TOM TAT BAI GIANG MON: LY THUYET THONG TIN
TOM TAT BAI GIANG
LY THUYET THONG TIN
CHNG 1: TIN TC
1-1 HE THONG TRUYEN TIN (HT3)
Nguon tin:
+ La tap hp cac tin HT3 dung e lap cac ban tin khac nhau trong s truyen.
+ Nguon tin c mo hnh hoa toan hoc bang bon qua trnh sau:
Qua trnh ngau nhien lien tuc.
Qua trnh ngau nhien ri rac.
Day ngau nhien lien tuc.
Day ngau nhien ri rac.
Kenh tin: la ni dien ra s truyen lan cua tn hieu mang tin va chu tac ong cua nhieu.
S0(t) = Nm Si(t) + Na(t)
+ Si(t): Tn hieu vao & S0(t): tn hieu ra cua kenh tin
+ Nm (t), Na(t) : ac trng cho nhieu nhan, nhieu cong.
Nhan tin: la au cuoi cua HT3 lam nhiem vu khoi phuc tin tc ban au.
He thong truyen tin so (ri rac)
Hai van e c ban cua he thong truyen tin:
+ Van e hieu suat, noi cach khac la toc o truyen tin cua he thong.
+ Van e o chnh xac, noi cach khac la kha nang chong nhieu cua he thong.
1-2 SO O THONG TIN
a. Lng o tin tc: Nguon A co m tn hieu ang xac xuat, mot tin do nguon A hnh thanh la mot day n ky hieu ai bat ky (ai ( A).
Lng tin cha trong mot ai bat ky:
I(ai)=logm
(1)
Lng tin cha trong mot day x gom n ky hieu:
I(x) = n.log m
(2)
n v lng o thong tin thng c chon la c so 2.
Khi m ky hieu cua nguon tin co xac xuat khac nhau va khong oc lap thong ke vi nhau th
I(xi) = log (1/p(ai)) (3)
Lng tr rieng:
I(xi) = -log p(xi) (4)
La lng tin ban au c xac nh bang xac xuat tien nghiem.
Lng tin con lai cua xi sau khi a nhan c yj c xac nh bang xac xuat hau nghiem.
(5)
Lng tin tng ho:
(6)
ac tnh cua lng tin:
+ I(xi) ( I(xi ; yi)
(7)
+ I(xi) ( 0
(8)
+ I(xi.yi) = I(xi) + I(yi) - I(xi; yi)
(9)
Khi cap xi, yj oc lap thong ke vi nhau th I(xi; yi) = 0
Ta co: I(xi; yi) = I(xi) + I(yi)
(10)
Lng tin trung bnh: la lng tin tc trung bnh cha trong m ky hieu bat ky cua nguon a cho.
(11)
Lng tin tng ho trung bnh:
(12)
Lng tin rieng trung bnh co ieu kien:
(13)
b. Entropi nguon ri rac: la mot thong so thong ke c ban cua nguon. Ve y ngha vat ly o bat ng va lng thong tin trai ngc nhau, nhng ve so o chung bang nhau:
(1)
ac tnh cua Entropi H(X):
+ H(X) ( 0
+ H(X) = 0 khi nguon tin ch co mot ky hieu
+ H(X)max khi xac suat xuat hien cac ky hieu cua nguon bang nhau.
Entropi ong thi: la o bat nh trung bnh cua mot cap (x,y) bat ky trong tch XY.
(2)
Entropi co ieu kien:
(3)
1-3 THONG LNG CUA KENH THONG TIN:
Toc o thiet lap tin cua nguon:
R= n0.H(X) (bps)(1)
+ H(X); entropi cua nguon.
+ n0 : so ky hieu c lap trong mot n v thi gian
Thong lng cua kenh C la lng thong tin toi a kenh cho qua i trong mot n v thi gian ma khong gay sai nham. C(bps)
Thong thng R < C, e R tien ti gan C ta dung phep ma hoa thong ke toi u e tang Entropi.
a. Thong lng kenh ri rac khong nhieu:
C = Rmax = n0. H(X)max (bps)
(2)
o d cua nguon:
(3)
Dung phng phap ma hoa toi u e giam o d cua nguon en khong hoac s dung o d cua nguon e xay dng ma hieu chong nhieu.
b. Thong lng kenh ri rac co nhieu:
R = noI(X;Y) = n0[H(X)-H(X/Y)] (bps) (4)
Toc o lap tin cc ai trong kenh co nhieu:
C = Rmax = n0[H(X)-H(X/Y)]max (bps) (5)
CHNG 2: MA HOA NGUON TIN
2-1. MA HIEU
2-1-1 Ma hieu va cac thong so c ban cua ma hieu:
C so cua ma (m) la so cac ky hieu khac nhau trong bang ch cua ma. oi vi ma nh phan m= 2.
o dai cua ma n la so ky hieu trong mot t ma. Nen o dai cac t ma nh nhau ta goi la ma eu, ngc lai la ma khong eu.
o dai trung bnh cua bo ma:
(1)
+ p(xi): xac suat xuat hien tin xi cua nguon X c ma hoa.
+ ni : o dai t ma tng ng vi tin xi.
+ N: Tong so t ma tng ng vi tong so cac tin cua xi Tong hop cac to hp ma co the co c: N0=2n., neu:
+ N
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