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