih;

n

a] rr.!i :..,, t') !r CD C-{ o ot

?'=

r0 oa2

(li

T';

(rr) crD) Lr r) trl tot ooo t t t c00 0 00

-)L>

'rr( ++rn) =) . _Z^1, ex z lL(z+ r) D= tt ot) 9r-ooo ooo r of 000 t tt l0l a Or cr) &

fr

t,

b

q=

Qr l.'\ to\ oo l.'tl o0 0 00

!'-'

ttotl

coo [01 It\ ooo 00 0 tDt r C1 = Ll I t r1 o \,

\\rtotl

(24)

d"&) . [ ; t, t\) 'tv ul-fur". tlr ^ufuh

fi

oE ,u) t2) r C2-) L.3I L{) I =) :) Lx 3Y n-(L+To)1L ooo-l ooo \

Lroj

r= hz LL=

[

t

tol

t0

t to oo o(D oCI ooo

f

oto

tto

ooo

I

oo0

olo

tto

I

ooo ooo oto

LLD

c>=

&

Qz-oo.-l 600 I It

,j

oCI0 t(0 ot0 Cz=toto., l

*9=

'3y= c0\) Lt D "#'=-CoO rL) \ d* '= (. tto)

I

0 o.

f

I oro o

,)

)/ 0

ctAtu^ f\r dirnctl 'olP 'td :)

(= q +LL

C1 lt\rLDl) ltl)tol

(25)

ulh"[, sLuil^lo ir.l PDfl? -7 qio= L t\) 2 ltr> ,r\ ?lrr= c ro) -- \ "rtO- [rt) = l+D

t;;(D)=

ttot) =

l+&

oo' ) ,r1t)*..,rr) : ) Cr +il t')=

?:')*Co

=

tt+ P ct

=

-frr

t,i;

t+uz+ D+#

.fr=

,nD+ **os * (t t

lt)

8)=

ff",^CD)

:

l+ DL= tto ro)

\D=

ofo-Cp)

=

C i+

p)

Clru') C1 = -(r rrr\y) L g

:

t+D-+D* o = t+D+**#,

;iittD

rrl I rut'| C r = UOL Ico; ou, ct= C ll'l ) lol, I ) 001,, t0 D 0 t C e ) I

6.

rrr.__.rmnxdh

a

c,ovw$"rfrfi.nQl wqd-rl il"4^^n g j/1 ffi ' ^ ^r rl o- n,orr^ff\ n '

,fl.

%

ffi

ffiY

\'^& c^rcDc,^'lr

ut)

tr,,\

"-^f

LD\t \

tti) v,^'t^d

tlr

rlr/rt

(26)

-EJo'sroJfu *r) oC\= Cl t) 1,q- rt r)

x'L'

cso -+ o ) [st+ i r) o) z) srolI,

@*oWe<

o t cr L o t .*)

1o

ol

U;rr) 7 /&a-trL \drrr!,| "fn .rcn -D o t O t 6 t o t o I o I i ' tr 'l

(27)

CDdr fr&a"-I s, ccd.oJ,:Ltrcl-''=

.tfl

Y^lfl= ( tottD fo 11 -> t] 3o Ib So

ot

,l

0 o So Si 0,..-5o )ol rol)l') (rtrto)ll cr r)

=

ttD) 0o-] oo I 60 I oo I I.OJ oo

13

ax (o+r)' 'x tL \r io 0o oo tl t0

co co

tt Cc 00 0o cc co oc oo 00 o0 00 lD 00 tr t0 Co tt q=

(28)

0 oo (= D'Ct

(=

Lr olrr]

L=ft

[ ; i,

fr

)lr l) o) l) l) o) ll o)l)l) o oo o 00 0 ?s3 tt I I lo o tt o o0 o oo 0 oo o0 00 t0 oc> f 1 t D ao t I o o oo o1 ol ol ol o_J ,( )z

References

Related documents

The importance of grassy and woody plants growing in the natural rangelands and plateau vegetation in Erzurum Districts in landscape architecture.. Utility fields of

Cash - Indian Currency (Not More than Rs. The contact information of International Student &amp; Scholar Services office at school. Please carry Addresses of your

The study further identified the reasons or factors for fetal/neonatal case admissions as well as the causes of deaths at the neonatal and paediatric wards of Taung

Vor dem Hintergrund, dass bereits heute in mehreren klinischen Studien makromolekulare Chemotherapeutika (Greenwald et al. 2002) zum Einsatz kommen, sowie der

As international dialogue opened in the early 1990s, Pop- ulation Council researchers in Cairo began discussions with the minister of state for population and family planning

Furthermore, we have shown that the wall stress response to thermal treatment seems to be similar to various surface stressors, leading to the activation of Mkc1 signal- ing,

Lastly, this study has provided multi-level evidence of signi ficant association between material deprivation and coercive sex among young women residing in two urban slums in

Because the surface of silver nanowires are hydrophilic, dipping polyester thread in the nanowire solution resulted in a resistance per unit length of &gt; 300 Ω/cm