system dig i wireless comm
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cac he thong vien thong khong dayTRANSCRIPT
-
. . . .
. .
* *
-
.. , .. , ..
- - , 201000 ; 201100 , ; 201200
, 2005
-
621.391.037.372 82.841
JI.H., .., ..
: : . . .: -, 2005. 392 .: .
ISBN 5-88405-071-2
, , - . - , . -- , . - . - , , .
, 6504 6542 . , - .
82.841
ISBN 5-88405-071-2 , 2005
( )
-
8
9
1. , 11 1.1. . 11
1.1.1. 11 1.1.2. 13 1.1.3. 16
1.2. 18 1.2.1. 18 1.2.2. 20 1.2.3. 24
1.3. - . 27 1.3.1. - 27 1.3.2. 30 1.3.3. 35 1.3.4. 37
2. 41 2.1. 41
2.1.1. 42 2.1.2. 44
2.2. 45 2.2.1. 45 2.2.2. 47
2.3. . 50 2.3.1. 50 2.3.2. 51
2.4. 53 2.4.1. 53 2.4.2. 55
3. 58 3.1.
58 3.1.1. 58 3.1.2. 60
3.2. 61 3.2.1. 61 3.2.2. 65 3.2.3. 69 3.2.4.
71
-
4
3.3. 72 3.3.1.
72 3.3.2. 75
4. 78 4.1.
78 4.2. 81
4.2.1. 82 4.2.2. 83
4.3. 85 4.3.1. 85 4.3.2. 88
4.4. 89 4.4.1. 90 4.4.2. 91 4.4.3. 95 4.4.4. 98 4.4.5. 102 4.4.6. 107
4.5. 111 4.5.1. 111 4.5.2. 116 4.5.3. 122
4.6. 126 4.6.1. 126 4.6.2. 128
4.7. 129 4.7.1. 130 4.7.2. 134
5. - 140 5.1. - 140
5.1.1. 140 5.1.2. - 144
5.2. 147 5.3. 150 5.4. 156
6. 160 6.1.
160 6.1.1. 160
-
5
6.1.2. 162 6.1.3.
164 6.1.4. 171
6.2. 173 6.2.1. 173 6.2.2.
177 6.2.3. 179 6.2.4. 185 6.2.5.
191 6.2.6.
195 6.3. 201
6.3.1. 201 6.3.2. 204 6.3.3. 208
7. 213 7.1. 213 7.2. 215
7.2.1. 216 7.2.2. - 216 7.2.3. 218
7.3. 223 7.3.1. 223 7.3.2. 226 7.3.3. 226 7.3.4.
226 7.4. 227 7.5. 228
7.5.1. 229 7.5.2. 233 7.5.3. 236
8. 237 8.1. 237 8.2. 244 8.3. 249
8.3.1. 249 8.3.2. 251 8.3.3. 252 8.3.4. 253
-
6
8.4. 08 254 8.4.1. 254 8.4.2. 256 8.4.3.
) 258 8.5.
261 8.5.1. GSM-900 261 8.5.2. GMR 265 8.5.3.
... 271
9. 275 9.1. ,
, 275 9.1.1. 275 9.1.2.
277 9.2. 280
9.2.1. 280 9.2.2. 283 9.2.3. 285 9.2.4. 289
9.3. 293 9.3.1. 293 9.3.2.
294 9.3.3. 296 9.3.4. .... 297 9.3.5. 302 9.3.6. ^ 304
9.4. 306 9.4.1.
() 306 9.4.2. 309 9.4.3. 316
9.5. 322 9.5.1. 322 9.5.2. OFDM- 324 9.5.3. 326 9.5.4. 328 9.5.5. OFDM- 332
-
7
10. 334 10.1. ,
334 10.1.1. 334 10.1.2. CAP 336 10.1.3. 339
10.2. 340 10.2.1.
340 10.2.2. 341 10.2.3. 343 10.2.4. 345 10.2.5.
349 10.2.6. 351
. 354 11.1.
354 11.1.1.
354 11.1.2. 356 11.1.3. 357 11.1.4. 358 11.1.5. 359 11.1.6. 360 11.1.7. 362
11.2. 364 11.2.1. 365 11.2.2. GSM: 367 11.2.3. GSM: 368 11.2.4. CDMA. 369 11.2.5. CDMA: 371 11.2.6. CDMA: 373
11.3. 374 11.3.1. 374 11.3.2. 376 11.3.3. Globalstar 376 11.3.4. Iridium 379 11.3.5. Thuraya 382
386
388
-
- , - . - . - - , . - , , , - .
. , .
, - , - , , - , .
- , ().
, - , , , - . -, - , , . -, - , . , - , , , , - . - .
- -. - . , -, , , , -, - .
4 7 11.3.5 .., 1 -3 , 5, 6 ( 6.2.4), 10, 11 ( 11.3.5) 9.1 9.2 .. , 8 9 ( 9.1 9.2), 6.2.4 .. . , .
-
, - . , , - 3000 . , , - .
, - 1979 ., -. ... , , , - . , -, .
. , - , , - (). , , - ; .
, , . , , -, , . , - , , - , - .
, , , . .
, . - , . , . , .
, , - , . . , . , - , . 2 .
, , - . / . 4, . 3. - . 7. - : - . - , . 5.
-
10
, . , - . - , . - . 6, , - -, ; . 7.
(8 9) , - . , , , , .
(11) - , - . , . -, .
. 10, . , , , - . - , ; - .
, , , .. , - . . 3, 10 , , . 4 , . , . .
-
1 ,
1.1. .
1.1.1.
, -, . , , - , : -. : - , , , .
- . - . , ( ) - . - ( ) , . , , . , - .
. 1.1, , .
, , - X.
-
12 1
, , - , , - , . , . , , . ( ) / = /. , , , , . , - ( ) v,
v ( \ . / = = / 1 . -
X \ ) , , . - , -
, ; . , . - . -, - , - ( ).
. 1.2 -, , , a z .
. 1.3 = /4 .
z
X
. 1.2.
. 1.3.
-
, 13
, ( ), , - . 1.3 = \11. , , - ( ,
-
14 1
. , , - . , - :
^ 25 .
(1.3)
G ; ( ) ( 3 ).
. , , , , , , -. , - - :
p = WS. (1.4) (1.4) S Sr,
. - ; (1.4) , Sr:
S = 4S r, (1.5) | , (0,5-0,8).
, . , -, , . . -
(1.6) 4
, . , - , - , - . , (1.6), , (1.4) . , (1.6) 1, - . , - , , , , -. .
, , . , , () , -
-
, 15
, -, , , -
, , , - ( 1 4) - 90, -
- , , - , -, ,
, , , , , , , - , , - ( 3 )
, - - 1 5, , -,
. 1.4.
+ - -Ei
J' . 1.5.
] + 3 =
2-,
I 5 , , -
-
16 1
90 . - 180; , , . ( , , , .)
. 1.5 , , -
^ (F.+F. V V (1.9) - *
I
+142
2 - j 1-. -
, () -. - :
= ( 1 + )/ (1.10) , .
- - . , . , , - . , ( ) , , , , . - :
= = (1.11)
1.1.3. -, , , . , , - . -, , - , /2XR , X , a R . , . (1.2). , , - .
-
, 17
-, - - . (1.2) ^ . -, - - , ( -); . , . (1.2) |2. -, , , . . , .. . , : , (1.2) - ,
= (1.12) 4nR '
G\ ( ) - , v > 1; (3 , RV1 , (1.12) , (3.
(1.12) -
PGfi 42
= |/2- , ,
(1.13) (3=v = 1. - ] = 1.
(1.13), (1.6) (1.4), - :
= ^ - . (1-14) (4ti)2/?2vTI Go ( ) - .
. () , , ( -). , . - ( ), -, ( -
w = . J ; , (1.13)
-
18 1
). ,
= 1,38-10"23 7^4/", (1.15) / , , .
(1.14) - , (1.15), - / . - .
[] = 106- [] +10 lg ^ 2 '"'1* ] - 20 lg [] + [] + U [/] -- 2 0 lg / [] - 1 0 lg / [],
= PG\ () ; U = G
-
, 19
( ), , , - (). . 1.6 - .
Sz, , , Sj. -
2{A} = SA/SZ. (1.17) , -
0
-
20 1
, . , - , .
3 {A!B} = SaJSb. (1.21)
- :
3{} = ^ = = 3{}3{/ ) = Sz
= 3{5}3{/1/}. (1.22) ,
- . ,
. 1.8.
3{/1/5} = 3{}. S S
: = , .. - S z
, . , -. , /} = 3{}, I ) = 3{). ,
- = , . , Sz SA Sz
: , . -
Aj j = 1,2,..., , , . . ,
3{} = X } = X } / ,}, (1.23) j-1 J- 1
. : 3{/4 t}3{5/ } 3 {At/B}~- 3{5}
(1.24)
1.2.2.
, . , - .
\ :
/^() = 3{ ( ) - / > ( * - ) = 3 { - < 4 < } . (1.26)
-
, 21
' 5()
1 1
^ " i
^
, , - , 0 - 1 ->. . 1.9.
- - . (1.26) , - . , 2 3 - .
- \, . (1.26) - , , . , -, , , . , , Pt(x) - (, ) , ^() . - ; . 1.9 .
)
. 1.9.
(1.27)
), , , . - , - 5- . > -, , .
j5(x)/(AOdx = / ( 0 ) , (1.28)
f(x) . , 5() , -
. , , . 1.9, , {) = (-\). (1.27), - , .
q, . . - , -
^(,) =
-
22 1
, ^ q , . 1.10, .
, - (a,d), (, ), (,) (b,d) (. 1.10, )
3{a
-
, 23
| = = (Mt,)(Mq). - , . -, % q ,
M(, + q) = , + Mq. (1.36)
, () - / (),
M[f&]= jf(x)p,(x)dx. (1.37)
: = 2 = /(, - )2 (2 , - ,). -
(1.38)
() ,
() = 1
/2< -
7ICT ( - ) 2
22 (1.39)
2 . , - , - ( ).
1
() = - 7 = fexp(-x2 /2)dx, (1.40) *v2n
. . 1.1.
1.1. () 0,5 0,3 0,2 0,1 0,03 0,01 - 3 - 4 - 5 10"6 - 7
X 0 0,525 0,843 1,21 1,88 2,33 3,09 3,72 4,27 4,75 5,25
-
24 1
: 1 (.
2 (*) = ( -*72) . (1.41) yflnxK ' , (1.39),
-~
() = 1 - (1.42)
, - , , - . , - 2 , ,
= J a 2 +2 . :
*) = - ' 2 2
* +0 2
(1.43)
/0() . . -
, = b = 0,
) = - 22 ; (1.43)
1.2.3. . (/), - . ,(f) ( t ).
- ,(4) = () tk(k= 1,2,..., ). - 4, , . , - - , - , . ( - , .)
, , , , .. - : ,(/) - ) .
, - (/). t; , :
-
, 25
= l im^L J^COdr 2 = l i m ^ / K ( * M ( 0 ] 2 d f . (1.44)
(/) = 0 . , - .
= (1.45) t, , -
, :
()= ^ W , T ) d / . (1.46) 7 -> 2 jT
. -, (1.35), :
R(x) = R(-x). (1.47) -, R{Q) = g2>\R{X)\. (1.48)
, (t) - ) , ( ) .
= = = (1.49) , ,
= (R(0) = 2), , . - , , , . - , :
N0{f) = 2 j(T)e_2" /TdT = 4j^(T)cos(2n/T)dT. (1.50)
- , N0(f) . -
(1.50)
*(*)= pV0(/)cos(27t/T)d/. (1.51)
: - , f\ /2,
h < 2 = J X U W - (1-52)
/ . : ,
-
26 1
. , , sinxlx . , - , (sinxlx)1 .
d(t), (), , . (1.50)
R( ) = - ^ 5 ( ) , (1.53)
8() 5- . , . ,
, = jd(t)b(t)dt, b(t)
. , ( - , ):
ME, = jd(t)b(t)dt = jM[d(t)]b(t)dt = 0).
2 = M{\d{t)b{t)dtf = M{[\d{x)b{x)dxi\d{y)b{y)dy]} = '^^( = 0 0 0 0
= J ?( - y)b(x)b(y)dxdy = | { S ( j t : - y ) b ( x ) b ( y ) d x d y = ^-jb2 (x)dx. (1.54) 0 0 2 0 0 2 0
- . , . , , , a(t). , , , - ; , - . - , . - , a(t) (), a0(t), . - . , () fF[a(/)]. , . , . , . . :
W[a(t)] = -'*1' ^ (1.55)
-
, 27
, . , , , . - . : , , , , . , , , , , - , .
1.3. - .
1.3.1. -
, , ( - ), , - , . -, .
, , . , . , ( ), - . , , - -, .
, , , , . - . , , , .. , , - .
, , , /, /0. , / /0. fo / , (. 1.11). , - , - .
N(0
f
. 1.11. -
-
28 1
, -, , . - - (, - ). 4 = + t0, ; t0 , ; , , . 4 . , . , , . , , - . = 2, - -. . 1.12 , -.
. 1.12. (), () ()
, () , - , . : . , , , - . ( , -) , - . , .
(;) = ^(0cos[rot + (p(0], (1.56)
A(t) ; q>(f) , , . - . , , , - .. . (1.56), - . -, -
-
, 29
. 0(f) = / + (/), - (/), () -. , , , (t) , .. (?) . - 0. (1.56) . - , A(t) . A(t), - (t) 180. , , A(t) , , , .
-, , . - , A(t) (/), ( ). - - A(t) (^) . //2, , - , , , - A(t) (t) . , / //2, (. 1.13)
m 0 ' " V 1 f O f 0
fnp>A/72
Wo (
fnp = Aff2
fnp
-
30 1
u(t) = ,4(/)cos[
-
, 31
- -, x(t) , -FI2 FI2, , .. = x(tk), tk = t0 + kq (=..., -1,, 1, 2,... ; t0 , - ), q < 1 IF. ,
n(t-tk)lq (1.61) . , x(t)
{ \) -
(1.61) . , , - (161) . x(t) - S(f), , ,
a 2 = 2 j S ( / ) d / (162) F / 2
, . , - , (i = 0, 1, ..,N+1), , - . = ^ = , , ( = 1, 2, ,N) - , - b, - ,
, , - . , - x(t) , , - , , N2,
2 = da2xl N2, (163) 2 x(t)\ d , cl - , -
- -, - d
-
32 1
- , , . , - , - ( ). - (N> 10) d 2,72.
. , , - ( ), . - (- ) - .
, - (- ) - . (1.62) (1.63):
(1.64) , , -
, , , . -, . - ,
G = F\og2N. (1.65) / ,
. - , - .
(1-66) , , ,
- (). , . , -, , -. , - . - . , .
*('*) = ! > / > (1-67) 1
-
, 33
; , bk = +1 -1 .
- - , , - (1.67). - , x{t). Fd = \/q, - - , . .
- G = Fd [/]. (1.68) , -
q, . - .
. 1.14 - - . ( ) x(t), . - ( ) q, ( ) . , - , -, , - , - +1. ( - .) - -, . - .
. 1.14. -
2 - 1339
-
34 1
, x(t) , . , - AIq, x(t), , , , . , - - : ( -) ( ). - : , - , , .
, . , x(t), , . , , . , , , , : - . , , -, . - , = , .
- , . - , . , , --, , - . , . +1 -1 +1 - . -, (+1 - 1 ). , .
. , - - . , - . , - , - ; . - , .. .
, - . - .
-
, 35
- . , , - , .. - . -, , - , . .
, - . - , - . . , , -, 0,3 3,4 . , - , . -.
-, -, , - , -. -, , - . , , , - ( ). - , , , .
. - - . , -. , -. , . - , . , . - -.
, . [1.3], .
1.3.3.
, - , - F (/72 - ), , - Q= 1 IF. , -
2*
-
36 1
, , , , - - , , , -, , ,
- , -
v(t) ( (1 57)) , -
v ( 0 = j r J 1 sm[27iA/(f - /(2)] ._ j p ^ sin 7i(x - ) ( 1 6 9 )
vk = v
I W y \ 2nAf(t - /(2/)) ( - * )
= 2 Aft U f ,
, , - , x(t)
= (170)
(1 69) (1 70),
, , , ^ 0,5( -)
, 1- , t - //(2/) (1 69) , /-, , , / - , , (1 71)
, -
A(t) = Jv\t) + v\t), (172)
0(0 = arccoor [v(0, v(0] (1 73)
arccoorfx ), - - , arctg, , -, arctg , //2, 0( = / + (, , - (1 72),
(0 = arccoor [v(0, v(0] (1 74)
-
, 37
. -, :
, - : , , -. - . . , , (1.75), (1.76), (1.72) (1.76).
, , . -, (1.69). , - , , , , . - . , - , , .
1.3.4.
, . , , . . : ; , . , - . - u(t) = Acos(aH( + ). - (-, ) . , , - -. , - . - . - , , , - ( , , ). - () -
(1.75)
(/ )= arccoor[/(0;?(01- (1.76)
-
38 1
, , . , , .
. , - , . - , . (), . , , , , - . , - . : - , , , - - .
, - .
(
Q(t)= |(7)+(7), ()
(/) : , Q(t) .
(t) = Q{t) -d /
, , ( - ). . -
u0(t) = ^(;)cos[co0/ + \|/(/)]. 0, /(/) = 0 , At
, : , - . : - .
, - , - . , , (AM), () () . - . , 4 , - ( 0, /2, /2).
-
, 39
. 1.15 2 ( ), 2 2 , ( - ). - ( ). , , , , - . -, , .
1 0 1 0 1 0
. 1.15. 2 (), 2 () 2 ()
, . -. , . 2. - , , , 0. 1. , , . , . - ; , , : 1 - 0, . . , /- . , , , , , -. , -. , - ; , - .
, . , - , . . , , - .
-
40 1
: - (), - . , - . -, , - . , ( ) . - , , /- . , ; - .
? , , - . - , .. - . . , : 0, , -. 1, - . . 4 - , , . 1.2. - .
1.2. 4
00 01 10
0 /2 - i t / 2
, , , , - , . - . . - , - : - . , , - .
- : (). , . , . , , ( . . 3).
-
2
2.1.
- , - , ( ), - , - - , - , , -, -, ,
, , , - , , - , , , - , - , , - , - , - ,
, , - , - , , , , , - , , , , -
-
42 1
2.1.1.
: -. - , . - . , . , , . - . , , . .
, . - . , , - , - . , - . . ( ) - . .
. , , - N . Q/,j = 1, 2,..., N. ? - , , , - : , , , - , .
. 1. N -
, (.. Q, = 1/N). -, , - .
2. N. , N .
3. , ( ). -, .
4. , , , ; -, - .
, , , .
-
43
, - .
,
(2.1) 7=1
> 0 , - . - , . = 1, 2,
(2.1)
,
H=-t,Qj iog 2 e , . 7-1
- .
, = 1 - . , . , .
, - . . Q\, Q2 = 1 - Q\. - Q\ . 2.1.
, . , .
,
= log N, (2.2) , N. , (2.1) = 0.
, - -. , , - , , . , , , , . , . Qn Qk , a QnJl . , (2.1),
a * = - a * a o g & + ] o g &,) = # , > 8 \ J
Qk,n > () , .
. 2.1.
-
44 1
/ ; , - , .
, QuJogQkln (2.3)
=+,. - (2.4) , , (2.4).
, / , < , (2-5)
, . . - , -.
(2.4), ,
-
45
, , ( ) , -, , Hf= .
, , - , . - . , -, , . -, , , - L = .
, . W;J, j ( 1 L), a i ( 1 ). , - Vr , , -
I 1
-, , - , . (2.9) , WJtl j ; , Tt ,
,= /7 | . (2.10)
2.2.
2.2.1.
(-) . , , - . . 2.2 . /, / . - , .
,
. 2.2.
-
46 1
, ,
, , - - , , , , , - , , , , , , - " , ,
, , ( ), , , , - , , / , - , , , , - , - , nv = *
(/) (,) -
, , , , , , , , , ( ), , , , , - ,
(2 11)
Bf = log , Bt = log 1
(2 12)
-
47
q
9 = (2-13)
, - , , - . , - , . - . . , , , .
, , . . (, -, ) 5,4 /. , . , , 10-15 . , 64 , 16 . , 6,3 , 39,4 /. , - 2,5 . -, . . , - .
, , ( ) . , - : , - . - , , - : , , . - , ( ).
, . - , . , , . - , -, - (). , - .
2.2.2.
. , , -
-
48 1
, - , - - , ( ) , - , , , - #*, , , - , , * - , , (/)
= max #,* (2 14)
, , , - ", , - N(T),
= (2 15) 7 J1
, , - ( )
- , > 0 , -, - , , - , > , , - , -
, , , , - , , , ( 2 1 3)
N - , , N
j-e V,N , ( ) j- /- V,Wj tN Qk
-
49
(-) (), - . -, , , - ( N),
= " . (26)
og (2.17)
M(N),
log M(N) = log = NH f . (2.18) Qk
, : , - * 1, 2 ' , , , . , - , - - .
, .. . , , , , , - ; , . - . - .
. , , , < , , . () , . , > , , - .
: , - , ,. , , , ,. , , , . - , . - .
-
50 1
2.3. .
2.3.1.
, . -, , - . - , - . -, .
, , - , , - , . , . #y/v ( ) / ( ). , - , , , , . , , , .. , , ; > 0.
, : = + = + 1,
, 1, h,y=H>-Hxly=Hy-Hylx=Iix. (2.19)
1, , , . , (2.19) , , . , - , , .. , - . (2.19) , , , . 1, . - (2.5), , , .
- , . 2.3. , . (?0)
, - j ^ ^ 1&.
-
/ / . - - .
. 2.3. , -
-
51
, - , , - , , - , - , , - , - /, . , - q=\-p , , ( ) - ( q) - log - q log q /
2.3.2.
- , - , - , , - (/,) (/) , - 1%{), N IK}{N),
I = im , / , = lim (2 20) / -QO / 7 ->00 /
, , , , , , , , ,
= /, (2 21)
R
, > R, - ( ) , ( ) < R, R
, 2 2 2 - , - S - g
-
52 1
S, . , , - t, , 1! 1/. , , , , .
, s.ylx 2 Zt*
S,
= 2
s,xly t,xly ,
2
. 2.4.
. 2.4 S. - HtJC/> = . - , - . g (MgK = 2 ) - S. , ( , . 2.4) , MgrJMSrX. - , (. . 2.4) .
= [1-/1]11). (2.22) ,
(1 +d)h= 1 + dh, dhMSJMS,X = 2T(R-Hlx + H,xly). - 1/ = . R 0. dh = 2~vT, v, dh - .
=\~ = 2~' 0, (2.23)
. - .
, - . , , , - . (1948), . - -, -
-
53
. - - ( ) - ( ).
- - , . , , - . , - .
2.4.
2.4.1.
, . ( , F) . No , , -. , . 1 . = NqF. , , , , -, . , - . , . - .
, . - . .
, F F0 = 2F. . FB = FL2 . z, - = + / t> . . z - DZ = N0FB = 0,5 . .
- - . , , ,
-
54 1
. - , . - . Dx = 0,5 . , Dy = 0,5(PQ + ).
, , , z 8.
00 00
, = " J{A()lg [8Px(u)]}du = - \px{u)\ogpx{u)du-\ogb. (2.24) 00 00
, (8 -> 0). , - . - - , , , .
1 z (2.24) -
00
= - J (") log /7 ()d - log 5. (2.25) -00
=}-1=-\{) log py(u)du + jp2 () log {u)du. (2.26) 00 -00
, 8, - , - , .
(2.26) , . -, , , -, ( ). (2.24), (2.25), - Hd ( 2 ). :
HJ= 1 %/22
JL1 22
log 1
/22
,2 du = 0,5 log(27ia2) + log ,
. ,
(2.26) , , , - , , :
/0 = 0,5 log [{ + )/],
= 2FI0 = Flog />c + /" J , (2.27)
, - .
-
55
2.4.2.
, - . - , - . /, . , , . / ( ) , - , No , -
h l = E J N 0 . (2.28) ,
, - . -, , , , - /6 , , ( - ) - . , - / 6 =1//, = 5 = PJI,. FK / , he - :
h l=P c / (N 0 F u ) = P c / P ^ (2.29) -
, -
= I,/F. (2.30)
/ .
(2.27), -
. , , - , / ,= . , = /^log[ 1 + PJN0F], log[ 1 + PcC/NFC\ = = CIF = . , = log(l + y/!g),
- 1 = (2.31)
,
() - . , (2.31) -, .
-
56 1
(2.31) he . 2.5. , . , .
- -, - .
, (2.31), h6 ->-1 ,59 . (2.32)
- . 2.5 .
- h6 [] = 3,01- 10 logy. (2.33)
, , - . , - GSM - - : h6 = 5 (- 10~5) = 0,675 //. ,
, 6 . 4 //, .. , , , . - , -, . - 1,5-2 .
, . 2.5 . , - ( = 2). , - -. . . - (. 4.3), h6 1,59 , , , - . , .
, //
. 2.5.
-
57
, . (). 56 /. - ( 0,3 3,4 ) 3,1 = 18 //. (2.31) / = 32,6 . / - 50 , - . , , - (- 2,4 /).
. 2.5, , 1. -; , - h^.
-
3.1.
3.1.1.
, - , . 3.1. -, , . . , . 3.1.
, y(f) 7(f) [
. 3 .1 .
-- , . , , ,
(3.1).
- 7 > 1 / S . (3.1) . 3.1
, - . , , , , , , . , , , .
, , - , -
-
59
. , , - , - y(t).
, -, j- m- s,{t). ; , s/ -, , , (). , , , . - , . , - , - . . S, = = S(\i,x,t), j = 1, 2,..., , % - , ( ) j , j-e . - . , , , , .
, , . , - , tk = tQ + kT, = . . . ,-1, 0, 1,.... - .
, y{t) ,
z{t) = y{t)+W)- (3.2) j , -
. , . , , ,
j ; , . , , , .
, :
- ; - , . ,
, -, t0, , . - , . , , -
-
60 1
z(t) -, .
, - z{t) , . , .
3.1.2.
.. XX . , , .. - - . - . . , , - , - . , - , , - . , - - , .
, , - . - ( ), , . , , - , . - , , , - - .
, . , , , - . - , - , - , . , , - . , , . , (. . 2), - .
-
61
-. . - , - , . - - , y(t) . , , ( ) . , (, -, -2 0 1 2), - , , ( - ). , , 2, . , , , 1- - , , , / - + /, . - , , , 1- . .
, - , .
, . , , , , , - , - , N0.
3.2.
3.2.1.
- , . , - - , .. tk = t0 + 3 tk+\ = t0 + ( + 1 )3, sk(t), m : S/t) = S(\x,x,t); j= 1,2,..., m .
, z(t), j, , - . () } (/'=1,2,..., ) , , , -, . z(t) .
-
62 4
() P(j) = 3{//z(f)}, - , z(t) - j- S/t) - 3{z(t)/j} , , j- , z{t). , ,() = z(t) - S/t) 1.2, - (1.55). ,
3{z(0 / ;} - W ^ O - S ^ t ) } = c e x p j - - ^ - J [ z ( 0 - s , ( 0 ] 2 d j - (3.2)
, j, . - -ro z(t):
3 {j,z(t)} = 3{;}3{z(0/y} = PjZm'J}-
: 3{; ,z(0} = 3{z(0}3{j/z(0} = 3 {z(t)}PaU). ,
PU) = gP?W/j} = gP,\, 0 = 1,2,...,), (33) g = 1/3 {z( ?)} , j
, j , (3.3) , , - . , :
- j (3 2) X/, (3.3) -;
- /, , -, (!) > Pn(j) j I.
- . -, , , g = 1 = 1, - , . j , ,
-, - , - (3.3) (3 2):
^ O ) = ln /> 7 +ln^ = /V 0 l n /> 7 + V (34) h+i 'k+i tk* l '*+l
v ; = - J [ z ( 0 - 5 y ( 0 ] 2 ^ = - j z2dt +2 ^zSfit- v, -ik it it it
-
63
, j. , ,
, = , = N0 In Pt - Et E} = J s * ( 0 d f j-ro . h 't
, , (3.4) ,
^ = 4 = , ~ - < 3 5 ) , ,
. , - , , - . . , , (- ), , } (3.5) j .
. , - , . . , . -. , , , . . , , , , - , -.
- - . . 3.2 - , . - Xf (3.5); z(t), . - . - tk tk4. .. . , , . , , - .
-
64 4
, - - - ; - EJ2 - eJ2. , -,
" . , -
-, , . , . 3.2 , -. . -
z(t) y(t) -
: y(t)= Jz(i)H(t - ) , H(t) . ,
I
0 , y{t) = J z(i)H(t - )1 . /-,
, Sj(t), :
( 0 = 5 - 0 , (3.6)
, Sj(t) , (, ,)- H(t)
. 3.2. -
y{tM)=']z(t)Sl(t-tk)At, (3.7)
;- . , , , - .
, . , , .. - , , - -. , . , , , . -
-
65
. ( ), . , 2 (. , 2 = , > 0, > 2, , .1 < 0, > < , 2 , - , .
3.2.2.
- . - ; - , - . - . .
, , . 3.2. ( , - , - .) / , . 3.2, . , -. - . -, , - .
. S\(t) S2(t), , 0 6. ( 3 = 5, .)
: , , , , , -. , , :
q(t) , . , -
(3.5), , :
z ( 0 = S , ( 0 + 0 , (3.8)
(3.9)
3 - 1339
-
66 4
= 2 ~ = j s , ( O S 2 ( O d ^ j ^ ) S 2 ( O d t - ^ = ^ - f + Q . (3.10) 1
\ J 7' U E 1 + E t - 2 y f E ^ r ) . (3.11) ^
, , ( ), 1.2. , -, (.. ) - 2, (1.54).
(t)~S2(t)]2dt = + 2 -2). (3.12) ^ 0 ^
= ^/ (3.11)
. (3.13)
, , , (3.11), .. ,
= 1
]1+2 - 2 ^ (3.14)
- . - . , , , . , , 1 /6 ( 5). . (3.14) , , , - ( , ).
-
67
(3.14), - . d st(i), s2(t), - ,
d = J J[,(0-(]2dt = ^ + -24~
(3.14)
= / \
d
(3.15)
(3.16)
. = 1, .. .
1 1 (3.17)
(3.17) , - ( ) , , . , AM AM -.
.... = 2 N
= (). (3.17)
(3.17) ; h] /. - , - , :
N. Nn /^
(3.18)
; /= 1/7 6 . , , , , . , 6 . 2 ( (2.28), (2.29)). / , . . , , . . 2 - , , , , - . (3.18) , , . / (. . 2),
3 !
-
68 4
. : - , - . , - /. /6 - , , , . , - / -, /6 , - , . , , , - , , , (3.18) . , - , , , .
AM = E/N0, 1 , 6.
: \ = 2 = . (3.14)
(3.19)
, - = -1, .. :
P=0(j2h6). (3.19) , . -
, , , .. 2.
(3.17) (3.19), , - , AM . , ( ) 3 .
, , (/ = 0) (- ). (3.19)
= - (3.196) ,
(2) ( ) - , , .. [rj 1. (3.17) (3.196) , 2 , AM - . , . , , AM . , , AM -, .
. 3.3 , - .
-
69
- 2 0 2 4 6 8 10 12 /), 1
10"1
-2
Iff*
10~*
-5
. 3.3. ,
3.2.3.
/- = 2, . , , , - . . , - = 6.
, - , . . -. , (3.15). - (3.16), , - . - , -, ; .
, , - , - . , . , 111 , . 110 100 - , . . , - (3.15), . , - , - . , - . , ,
-
70 4
. , , . - ( ) .
(k = 2) 4, - :
1 - 1 -> - (3.20) ^ ( 0 = /Icos^co0; + y J , 7 = 1,2,3,4.
(. 3.4). - . , - . , . 3.4 , - 45 . (3.15) - . *JPC / 2 .
, , - , - , - . = PJ2.
-. 4 - , , . 3.4 . - , , -, , . -, - , = 26. -
, 4 2, - 2 = PJ2. 2 ( - cos(o0^ sinco^) 3. - (, : , .) - 2, im (, ..) - . , D2 2 - >4 4: D2 = DJ2. -
. 3.4. 4
/ 4 =
d2N0 2
2 D4N0 . , 2 =
= V 4 2 -
4 2.
(3.21)
-
71
( ]
. 3.5. 4: ;
, -, 2, - 4. - . 3.5.
- 2. , , sin * cos oi(lt . - - 2 = 25. (). , . , - 2. () 7'6. , , 27 -. , ( 7 ) . , .
, - 4. , , - , , . - 2 , - , - . , , . 3.5, , - . , . 3.5 4. , .
4. , . 3.5, - , (3.19)
=(72//62) = 0 ( 7 2 / 0 . (3.22) (3.21).
, 4 2.
3.2.4.
, , . , - . ( ) .
-
72 4
, , , z(t) =~S\{t) + (0- (3.9) (3.10) , , , - Xj - pj. 0
X* = + i . (3-23)
Xj = , ; = 2, 3 , . . , . ^ -
: 2 =2 = ENB (.(3.12)). .
- ,
X, > \ j 2 . (3.24) , .. -
, -1
Jd -
/2. -0,5 Y -
(3.25)
Y = /. = log2, . , -
, 6 = /, wpwewi
= 1 - ^ = 1 - - ^ = } [ - 0 , 5 ( - ^ ) 2 ] [ 1 - ( ) ' 1 . (3.26)
. , , . 4 -, . , (3.26) (2.32), - , , .
3.3.
3.3.1.
-. , . , .s(H,X,0> . ).
-
73
. , ( j = 1, 2,..., ), -. ? , , , - . -
N = .
j=| . , , , ( z{t)). - , , - , .. , . .
. 3.6.
, (, = ), - . , , - , . 3.6. - j-Pi ( /= 1, 2, ..., , = 1, 2,..., ). Xzj - , . - (3.2). , , , -. , -
-
74 4
. . 3.6 . -, (3.2)
, . =
jz(t)Sjll(t)dt (3.27)
I (3.28)
- .
, , , - , . , (0, 2). , - , ; . .
, St(?) = As(t)cos[to0? + ,(t) + ], 0 , a A,(t) ,(?) j- . ,
s j (0 = Sjc ( c o s + Sjs ( 0 s i n > ( 3 -2 9)
SjC(t) = ?)8[0? + (|> (*)] (t) = -A (t)sin[to0? + ^(?)].
j- . (3.27)
Xltl =
(k j C + XlS sin|x) (3.30)
XjC = Jz(?),S,c(?)d? l j S =
j- - (3.30) :
2 ^ "I cos + \ j S sin ) d = + l j S 2 ) , 4 = i - J e x P
J (3.31)
Ig(x) . .
(3.31) . . , , , . 3.6 -. , . 3.6, , . 3.7.
- . 3.6 - .
-
75
. 3.7.
3.3.2. , . . - , , , . -, , .. . , (3.29) *1 , 2 -
- ( cos , + S ty (0 sin , ] [S r (0 cos 2 + S/s (t) sin 2 = 0. (3.32)
0 ,(0
A2(t)
t
, - .
. - , /0 = 0, a Aff,) . , (3.32), . - A/t) , , (. . 4) , . . 3.8 . , (. . 1). = 26 - : ; A2(t) - -, ,(0 .
. - (Aj(t) = A;J =1 ,2 , . . . , m), //) = (j - 1)Q/, Q . Q7, 2 , .
, , :
2(0 = (0+5(0 . (3-33) ) . ,
VJ = YJXJR2 + \/2.
. 3.8.
-
76 4
, .
7, , 7,
X ; = jz(0S, r (t)dt= (0SX. (t)dt + J^OS^ (t)df, (3,34a)
(3.346)
( C,jC C,jS -) - () (. (1.54)) 2 =-N0E. -, , ( 2) . ] 1, . - ^ 1, cos sin .
, Vj - (3.34) (3.346). , , {J 1),
Pj(x)- -
"22
(/' = 1)
) = - ' . |
2 + 2
22
(3.35)
(3.36)
, - . , , -, . ( ) (3.35) (3.36)
:
2 +2
22
2 + 2
22
I X - ^ dx d =
1- -22
-\
dy. (3.37)
, , , ,
1 { * =1-, = Z ( - l ) i C 1 ~ e x p | - - h 2 |, (3.38) + 1 +1
, , h2 = E/N0 . - (3.38) :
-
77
= | ( - 2 / 2 ) . (3.39)
, , : . , = 26, h\ = /2 / 2
= ^ - ^ 2 - (3-40)
, . . , , . - , 2, . - (3.19). , , - , . - , , . , , ..
(3-41)
(3.40) (3.41), -/ h6, , . h6 v, -. . 3.2. 2 (3.39) (3.196).
3.2.
^ - 1 3 10"2 -2 10"3 10"4 10"5 10"6
v, , 2 0,75 0,75 0,69 0,59 0,5 0,43 0,38
v, , 2 2,93 2,01 1,57 1,1 0,9 0,74 0,48
, - , , , - . - , .
, - (3.38) , ( . . 4).
-
4
4.1.
, , /, -. , , - 10"510~7 / (5/0) 6 - 8 , .. (), 6 - 8 . . , - E6/N0 1 - 1 . . , -/ .
- [4.1], 1948 . , , - , - . - . , . - . - , . (), - 1980- . - . , .
- , , ,
-
79
. , , - . - [4.2, 4.3].
. -. , , - , - . - , -, , -. ( , - ) , . ( .)
, , .
, , . - , , , , - . , ( - ) , , - , - .
. . - , , - . 3 . 3.1, . 4.1.
, , . - , -, , . (. . 3) - . :
- () ; - ; - .
(0 1), (0 1), .. . - . , - , -. . 8.
-
80 4
. . . () - , . - , , [4.2-4.6].
. 4.1.
- .
- {,} -
{bj}. 4.1. .
- . , - () - () (. 4.1).
. , , - , .
. S(t). -
S (/).
-
81
, . 06 , . , , 3.2 -
(4.1) . , - S*(t) (4.1) S(t), - .
, (4.1) - S,(t), 0 < i < qk - 1, q ; . , (4.1) S{t) S'{t), . (q = 2), ( 1). . , ( ). - .
. . 3.2, , . . - .
, , - . , (4.1) , . - .
, , , - , .
4.2.
, , , . - . ,
(4.1)
-
82 4
. , , . , - .
. v
, -. .
4.2.1. , . q . , ( 1), {q = 2).
- . , . -, > . , , . . (, ), , 2
. -. F*
: ( -) . , , q ; - . - 2 (mod 2).
(. 4.4) R = /,
dmm ( -) w(B) , - , , . ( ) dmm , - . () , - .
, - . - . ( , - .)
-
83
, dmm = d, / = d - 1 t = |_(/ - 1 ) / 2 J . (
|_xj .) , d = 3 - . , - ( ) dmm, .. - .
, - [4.2]. t (t = \_(d 1) / 2J ) . , , d ^ , .. - . - , .
4.2.2.
, , - . , - , . - . - -. , - 0 v . = v + 0 . . R = 1 - dCB. ( dCB 4.5.)
. - . 1 / . - ( ) - , i - 1 . /- ( ) - 1. -, , . R = 1/2, = 3, : G\(X) = 1 + X2 G2(X) = = 1 + X + X2, . 4.2. - G|() , - , . - 1, - 2 .
-
84 4
^ ^
10110 X X
. 4.2. () R=M2,v = 2viK=3
. 4.3.
= 1/2, v = 2 = 3
. 4.3. - , . - , -, 0 () . 0 = 1 0 = 2. - - . 0 , 1 . . 4.3 - () 0 3 -. . , , , - , . , () - - () - .
- 10110. - , - (1), - , (11). (0), , - (01). (1) , (00) .. , (10110) - - (1101001010).
- . 4.3 .
-
85
, , , -. , - .
. , , : , , - (), , ( , , ) . - 4.3-4.7.
4.3.
4.3.1.
- (., , 3.2). - . (w- ). , . w > (E6/N0 = 12) . - .
- = 2 , .. ( ) w- . w- . - w- 3.2. - . ( - .) , - - :
- , ;
- , - 1 (0) 0 (1). - w- (w - 1) . .
w- .
. w- (3.25). . w- , , - / ,
-
86 4
c l / z c ' , (4.2)
[ /. (4.2), , :
/ J.'yk-t I X / X ( 4 . 3 ) / -1
, , ,
(4.4) 2(-\)
(4.4), m- - :
2(-1)
1 1 /2 .
+ 2 dx (4.5)
m- . , 1, = 2, (4.5) -
( " \
= ' (4.6)
(4.5) . - E6/N0 - , [4.4], . 4.4.
. 4.4 , - E6/N0 . , 6 = 10~5 = 8 - 4 , = 64 6 . - - . , - , E6/N0 12 = -1,59. - E6/N0 = 12 (. . 2), .
EJN
. 4.4. // ( )
-
87
. - () . s,(t) Sj(t) -
= J S, ( X {t)d(t) = 0 i (4.7)
- . - .
( = 1, = 2) : 1 1
, = (4.8) ' 1 - 1
( = 2, = 4): 1 1 1
, , - ,
I - I I - I 1 1 - 1 - 1 1 - 1 - 1 1
(4.9)
-, |. , 2 -
( = 2)
, * .
* - .
(4.10)
, (4.8)(4.10), (). ,
(4.10) , . - log2 .
= 2 , 2~[ , 2 -
,
. (4.11)
= 3 (4.11)
,, , (4.12)
-
88 4
(4.12) 1- 5-, 2- 6- .. . = 2 -
. -2 -
= ^ 2 6
(4.13)
- w- > 8 - w- .
. = 2 ( ) - -, . (/2) - 1 , , , /2 -. :
(4.14) w - 1
, w = 2 .
, w , E6/N0 (- 1 )/ , . w , -: , - - . - w, w- , , -. , /2.
4.3.2.
, . w- - , .. , .
() w- (3.37). , , ( 4.11), (4.5) :
6 2 ( w - l ) '
(4.15)
-
89
= 2
^ = ^ e x p ( - e / ( 2 t f 0 ) ) . (4-16)
E6/N0 - /- . 4.5.
-2 0 2 4 6 8 10 12 //0,
( )
, , E6/N0 . E5/N0 .
10""5 = 16, 32 0,2 . E5/N0, - ~2-10~3, .
4.4.
- . , .. , - ( ) - , . , - . - , , .
-
90 4
4.4.1. - . - : , .
G , ( ) :
) , ;
) , ( + ) + = + ( + ), (ab)c = (), ;
) () . - , 0 - 0 + = + 0 = . , - 1 1 = \ = ;
) . , , -. , - + (-) = (-) + = 0 -, ~[ ~1 - = 1.
+ = + = , - . - . , , - .
R , . + , - , R , - :
) R ; ) 6 R , -
R\ ) , R () = (ab)c; ) , R
( + ) = + ( + ) = + , , .
= F , -
, , 0; , 0, 1. .
, q, , , q . q = , , a w , GF(iy). i = 1. - 0 - 1
-
91
mod . . i > 1 . GF() = [_2 ... b\ bQ _i]> , .
= [_, 6_2 b{ 0] () < 1, , - :
() = 6_i "~[ + 2 X"'2 + ... + 6, X + bo. (4.17)
() . , [6_2 ... b\ bQ ft_i],
(\) = ^"'[ + -"~2 + ... b,X2 + b0X+ -,, (4.18)
() X, .. (1)() - [] (X" - 1). ('\) - i
[- ()] (X" - 1), i = 0, 1,. . . , - 1. (4.19) (4.17)(4.19)
. () , -
: () = ' + . ~2 + ... + , X + 0, (4.20)
= [-\ ^2... \ 0] . (, ) , -
g(X) - , - X" - 1 :
g(A) = "~ + grl^X"-k-1 + ...glX + 1. (4.21)
-
92 4
g(X) .
, -. - (, ) . 4.2, = 7, 15, 31, 63 127. - [4.2].
, () g(X) - 1; (, ) -. qk () , , qk , - g(X).
('\) = Cb\X)g(X), (4.22)
i = 0, 1,..., qk. , (4.22) ,
- (). ()
\)={) + (" - 1) (4.23)
, X" - 1 () g(X) , [[,() g(X) , .. {)() :
B0)(A) = C(1)(A)g(A). (4.24) , (),
(4.22) g(X), (, ) .
= 7. - . 4.2, = 7 13, (7,4). 13 - 001 011.
g(X)=X} + + 1. (4.25) () ^- ( = 4)
, 0 0 11. , (4.20), () = X + 1.
() g(X), X4 + X3 + X2 + 1, - 0 0 1 1 1 0 1.
, g(X) X" - \ . , "1- 1
X" - \ = g(X) h(X). (4.26)
h(X) (4.26) , , (, ) - . h(X), - g(X) = X3 + X' + I, :
h(X) =* +2 +' + 1. (4.27)
-
93
4.2. ( )
t
-
94 4
, g(X) h(X) = X" - 1. h(X) ,
(, -) , g(X). , g(X) = + X' + 1, . 4.3.
4.3. (7, 4)
/ X1 X 6 X' -0
1 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 1 0 0 0 1 0 1 1
3 0 0 1 0 0 0 1 0 1 1 0
4 0 0 1 1 0 0 1 1 1 0 1
5 0 1 0 0 0 1 0 1 1 0 0
6 0 1 0 1 0 1 0 0 1 1 1
7 0 1 1 0 0 1 1 1 0 1 0
8 0 1 1 1 0 1 1 0 0 0 1
9 1 0 0 0 1 0 1 1 0 0 0
10 1 0 0 1 1 0 1 0 0 1 1
11 1 0 1 0 1 0 0 1 1 1 0
12 1 0 1 1 1 0 0 0 1 0 1
13 1 1 0 0 1 1 1 0 1 0 0
14 1 1 0 1 1 1 1 1 1 1 1
15 1 1 1 0 1 1 0 0 0 1 0 16 1 1 1 1 1 1 0 1 0 0 1
/;- - g(X). () : - 1. "~,
"~() = ^' + ^"'1 + .. + + "-. (4.28) (),
(). , - () , "~1 {) , - . "~ () g(X) -
+ (4.29) g(X) g(X)
Q(X) , () , , - . (4.29) aag(X),
X"kC(X) = Q(X)g(X) + r(X). (4.30) () 0 + \ + + ... + _ " . -
(4.24) (4.30) , Q(X)g(X) (, ) . , mod () ' (), - - (, ) .
-
95
(, ) - ( + 1, ) (-/, -) . , ,
( + 1, ) (, ) , , , . - , -, .
(-/, -) / . / , - , . (-/, -) 2 . - , - (, ) .
h(x) - , , , . h(x) -
(4.31) , , ,.
S S, ,. - -. S. , . , , .
4.4.3.
[4.2], - , . ( ), -. GF(p) - mod . , - X.
, .
. () = ck^\Xk~l + -2~ + ... + + ,+ , h(X) = hjC + + ... + h\X + h0.
C(X) h(X) = ck^hrXk+r~] + {ck-2 hr + ck-\ h^)Xk+r-2 + (c*_3 hr + c*_2 hr., + hr.2) x xXk+r~3 + ... + (0 i + clh0)X+ c0h0. . 4.6, .
(4.31)
-
96 4
a
. 4.6. : 1 , 6 2
( ) . (), - X. - ~\, h, - () ct_2, -\, . - 2 hr + - .2, _{, - . ck^hr + ... + --\ + Q-i hr_2. . , + - 1 ,,,..., 0 0 h0 - () h(X). , 0 .
, . 4.6, .
, 4_, - _\ hr. c w h0r, ... hr_ c H hr_{ + 2 hr. - hr_2 + -2 /_1 + q_3 hr ..
, . 4.6, , . . 4.7.
^) 2(), () = ,() h(X) + {)), (4.32)
h(X) = hrXr + - + , f(X) =frXr +fr-iXr~[ +/o-
-
97
,() = ,() h(X)+ 2() f(X)
h{X) uJ[X) . , - .
. () = X" + a_i "~' + . . + 0 g(^) = grXr + gr-\ Xr~l ... + go . 4.8. . , ( ), . - a/gr, - bi.
. 4.8. () ()
6, () 6, g(X), . () g(X), . () g(X) , - .
() = X + X + + 7+4 + 3++1 g(X) = X6 + X5 + X4 + X3 + 1 GF(2). . 4.9.
- X' X
2 X3 5 "^
. 4.9.
, , - . 4.4.
4 - 1339
-
98 4
4.4.
() g(X) X" Xw 0 0 X1 0 0 X* X3 0 X 1 X6 X5 X4 X3 0 0 1 X X X9 Xs 0 0 X5 0 0 0 0 0 ()
X9 Xs X1 0 X5 X* X3 0 X 1 X5 0 X3 0 0 1 X9 Xs X1 -6 0 0 X3 0 0 0
-6 X5 X* 0 0 X 1 -6 X5 X4 X3 0 0 1
X3 0 X 0
, . . 4.10.
I i
. 4.10.
, - . , (), - (). - (). () .. .
, , , .
4.4.4. - . - [4.2-4.8].
-
99
, . - - 2 * = 2'~1- \
-
100 4
(7,4), . 4.11, . , , , - 1 . - = 4 (0110), 1 - (), , , (0 0 1). 0 1 1 0 0 0 1.
, , , - , .. , - .
. 4.11, , , > (/2), -.
= 23, = 12 d=l.
g(X)=Xn +9 +1 +6 +5 ++ 1. (4.33) h(X) = +Xl0 + X1 + X4 + +2++ 1. (4.34) , ,
. , - . 4.11, . . 4.12 , - .
--
. 4.12.
. = 24, = 12 d = 8. . .
-- () - . .
t0< (/2) = 2 - 1, t0 mt0 .
- () ,() X2 ' - 1 :
gpO = HOK(m,(^) () ... m2,ri{X)\ (4.35) g(X) mt0.
-, (4.35), < 1023, . 9.1 [4.2], = 7, 15, 31, 63 127 . 4.2.
-
101
, -, 15, -, , , .. . , , , -.
- , . 4.11.
- () -. - PC- - {0,1,2, .. . ,
-
102 4
mod 2. ( GF(2) - .)
, , - 0, 8, 9 11. - , ,
0 flo = + + 1 1 0 - az + \ + al4 9 flo = + 9 + 1l3 11 a 0 = a 2 + + fli i (4.39) ,
(4.39) . , . , , (4.39), , , - . - .
4.4.5.
-, .. 4.1 /- . - - . = 20 , , 109 - .
: - . -, . - -, .
, - , - , .. , - (0 1), .. , , -.
, - , , [4.2-4.8]. , , - .
. - (5, 2). :
00000 01011 10101 11110.
-
103
, . - d ^ = 3, , , . . 4.6 . , , , , .
, , - 0 0 0 0 0 0 0. - . , 1 0.
4.6.
/
/ 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0
1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1
2 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0
3 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0
4 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0
5 1 0 0 0 0 1 1 0 11 0 0 1 0 1 0 1 1 1 0
6 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0
7 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0
, , , 0 0, G 1, 1 0 11. - < (15-20). , - , .. - .
. - _ _ . , _ v . . 4.7. - - . -, S S, , (4.31), ,.
- -. - - . (5, 2) . 4.7.
/
1 0 0 0 0 0 0 0 0
2 0 0 0 0 1 0 0 1
3 0 0 0 1 0 0 1 0
4 0 0 1 0 0 1 0 0
5 0 1 0 0 0 0 1 1
6 1 0 0 0 0 1 0 1
7 1 1 0 0 0 1 1 0
8 1 0 0 1 0 1 1 1
-
104 4
, , -, . 4.8, {) g(.X). (), , - , - , , -, . , - , .
. . -, . (15,7). = 5 . - . 4.13. = 15, - mod 2, () mod 2, . - (4.39), . . (-), (4.39). . , , , . > 2.
. 4.13. (15, 7)
,= {,\...}. . , , 0 14- . 2. - , . (0), 0 - 0 . , 14 \, 0 0. -, (0), ,
-
105
) . - = 15 . 15- - , .
, , . 3 3, 11, 12 14 (4.38), - -], 9 , , > 2 , , 7 9 ,0 . - 11 0, 2 , 12 4 14 5, - , ; . (3) 3, , 12 14 (4.38), , ( > 2) , 1, (3) .
. , , ( 0), - - 0 111 . , . , 1 1 1 1 . - , .
.
-. , - [4.8, 4.5]. - . - (23,12), - 3 . - - - 1.
[4.5] . 4.14. ,
. 4.10. , , , . , . , - ( , ) { ) , ( = 23) - ( ) . S0 ( ) . , (4.31). ( ) ..
-
106 4
- , = {0, . }- 1, 4 , 2 . 23 - , - ,. 4 .
() - , - . - , 12 , 16-, 17- . - . - , ( ) . , - t = 3 = , . > , , - . X, - . 2 2 , 2, 16- 17- - . , - (4.31) -, 16- 17- . - 2
coi < 2 2 < 2, , . , 24- . - 1(), , . , ( + ')- .
-
107
, (1) , . -. 1(). (-) , - = 12 . 1 , 2 , ; . - 2 .
- .
- , - . , , 2 , , 4096-23 , . - .
, , --, [4.5].
4.4.6. , (). - E5/N0, , .
, , , - , , .
^ = -/== 1 e-x'ndx =
-
108 4
(4.42) , -, , .
, , .
P o ^ v - i i Q P U l - P ^ r 1 . (4.43) /=/+1
% ~ ( 1 " - ^ )
(4.40)-(4.43), E6/N0, 6 . - E6/N0, , - , . . 4.15 .
- R , - . . 4.16 R 6 = 1(5.
, - ( R 0,6), - .
, -> R = 0,5. - .
, - . , (23, 12) - - (31,16), , - , . .
-
109
,
0,3 0,4 0,5 0,6 0,7 0,8 0,9 R
. 4.16. R
, . 4.15, 4.16, , , (10~5-1(7) (2-4) . - 5 . 1(2 , .. / - .
. - , - , 1 0. - , (-) .
. 4.15, 4.16, , -/ (E6/N0). , - . ( - , .)
, . . - - . , - [4.6] - :
6 7 ,//0, 10"
10^
-
^ I =2
1 - F 2\
Nn (4.44)
-1
. -
[4.4]. . 4.17 -
- .
VV \ N \ %
\ N %
1 \ \
% \ %
% % %
"-\ \ -
% %
I I \ \ \
t % \
\ |
% %
\ \ \ % %
1 \ 1 1 1 %
. 4.17. :
-
110 4
, 10 3 10~ / - 1 2 . , , 2,5 .
\ , . , -. , . - [4.10]. - .
, - i , [4.11]
P(i) = Cnp-(l-py. (4.45)
, - ( ) , ..
0 = V ' ' { ' fi OU /=(+1)/2 :(1-/7)" (4.46)
; = (2E6/N0 ). {AM) 1 (4.46) . -
. , (4.45) -
) = 1
/2! - ( * - )
2
2 (4.48)
, 0 1, 2 :
= -0,5; 2 =(\-). (4.49) ( (4.47)). 1 > 0,5. , -
(4.46), (4.48) (4.49), :
* = J(*)d * =
2-\ (4.50)
() [. 4.11] > 0,5
() = = (4.50) (4.41) (4.13), 2 / 2
6= 2-\
2 ~) = 1 4
Nn (4.51)
-
111
(4.51) (4.40) , , / - ( ) /2 , .. 2 , ( ), .. 2 , .
/. [4.12], E5/N0 -> :
= R(t +1); = Rd. (4.52) (4.52) , E6/N0 >
( 3 ) , .
4.5.
4.5.1. 4.2.2, . , - . , . . , - . .
g,(X) - , , R = kjna - dQB. R = 1/2, v = 2 = 3, : gi(X) = 1 + X2, G2(X) = 1 + X + X2 (. . 4.2). - (. . 4.3) , - , - - .
, , . , , . , . 4.2. . () . , , -, 100 , , - ( = 3) . - [4.13], - . - , 2~.
-
112 4
. 4 .18 . , , . 4 .3 . : 0 = (00) , 1 = ( 1 0 ) , 2 = (01 ) 3 = (11). . ( ) , - 0, , - 1.
. 4.18.
, ( = 3). , 0: 0 0, 00 , 1 1; 11. 1: 0 - 2 , 01 , 1 - 3, 10. 2: 0 0; 11, 1 1; 00. 3: 0 2; 10, 1 3; 01 .
(. . 4 .18 ) , 0 0 0 1 0 1 1 0 . , , . 4 .3 , 1 0 1 1 0 - 1 1 0 1 0 0 1 0 1 0 . , - - . , , , , - .
-
113
R = 1/2. - . R = 1 /. - - . - R = 1/3, = 3, g)(X) = 1, g2(X) = = 1 + X2 g3(X) = 1 + + 2 . 4.19.
, , g ( l )= 1 . - . 4.20.
, -: 0 = (00), 1 = (10), 2 = (01) 3 =(11). -. , , - , gi(X) = 1.
. 4.19.
= (00)
1 =(10)
2 = (01)
3 = (11)
000 000 000 000 000 000
3
. 4.20. R = 1/3
R = /,
-
114 4
, .. = 2/3. (. 4.21) - 0 1 X.
. 4.21.
R = !
. , , - . . , () - () -, . , , - - .
. (. 4.2), - d. ( - .) - . , - , , -, . , dCB ( ), - -. , , . 4.22 . 3 6 , , , -
-
115
dCh = 5. < 3 V * .
R = 1/3, = 3, gl(X) = l, g2(X)=l+X2 g3(X) = 1 + X + X2
3 , dCB = 6.
- 10 R = 1/2 R = 1/3. - . , - , dQB, . 4.8.
4.8.
R= 1/2
R=1I3 dCB
3 ft = 5 ft = 7
R=M2 5 ft = 5 ft = 7 ft = 7
R= 1/3 8
4 ft = 15 ft = 1 7
R= 1/2 6 ft = 13 ft= 15 ft = 1 7
= 1/3 10
5 ft = 2 3 ft = 35 = 1/2
7 ft = 2 5 ft = 33 ft = 37
R= 1/3 12
6 ft = 53 ft = 75
R= 1/2 8 ft = 4 7 ft = 53 ft = 75
R= 1/3 13
7 ft = 133 ft = 1 7 1
/?= 1/2 ft = 133 ft = 1 4 5 ft = 1 7 5
= 1/3 15
8 ft = 2 4 7 ft = 371 R= 1/2
ft = 2 2 5 ft = 331 ft = 367
= 1/3 16
9 ft = 561 ft = 753 R= 1/2 12
ft = 557 ft = 663 ft = 711
= 1/3 18
. , , ft = 23 = 10 011 = 4 + + .
, - - . -
\11
. 4.22.
-
116 4
, . [4.15], .
. - :
- [4.14]; - [4.15]; - [4.16]. ,
, [4.17]. - .
4.5.2.
(. . 4.18), . , , , - , - , - - . , ( ) -.
. 9 ( ) - . , , - R = 1/2, = 3, g\(X) = 1 + X2, g2(X) = 1 + X + X2. - , , . 4.23, -. - , , , . , () (0) (1) - . .
- ( ) - 00 00 00 00...00 , , 00 10 00 10 00 00...00. (. . 4.23, ) 0. 0 0 1. (00) 0 - 0, 1 2. . 4.23 - . 1 - 2 3. - (10) 1 2 2, 3 0, 0 0 1, 1 1. () , - (. . 4.23, ).
-
117
1 0 (00) (10) (00)
(00) (10) (00) (10) g (> (10> (00) (00)
(
-
118 4
. (00) - . . , 1 0 3 2 - 4. , , . , (. . 4.23, ). , . - . , , . , , . , , . 4.23, . , 0 -. , 0 , . , - . 11 .
(), () 11- . 0, - 0, . -, , , - . [4.15], - L = (5-9>). ( L .) , - , .
, - ( ) - 00 00 00 00.. .00 -, , 11 01 00 00 00...00. - , dCB = 5. . 4.24, -. - , 0. , - ( ) . 11 .
, , , . , - , 1 0 0 0 0 . . . 0 , . , : (1-3)/, .. . , , .. -. , (5-&), , , (5-8)/ .
, .
-
119
1 ) 0 1 (11) (01) (00)
(11) (01) (00) (00) 2 (11) (01) (00) (00) (00)
(10) (01) (00) (00) (00) (00) (00)
. 4.24.
-
120 4
. . :
- ; - ; - ; - ; - . ,
, . , - . , - . - - .
- - .
. - , , . - ( ), , - 2 . , [4.6], -, 0,5, - , - 0,25 - E6/N0 . 16 - 0,1 . , , 1 . 0,5, . - 8 16 . - .
- R = 1/2, -, gi(X) = 1 + X1, g2{X)= 1 + X + X -. 000 111 - 0 1. , 010 (2) 110 (6). (00), (01), (10) (11)
(00) 010+ 110= 1000, (01) 010 + 001 =0011, (10) 101 + 110= 1011, (11) 101 +001 =0110. -
2~1 - . - (. . 4.18), , . , -
-
121
, , - .
, - , . - , . , , , - , . , , .. - . .
. . (5-8) 2~{ . - . - , . , - , , , .
- .
, , - . - . , : gi = 171, g2 = 133, -7, R = 1/2 3/4. , - 2, -
-
122 4
2 3 4 5 6 7 ,//01 2 3 4 5 6 7 EJN
. 4.25. 6 // () ():
4.5.3.
- . - , [4.16] . , - >9. < 9, , - , - .
, , , . - . - , . - . - , , - , . , , - . , - .
, - ,
-
123
. - , . . - , , . , , . , , - . () , - . () , - . () , .
. 4.9 . 1 . , , , - Lk . - , - 3, , , . 4 5 - , Lk-X .
4.9.
1 Lk_x < + , Lk >
( )
2 > + , Lk < 3 , Lk < 4 < + , Lk 5 > + , Lk
> , , , . Lk_\ < , - , , , . 2. , Lk_{ > - , , - .
R = 1/2, = 2, v = 1, . 4.29. - . , ( - ) - 1 0 0 0 0... S = 01 01 00 01 00 00..., .. . , -, , . 4.26.
-
124 4
- 4
- 4 1 - 9
- 4 - 4
+ 1 +1 f
- 4 - 9
9 9 - 4
* - 4 +1
- 4
\J - 4 +1
* - 9 - 4
- 4
+1 m - 9
- 4 - 4
+1 - 9
, - 0,5, - 4,5. - - , , - [4.14] . -
- (4.55)
01 01 00 01 // ; .?/ -
, . , -
. - -
. 4.26.
(4.56)
, + 1 . , , . (4.55) - . , - , - .
. 4.10 . , - ( ) . , - . , - 5. d . . , - . - -10. , .
a-cf-1-, . , - . , - , .
-
125
4 .10 .
Lk
0 1 - 4 0 0 0 0 - 5 b - 5 1 - 4 - 5 d - 5 2 - 8 - 5 b - 5 1 - 4 - 5 - 5 1 - 4 - 5 / - 5 2 - 3 - 5 / - 5 3 - 2 - 5
- 5 4 - 6 - 5 1 - 5 3 - 2 - 5 f - 5 2 - 3 - 5 - 5 1 - 4 - 5 - 5 0 0 - 1 0
, - , - , . - , - - . , , , . . -, , , - .
. - . , - . , - .
. - - , , - . . . 4.27 = 41 R = 1/2 1/3 - = 9 7? = 1/2 1/3 .
, - ( >9) - , , 6 = 10 5 (7,5-8) ,
-
126 4
- (5-6) .
, 1 0 "
1 0 "
1 0 "
10"
I = ,
4- ! 1 1
-
\
= 1/2 9, = 1/3
' = 41, = 1/2 , = 41, = 1/3
"1I I I I
\ | ( , \ = 41,=1/2 | V = 41, = 1/3
- t ^ ^ r - ^ -1-
. 4.27.
4.6.
, . : ( ) , ; , - . , . - [4.19], () . .
4.6.1.
, -, . 4.28.
: , , -. g- {q = 2k) -. , TV .
-
127
. 4.28.
PC- (4.36). : - N = - 1 = 2*- 1, = 1, 2, 3,..., - 1; - = N- 2t; - dmm = N-K+ 1; - Rc = K/N; - t. PC- (4.37)
t = .
-, . , , .
. - . g- . - g- PC- N g- , , N . .
, , , - - - . N" = N , ' = , -
* = =Kk/ (N) . ( -
) /- - - /- . , 4.3, - /- , , - , - .
-
128 4
PC- . N' = Nn0 , = 10, R' = 1 = k0 /(N 0).
. - , . , , - .
4.6.2.
. , , . , 2 , - .
(. 4.3) - , , , .. , ( 1 ) . (.. ), . - . , , - 2, - < 10. . 4.29, - PC- R = 1/2 - (2,) .
. 4.29. : ? =1/2; ? =3/4 ;
-
129
. 4.29, , PC- R = 3/4.
: - = 1
= 5 E^/Nq = 2,7 , - 7 ;
- R = 3/4 (0,3-0,4) , R = 1/2.
- , (0,8-1,0) . - . - - - . - - . . 4.30 - - PC- (255, 239) = 7 aR = 1/3, 1/2, 3/4 7/8.
- = 1 R = 1/2, 3/4 7/8. - . . 4.30 :
- (R 0,47) 0 = - 5 - E6/N0 = {2,1-2,%) , 7 ;
- R ( = 1/3) - 0,5 , R = 3/4 1,2 , R = 7/8 1,5 .
, , , , , : - -, .
4.7.
() . 1993 . [4.20], , -
2 3 4 5 ,
. 4.30. (PC- + )
5 - 1339
-
130 4
. , - R = 1/2 - = 5 E6/N0 = 0,7 , (1,5-2) , - R 1/2. - .
: - (), -
; - (), (Turbo Product Code, ),
- .
, . .
4.7.1.
4.2.2 (. . 4.2) - R = 1/2, = 3, g\(X) = 2 + 1, g2(X) = 2 + + 1.
- , - ( ). = 4, g\(X) = = X3+X2 + l, g2(X) = X'+X - . 4.31.
- , [4.13], , -
E^/NQ - () , . - () - - .
. - ( ) - ( 3-5) . . 4.32.
R = 1/2. , - -. , . . , . , - , , -
. 4.31.
-
131
- -, , , .
- , . , - - - , - : , . R 1/3. R = 1/3 , ( , ). , - . , - 1/2. - , 4.5. , - R.
, -. - () dmm -. , , dmm , , -. , , , -, dmm, dc, (). , dcp , dmin - . -, d , , S(d), , , d < dQp.
, , - , - S(d). , S(d) , . [4.21] , , , -
/ 1 1 - 11 12 1 3
2
t . 4.32.
= 4
5*
-
132 4
S(d) - .
, - , , . - - , .
, , - , - . . 4.33.
. 4.33. ( )
- \ , \ , -, . - \ . - () . ( ) - . .
[4.22]. -, -, - , - . - - (Soft Input - Soft Output, SISO). , .. - . , , , - , -, .. - . -
-
133
. . -. , . 4.33, : . (Maximum A Posteriori, MAP), - .
- . . 4.34. , . 4.33 .
. 4.34.
- () . - . , - . Q , , - .
. - [4.20]. - - . = 5, R = 1/2 g t = 37 g2 - 21 ( 0 ) E6/N0 -. N = 256-256 = 65 536 - . 256-256. E6/N0 Q . 4.35.
, , E6/N0 > 0,5 .
Q = ~5 - 0,5 , >>(3-4) Q > (6 -8 ) (0,1 - 0,2) . 18 . 2 = 1 8 6 = 10 5 - E6/N0 = 0,7 , 4 , - = 7 .
-
134 4
1 0 "
10"
1 0 "
1 0 "
10"1
1 0 "
0,5 1,0 1,5 2,0 EJN, [4.20] , ( >5) Q = ( 1 - 2 ) - . 6= 10 "5 E6/N0 = 0,7 , = 5 Q = 18. = 4 6= - 5 E5/N0 = 0,9 . = 5 - . , - g, = 37 g2 = 21.
-
6 < (10 5-10 6). , . , N (4-5) -. . , - S(d), , , d < dcp. , d - dmm N. , - , .
NT
\ \ \ 4,2
\ \1 0 3
181 \ 3
. 4.35.
- V
4.7.2. () SISO - , . - , , ( ) R > 0,7.
--"i , -
[4.23]. - - . . (). - , . 4.36.
. 4.36. ,
-
135
, , - . - { { () (\- \) . . - 2 2 (2 - 2) . .
R = R{R2 = \2/(\2). : d = d\d2. - , , ( ) . , , - - .
.
. 4.11 . .
4.11. 7
-
136 4
= 462 0,6. - (31, 26). , , (27-28, 21-22) = (756, 462) R = 0,61.
: . - , , , . , .
. - , .
. , , - , - , . - , , . - .
, , - - ( ), .. SISO.
( - ) () L(a ).
: LLR (Log-Likelihood Ratio) ; L(a) ; Lc(x*) LLR (
); LL(a ) LLR, [4.20], Lc(x), Le(a) L(a) -
, -
L{a) = Lc(x) + Le{a) + L{a). (4.58) L ( a ) ,
, - . (4.58) . - .
1. LLR L(a). , L(a) = 0.
2. , (4.58), - LLR
Leh{a) = L{a) - Lc(x) - L{a). 3. L(a) = Leh(a).
-
137
4. , (4.58), - LLR
Lev(a ) = ) - Lc(x) - ). . . 5. ) = Lev(a) -
. 2-4 . 6.
: L(a') = Lc(x) + Leh(a) + Lev{a)q. 7. L{a ) . Le(a ) LLR. -
[+].
L ( a { ) [ + ] L ( a 2 ) = In l + e ^ V ^
(4.59) ) [+] = -)\ ) [+] 0 = 0. LLR Lc(xk) - , -
1 0 , .. L(a) = 0, - :
Lc(xk)= In ( I =
( | = -1) = 1
1 /21
/2i
-1
+\ \
(4.60)
-1 +] Xt. ,2
4= 1
= , (4.62)
-
138 4
mod 2. , - , 3 4 { 4 24 = I 10 0 1 1 1 1 1. - + 1 + 1 - 1 - 1 + 1 + 1 + 1 + 1. , - {*,}, {*,} = 0,75 0,05 0,10 0,15 1,25 1,0 3,0 0,5.
(4.61), {,}, {xj} (LLR) -. . 4.13.
4.13.
Lc(x,)=l,5 Lc(x2) = 0,1 LC(X12) = 2,5 -(*) = 0,2 Ux4) = 0,3 Z,c(x34) = 2,0 Lc(x 13) = 6,0 Lc(*24)= 1,0
- , /,( ) Lev(a) , L(a )
L{a) = Lc(x) + Leh{a) + Ley(a). (4.63) , , . 4.13,
:
,*) = Lc(x,) + ,) + Le(a,') = Lc(x.) + L(a,) + {[Lc(Xj) + ,)] [+] Lc(xy)}, (4.64) Lc(Xj), L(cij) () LLR , , , - (4.63), (4.64), ,
LEH{A,*) = {[Lc(x2) + L(A2)] [+] Lc(xn)}
Lev(a') = {[Lc(x3) + )} [+] Lc(x13)} Leh(a2') = {[Lc(x.) +L(a,)] [+] Lc(x12)} LJci2') = {[Lc(x4) + L(a4)] [+] Lc(x24)} (4.65) Leh(a}') = {[Lc(x4) + L(a4)] [+] Lc(x34)}
= {[ic^O + i(a.)] [+] U*.)} M i , ' ) = { [ L c f e ) + 3)] [+] Lc(xi4)} LJ.04) = {[Lc(x2) + 2)] [+] Lc(x24)}.
, ,) = 0, = 1 0 . 4.13 Lc(x,) ,
Leh(a*) = (0,1 - 0) [+] 2,5 -0 ,1 {) Leh(a2) = (1,5 - 0) [+] 2,5 -1,5 2) (4.66) Leh(a^) = (0,3 - 0) [+] 2,0 -0 ,3 ) Leh(a4*) = (0,2 - 0) [+] 2,0 -0 ,2 ). L(a,) .
-
139
Leia|*) = (0,2 - 0,3) [+] 6,0 0,1 L(a,) LJ,a2") = (0,3 - 0,2) [+] 1,0 - 0 , 1 2) (4.67) * ) = (1,5 -0 ,1 ) [+] 6,0 1,4 L(a3) / ) = (0,1 1,5) [+] 1,0 0,60 L(aA). L(a,)
. .
, . (. . 4.13): !(*,) 1,5 i c (*2) -0 , l Lc(x3) 0,2 Lc(x 4 ) 0,3. : Leh(ai)~~0,l Leh(a2)*>-1,5 Leh(a) -0 ,3 Leh(aA) -0,2. : Lcv(a,) 0,1 / , (2)-0,1 ) 1,4 (4) 1,0. LLR, ,
( Lev(a,)) , .
, -. (4.66), (4.67) - Leh{a*)\
M a , * ) = (0 ,1- 0,1) [+] 2,5 0 Leh(a2) = (1,5 - 0,1) [+] 2,5 -1 ,6 Ld(fl3*) = (0,3-1,0) [+] 2,0 - 1 , 3 Leh(a4) = (0,2 - 1,4) [+] 2,0 1,2. Leh{at )
LJ^a,): = (0,2 - 1,3) [+] 6,0 1,1
= (0,3 - 1,2) [+] 1,0 - 1 , 0 L^as ' ) = (1 ,5 -0 ) [+] 6,0 - 1 , 5 M a / ) = (0,1-1,6) [+] 1,0*1,0. (4.64) L(a,) -
, : (,) 2,6 Lc(X2) -2,5 ) ~ -2,6 Lc(x4) 2,5. : ci\ = 1; 2 = 0; = 0; 4 = 1. . -
- . - .
-
5 -
5.1. -
5.1.1.
() 1.3. - - D. , . -.
. > 2 (). , , , - . , (AM), () - () . - . , , - ( ), . 7.
(-) ; - . , - - , . , : - I ; I - , . , ( . . 9). - -, .
, , , - .
-
- 141
, /= 1 /3 . , .. 90, - . . - , , . , . , / = 1 /3 2 3. -, , . , - . , /= v/T3, v , m = 2v - 3. , m - .
. 4, - . , - , . , m = 4 , 4, , - , . , m - , , m -> , . -, . 4 , , , .
3, , , = 1 /3, . - , .. 3 - m , , -, k = log2m . , -, D = . > /2, . , - /2, , . - .
- . / 6 3.2. . , , , . 2.4. , , .. .
-
142 4
, h6 . , -, , , , - .
- . - , . , 3 ( ). , -. .
/n- - - . , . 3. - . s,(t) s/t) , - . (3.16)
= ^ / 1 ^ ) , (5.1.)
(5.2)
i j. . 5.1 -
du . ,
. - d0.
, - . - , -
. 5.1. = M < I > ( d J j 2 N ~ , ) . (5.3)
, , - . -, , . (5.3) . , , () , , d0 . -, , ,
-
- 143
. = 1, - . , () - (). , () . .
. - , . ( ), , - d0 1 .
^* (5.4) , ~ 0,5 > (5*5)
.
, - , , (5.4), .
/
_ log, (2m) , ^ 2log, (2m) D = ^ = / ^ > 2 . (5.6) m
m = 2 D - 2/ (5.7)
4. 4 ,
, , (. . 4). - - , . 5.2.
. 5.2.
-, . , , , , - ( ) ( ).
, , - 7 R = 1/2, 4.5. :
-
144 4
- 0 =RD = 0,5D = Af ; (5.8)
-
= 7 = 1 > (5-9) /
- /, - = -5:
= /^ = 2,95 = 4,6 , (5.10) , .
, , , , (5.7). - . - (. , (3.10)), 0 1.
5.1.2. - = 2, . -, . , - .
: - (); -
. 5