View
238
Download
0
Category
Preview:
Citation preview
8/21/2019 Source Code Design
1/18
E
E Data Communications andNetworking
ource o e es gn
E Dr Salem Aljareh
8/21/2019 Source Code Design
2/18
Source Code Design
Decision Tree10
0 11 0
0 10 10 1 0 1
x1 x8x3x2 x7x6x5x4
111110101100011010001000
8/21/2019 Source Code Design
3/18
Weather Info System
Very Poor Poor Good Moderate
10
0 0 1Moderate
0 110Poor
110 111GoodVer Poor
8/21/2019 Source Code Design
4/18
Shannon Fano Encoding
1. List symbols in descending probability order
. v e a e n o equa or near y equa va ues o pro a y
.
4. Divide both u er and lower section in two
5. Allocate binary 0 to top half and binary 1 to bottom half
6. Repeat (4) and (5) until cant go further
8/21/2019 Source Code Design
5/18
Shannon Fano Code Example
x1: P = 0.25 x2: P = 0.25
x3: P = 0.15 x4: P = 0.1
5 . 6 .
x7: P = 0.06 x8: P = 0.01
8/21/2019 Source Code Design
6/18
Shannon Fano Solution
0.25 0
0.25 0 1.
0.1 1 0 1
.
0.08
1
1
1
1
0
1 0
0.06
0.01
1
1
1
1
1
1
1
1
0
1
8/21/2019 Source Code Design
7/18
Shannon Fano Encoding (con.)
X1 X2 X3 X4 X5 X6 X7 X8
. . . . . . . .
00 01 100 101 110 1110 11110 11111
Calculate the following:-
The code length
The code Efficienc
8/21/2019 Source Code Design
8/18
Shannon Fano Encoding (solution)e co e eng s g ven y:
lxPLii
i
i )(81=
=
=
3)10.010.015.0(
..
+++
5)01.006.0(408.0 ++
sym og ts.=
8/21/2019 Source Code Design
9/18
Shannon Fano Encoding (solution)
The entropy H(X) is given by:
i 18= =
xPi i
11
)(1=
1115.0
.
25.0
. 22
1lo01.011lo06.0
08.0.
10.0.
+
symbolbits /67.2
01.006.0
=
8/21/2019 Source Code Design
10/18
Shannon Fano Encoding (solution)
The efficiency of the code is :
100)(=
XH
67.2
72.2
.
8/21/2019 Source Code Design
11/18
Huffman Encoding (The Algorithm)
List the symbols in descending order of probability.
Combine the 2 smallest probabilities to make a newprobability.
Repeat the process until all the symbols have been.
.
8/21/2019 Source Code Design
12/18
Huffman Encoding (Example)
x1
: P = 0.25 x2
: P = 0.25
x : P = 0.15 x : P = 0.1
x5: = . x6: = .
x7: P = 0.06 x8: P = 0.01
8/21/2019 Source Code Design
13/18
x1 0.25
0
000
02
x3 0.15
.
0.55 1.00
x4 0.10.45
0
1
x5 0.1
0.2
0.301
1
1
x6 0.08 0
x7
x8
0.060.07
0
1
1
101111
8/21/2019 Source Code Design
14/18
0 0
Huffman Encoding (Solution)
x2
1 0
x3
x
0 1 0
x5
1 1 1
x6
x
0 1 1 0
0 1 1 1 0
x8
0 1 1 1 1
8/21/2019 Source Code Design
15/18
Huffman Encoding (evaluation)
For the above Code,
Calculate the following:-
The code length
The code Entropy
8/21/2019 Source Code Design
16/18
Huffman Encoding (Evaluation -result)
The code length = 2.72 digits/symbol
The code Entropy = 2.67 bits/symbol
The code Efficiency = 98.2%
Compare to those for the Shannon Fano Coding
8/21/2019 Source Code Design
17/18
Practical Example
circuit.
At encoded 2.72 bits/symbol this is equivalent to 882 symbols/sec
Improvement = 82/800 = 10.25%
8/21/2019 Source Code Design
18/18
Implementation of Huffman Code
A4 page scanned from top left-hand corner to the right-hand bottom corner
Each line is subdivided into 1728 icture elements els .
Each pel quantized into either black ple or white pel.
The total number of pels is approximately is just under 2 pels.
If a binary 1 is used to represent a white pel and binary 0 represent a blackpel and
If the signalling rate is 4800bps the time taken to transmit a page using theabove scheme is:
6
The scanned data contains considerable redundancy.
the transmission speed can be reduced by a factor of about 10.
the probability of occurrence of each run length.
Recommended