AN2121 Freescale Semiconductor / Motorola, AN2121 Datasheet - Page 10

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

Background Theory
proportional to the probability associated with each symbol. For example, the symbol
interval of width 1/2 at position [3/8, 7/8).Note that for arithmetic coding the ordering of the intervals is
arbitrary, whereas in Huffman coding the ordering depends on the probabilities of the symbols.
104
128
The algorithm for coding the sequence ‘
For example, for the first symbol,
left of
associated with these two symbols. This cumulative probability is then multiplied by A
interval for the first symbol, which is 1.
For
6
16
6
0
420
512
1. Initialize A
2. Update code word, C, using the equation
c
, the first symbol in Figure 4, the code word becomes
c
code
coe
where P
where, as before,
C
on the interval [0,1). Therefore, the cumulative probability entails adding up the probabilities
e
ce
1
= C
= 0 + (1
Figure 4. Arithmetic Encoding Example with Probabilities Restricted to 2
105
128
421
512
16
0
1
8
7
+ (A
X
(x
0
n
= 1 and C
0
) is the cumulative probability of x
(1/4 + 1/8)) = 3/8
JPEG2000 Arithmetic Encoding on the StarCore SC140
(
codd
cod
f
X
d
cd
f
Freescale Semiconductor, Inc.
X
(e) +
(x
For More Information On This Product,
0
i
)
= 0
C
is the probability of symbol x
f
c
X
n
, n = 1 and P
(
= C
d
P
)))
107
128
423
512
16
Go to: www.freescale.com
3
8
9
code
X
n–1
(x
n
+ (A
) =
’ is as follows:
X
i = 1
n–1
n–1
(
c
) =
f
X
(x
f
P
X
X
i
(e) +
)
(x
n
and is equal to
n
codc
coc
))
cc
f
c
X
i
(d) because symbols
occurring.
c
0
e
is mapped to an
111
128
427
512
, the current
13
16
7
8
and
i
codo
d
coo
co
o
lie to the
Eqn. 3
Eqn. 4
112
128
1
14
16
428
512