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Giao trinh ly thuyet thong tin

Giao trinh ly thuyet thong tin - www.tech.com.vn Gio trnh L...

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Giáo trình: Lý thuy ế t thông tin. M C L C GI I THI U T NG QUAN ............................................................................................................. 6 1. M C Đ ÍCH ........................................................................................................................... 6 2. YÊU C U ............................................................................................................................. 6 3. N I DUNG C T LÕI ........................................................................................................... 7 4. K T TH C TIÊN QUY T .................................................................................................. 7 5. TÀI LI U THAM KH O ..................................................................................................... 8 6. PH ƯƠ NG PHÁP H C T P ................................................................................................. 8 CH ƯƠ NG 1: GI I THI U ............................................................................................................... 9 1. M c tiêu ................................................................................................................................. 9 2. Đố i t ượ ng nghiên c u ............................................................................................................ 9 3. Mô hình lý thuy ế t thông tin theo quan đ i m Shannon ........................................................ 10 4. L ượ ng tin bi ế t và ch ư a bi ế t ................................................................................................. 10 5. Ví d v l ượ ng tin bi ế t và ch ư a bi ế t .................................................................................... 10 6. Đị nh lý c ơ s c a k thu t truy n tin .................................................................................. 11 7. Mô t tr ng thái truy n tin có nhi u .................................................................................... 11 8. Minh h a k thu t gi m nhi u ............................................................................................. 12 9. Chi phí ph i tr cho k thu t gi m nhi u ............................................................................ 13 10. Khái ni m v dung l ượ ng kênh truy n ............................................................................ 13 11. V n đề sinh mã ................................................................................................................ 13 12. V n đề gi i mã ................................................................................................................. 13 CH ƯƠ NG 2: ĐỘ Đ O L ƯỢ NG TIN ............................................................................................... 15 BÀI 2.1: ENTROPY ....................................................................................................................... 15 1. M c tiêu ............................................................................................................................... 15 2. Ví d v entropy .................................................................................................................. 15 3. Nh n xét v độ đ o l ượ ng tin ................................................................................................ 15 4. Khái ni m entropy ............................................................................................................... 16 5. Entropy c a m t s ki n ...................................................................................................... 16 6. Entropy c a m t phân ph i ................................................................................................. 16 7. Đị nh lý d ng gi i tích c a Entropy ...................................................................................... 16 8. Ví d minh h a .................................................................................................................... 17 9. Bài toán v cây tìm ki ế m nh phân- Đặ t v n đề ................................................................... 17 10. Bài toán v cây tìm ki ế m nh phân - Di n gi i ................................................................ 17 11. Bài t p ............................................................................................................................. 18 BÀI 2.2: CÁC TÍNH CH T C A ENTROPY ............................................................................. 19 1. M c tiêu: ............................................................................................................................. 19 2. Các tính ch t c ơ b n c a Entropy ........................................................................................ 19 3. Minh h a tính ch t 1 và 2 .................................................................................................... 19 4. Minh h a tính ch t 3 và 4 .................................................................................................... 19 5. Đị nh lý c c đạ i c a entropy ................................................................................................ 20 6. Ch ng minh đị nh lý c c đạ i c a Entropy ............................................................................ 20 7. Bài t p ................................................................................................................................. 21 BÀI 2.3: ENTROPY C A NHI U BI N ..................................................................................... 22 1. M c tiêu ............................................................................................................................... 22 2. Đị nh ngh ĩ a Entropy c a nhi u bi ế n ..................................................................................... 22 3. Ví d Entropy c a nhi u bi ế n .............................................................................................. 22 4. Đị nh ngh ĩ a Entropy có đ i u ki n ......................................................................................... 22 Biên so n: TS. L ê Quy ế t Th ng, ThS. Phan T n Tài & Ks. D ươ ng V ă n Hi ế u. 1 www.tech.com.vn
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Giáo trình: Lý thuy ế t thông tin. 5. Ví d Entropy có đ i u ki n ................................................................................................. 23 6. Quan h gi a H(X,Y) v i H(X) và H(Y) khi X, Y độ c l p ................................................. 23 7. Quan h gi a H(X,Y) v i H(X) và H(Y) khi X, Y t ươ ng quan .......................................... 24 8. Bài t p ................................................................................................................................. 25 BÀI 2.4: MINH H A CÁC ENTROPY ........................................................................................ 26 1. M c tiêu ............................................................................................................................... 26 2. Yêu c u c a bài toán ........................................................................................................... 26 3. Xác đị nh các phân ph i ng u nhiên c a bài toán ................................................................ 26 4. Minh h a Entropy H(X), H(Y) và H(X,Y) .......................................................................... 27 5. Minh h a Entropy H(X/Y) và H(Y/X) ................................................................................ 27 6. Minh h a quan h gi a các Entropy .................................................................................... 27 BAI 2.5: Đ O L ƯỢ NG TIN (MESURE OF INFORMATION) ...................................................... 28 1. M c tiêu ............................................................................................................................... 28 2. Đặ t v n đề bài toán .............................................................................................................. 28 3. Xác đị nh các phân ph i c a bài toán ................................................................................... 28 4. Nh n xét d a theo entropy .................................................................................................. 28 5. Đị nh ngh ĩ a l ượ ng tin ........................................................................................................... 29 6. Bài t p ................................................................................................................................. 29 CH ƯƠ NG 3: SINH MÃ TÁCH ĐƯỢ C (Decypherable Coding) ................................................... 31 BÀI 3.1: KHÁI NI M V MÃ TÁCH ĐƯỢ C .............................................................................. 31 1. M c tiêu ...............................................................................................................................
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