I H C TN KHOA I N-
C TH NG I NT
L THUY T THNG TINThS. nh Thu n
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Chng 3: M ho knh truy n3.1 Khi ni m v m pht hi n v s a sai C ch
pht hi n sai Kh nng pht hi n v s a sai Phng trnh ng truy n Vector
sai C ch s a sai 3.2 M kh i tuy n tnh nh ngha Phng php t o m Phng
php gi i mDinh-Thuan Do 402021 - Ly thuyet thong tin 2
Chng 3: M ho knh truy n3.3 M Hamming 3.4 M vng Khi ni m Thi t l
p m vng Ma tr n sinh v ma tr n ki m tra S m ho
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Khi ni m v m pht hi n v s a saiD ng sai l m c a m hi u c truy n
ty thu c tnh ch t th ng k c a knh: Sai c l p d n n sai l m ng u
nhin: 1 ho c 2 sai Sai tng quan d n n sai chm Xc su t xu t hi n m t
t m n k t c t sai b t k
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Khi ni m v m pht hi n v s a saiC ch pht hi n sai c a m hi u: S t
m c th c: N0=2n S t m mang tin: N=2k S t m khng dng n 2n-2k m ch c
th pht hi n i l i th ph i th a mn i u ki n
trong
l t p h p vector sai 1,2,,i l iDinh-Thuan Do 402021 - Ly thuyet
thong tin 5
Khi ni m v m pht hi n v s a saiC ch pht hi n sai c a m hi u: c
th s a sai 1 l i
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Khi ni m v m pht hi n v s a saiC ch pht hi n sai c a m hi u: VD
1: Chu i tn hi u sai 1 bit
VD 2: Chu i sai c m bit
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Khi ni m v m pht hi n v s a saiC ch pht hi n sai c a m hi u: C u
trc b m ha/gi i m
Chu i sai c m bit
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Khi ni m v m pht hi n v s a saiKh nng pht hi n v s a sai: Tr ng
s Hamming c a vactor t k t , w(t) c xc theo s cc thnh ph n khc khng
c a vector VD: nh
Kho ng cch gi a 2 vector t1, t2, k hi u d(t1,t2) c ngha l s cc
thnh ph n khc nhau gi a chng VD:
nh
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Khi ni m v m pht hi n v s a saiKh nng pht hi n v s a sai: Kho ng
cch Hamming gi a 2 vector m t1, t2 b ng tr ng s c a vector t ng
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Khi ni m v m pht hi n v s a saiKh nng pht hi n v s a sai: V d :
ta tm kho ng cch Hamming gi a 2 t m 1. Kho ng cch Hamming d(000,
011) l 2 v
2. Kho ng cch Hamming d(10101, 11110) l 3 v
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Khi ni m v m pht hi n v s a saiKh nng pht hi n v s a sai: V d 2:
ta tm kho ng cch Hamming t i thi u cho b ng sau
2. Kho ng cch Hamming d(10101, 11110) l 3 v
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Khi ni m v m pht hi n v s a saiKh nng pht hi n v s a sai: V d 2:
ta tm kho ng cch Hamming t i thi u cho b ng sau Tm t t c cc kho ng
cch Hamming
Suy ra dmin=3
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M kh i tuy n tnhTrong m kh i, ta chia b n tin thnh cc kh i, m i
kh i di k bit, g i l datwords. Chng ta thm r bit vo m i kh i t o ra
kh i c di n= k+r. K t qu l ta c kh i n bit, g i l t m
(codeword)
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M kh i tuy n tnhC ch pht hi n l i trong m kh i
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M kh i tuy n tnhC ch pht hi n l i trong m kh i V d : ta c m c u
trc k = 2 v n = 3. B ng sau li t k cc dataword v codeword. Sau ,
chng ta s suy ra codeword t dataword.
Gi s my pht m ha dataword 01 thnh 011 v g i my thu. Xem xt cc tr
ng h p sauDinh-Thuan Do 402021 - Ly thuyet thong tin
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M kh i tuy n tnhC ch pht hi n l i trong m kh i V d (tt): 1. My
thu nh n 011, l codeword h p l . My thu tch 01 ra t chu i thu c 2.
Codeword b l i trong qu trnh truy n, v thu 111. y l codeword khng h
p l v b lo i b 3. Codeword b l i trong qu trnh truy n, v thu 000. y
l codeword h p l v my thu tch ra tn hi u sai l 00.
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M vngM vng l m kh i tuy n tnh c bi t. Trong m vng, n u m t
codeword b d ch vng (xoay), k t qu ta s c codeword khc
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M vngHo t ng c a b m ha/gi i m vng
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M vngBi u di n d ng a th c cho m nh phn
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M vngV d :
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M vngCc m CRC chu n:
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