Databases Reference
In-Depth Information
T A B L E 3 . 23
Code used for zero block
option.
Number of All-Zero Blocks
Codeword
1
1
2
01
3
001
4
0001
5
000001
6
0000001
.
.
6
30
s
000
···
01
63
ROS
00001
Fundamental sequence:
This is a unary code. A number
n
is represented by a sequence
of
n
0s followed by a 1 (or a sequence of
n
1sfollowedbya0).
Split sample options:
These options consist of a set of codes indexed by a parameter
m
.
The code for a
k
-bit number
n
using the
m
th split sample option consists of the
m
least
significant bits of
k
followed by a unary code representing the
k
m
most significant
bits. For example, suppose we wanted to encode the 8-bit number 23 using the third split
sample option. The 8-bit representation of 23 is 00010111. The three least significant
bits are 111. The remaining bits (00010) correspond to the number 2, which has a unary
code 001. Therefore, the code for 23 using the third split sample option is 111011. Notice
that different values of
m
will be preferable for different values of
x
i
, with higher values
of
m
used for higher-entropy sequences.
−
Second extension option:
The second extension option is useful for sequences with low
entropy—when, in general, many of the values of
x
i
will be zero. In the second extension
option, the sequence is divided into consecutive pairs of samples. Each pair is used to
obtain an index
γ
using the following transformation:
1
2
(
γ
=
x
i
+
x
i
+
1
)(
x
i
+
x
i
+
1
+
1
)
+
x
i
+
1
(10)
and the value of
γ
is encoded using a unary code. The value of
γ
is an index to a lookup
table with each value of
γ
corresponding to a pair of values
x
i
,
x
i
+
1
.
Zero block option:
The zero block option is used when one or more of the blocks of
x
i
are zero—generally when we have long sequences of
y
i
that have the same value. In this
case the number of zero blocks are transmitted using the code shown in Table
3.23
.The
ROS code is used when the last five or more blocks in a segment are all zero.
The Rice code has been used in several space applications, and variations of the Rice code
have been proposed for a number of different applications.
