, , ( ) . , , (data compression). - (frequency-dependent encoding), . ֳ () (variable-length codes), , , Unicode, 16- . -- , - (Huffman codes).
: , ( ) .
3.2 г
г . : , N = 6 1...6 0,3; 0,2; 0,2; 0,15; 0,1; 0,05. ̳ :
K.. (A, 2) ³ log2 N,
N - .
K (A, 2)..min ³ log26 ≈ 2,58 Þ K. (A, 2).. = 3. 3.1.
Q(A,2):
Q(A,2) = (K (A, 2) × I(B)) / I(A) 1, | (3.1) |
I(A) A:
I(A) = - å pi log2 pi, ,
pi = ni / n i - , ni i- , n .
:
I(A) = - (0,3 × log20,3 + 0,2 × log20,2 + 0,2 × log20,2 +0,15 × log20,15 + 0,1 ´ log20,1+ 0,05 × log20,05) ≈ 2,409 .
I(B) - B. , :
I(2) = - å pi log2 pi = - (p 0log2 p 0 + p 1log2 p 1), , | (3.2) |
p 0 0 , p 0 = m 0/ m,
p 1 1 , p 1 = 1 - p 0,
m 0 0 ,
m .
m 0 m , p 0 :
p 0 = å (pi × p (i)0) = å (pi × (k (i)0 / k (i))), | (3.3) |
i = 1..N,
pi i - ,
p (i)0 0 i - ,
|
|
k (i) i - ,
k (i)0 0 i - .
3.1 , :
p 0 .. = 0,3 × 3/3 + 0,2 × 2/3 + 0,2 × 2/3 + 0,15 × 1/3 + 0,1 × 2/3 + 0,05 × 1/3 = 0,7.
, (3.2), I(2) .. = - (p 0 .. × log2 p 0 .. + (1 - p 0 ..) × log2 (1 - p 0 ..)) = = - (0,7 × log20,7 + 0,3 × log20,3) ≈ 0,881 .
(3.1) : Q(A,2) .. = (K (A, 2) .. × I(2) .. ) / I(A) 1 =
= 3 × 0,881 / 2,409 1 ≈ 0,101.
3.3 .
( ): , () - .
, . , , .
. . , , , , .
3.1. . 1, ' ( 5 6) (, (1)); , , 0,15. . , , 1 , . , ; , N - 2, N - ( N = 6, , 4 ). .
. 0 1 ( ; , 0, - 1). a 1(4) (4), 0,6, 0, a a 2(4) 0,4 - 1. (3) a 1(3) a 2(4) 0,4 (1); a 2(3) a 3(3), a 1(4) 0,6, : ( 0), - - 0, 1. , a 2(3) 00, a 3(3) - 01. 3.1, 3.2:
3.1
3.2
|
|
, .
:
K (,2)= å (pi × k (i)),
i = 1..N,
pi i- ,
k (i) i- .
:
K (,2).. = 0,3 × 2 + 0,2 × 2 + 0,2 × 2 +0,15 × 3 + 0,1 × 4 + 0,05 × 4 = 2,45.
(3.3) p 0 .. = å (pi × (k (i)0/ k (i))) = 0,3 × 2/2 + 0,2 × 1/2 + 0,2 × 0/2 + 0,15 × × 2/3 + 0,1 × 2/4 + 0,05 × 1/4 = 0,563.
p 1 = 1 - p 0 = 1 - 0,563 = 0,437.
. (3.2) :
I(2) ... = - (p 0 .. log2 p 0 .. + (1 - p 0 . log2 (1 - p 0 ..) = - (0,563 ×
× log20,563 + 0,437 × log20,437) ≈ 0,988 .
³ (3.1) :
Q(A,2) .. = (K (A, 2).. × I(2) .. ) / I(A) 1 = 2,45 × 0,988 / 2,409 1 ≈ 0,005.
3.2. , , , 1) 12% I(2) p 0 p 1, 2) 22% , 3) 20 .
3.1 3.1
A | ³ i | г | |
1 | 0,3 | ||
2 | 0,2 | ||
3 | 0,2 | ||
4 | 0,15 | ||
5 | 0,1 | ||
6 | 0,05 |
3.2
I(A) | p 0 | p 1 | I(2) | K(A,2) | Q(A,2) | |
г | 2,409 | 0,7 | 0,3 | 0,881 | 0,101 | |
2,409 | 0,563 | 0,437 | 0,988 | 2,45 | 0,005 |