AN2121 Freescale Semiconductor / Motorola, AN2121 Datasheet - Page 11

• Manufacturer Part Number: AN2121
• Description: JPEG2000 Arithmetic Encoding on StarCore SC140
• Manufacturer: Freescale Semiconductor / Motorola

In binary fraction format,
For the first symbol in the example,
In binary fraction format,
Thus, the ’
Figure 4.
The procedure for mapping the rest of the symbols in the sequence
Binary fractional representations are included to show how a code word is derived in a practical
application.
For sequence
In binary fraction format,
For sequence
In binary fraction format,
For sequence
3. Update the interval, A, using the equation
4. Repeat steps 2 and 3 until the entire symbol sequence is mapped to an interval.
C
A
A
C
A
C
A
C
A
C
A
C
1
2
2
3
3
4
1
1
2
2
3
3
c
=
= 0.01 + 0.001 = 0.011
= C
= 0.011 + 0.0111 = 0.1101
= C
= 0.1011 + 0.0000001 = 0.1011001
= C
=
= 1
= 1
’ symbol is mapped to an interval of width 1/2 at position [3/8, 7/8), as shown in the top line of
=
= A
=
= 0.1 0.001 = 0.0001
=
= A
= 0.0001
16
13
16
105
128
1
3
8
1
2
co
cod
code
1
2
3
1
2
+
+
+ (A
+ (A
+ (A
+
(
(
1
4
1
8
f
f
(
X
16
X
1
2
1
64
=
1
1
2
3
=
(
(
o
d
0.01 = 0.000001
16
64
)
)
1
1
(
(
(
1
8
(
(0)
f
f
f
1
2
X
X
X
)
Freescale Semiconductor, Inc.
(
(
(0))
)
+
=
e
e
= C
For More Information On This Product,
) +
))
105
128
1
4
+
f
3
X
1
8
f
(
X
))
d
A
(
) +
Go to: www.freescale.com
c
n
=
) = 1/2, so
Background Theory
= A
f
13
16
X
(
c
n–1
)))
f
X
(x
n
)
code
as shown in Figure 4 follows.
Arithmetic Coding
Eqn. 5
7