huffman coding

1. HUFFMAN CODING
By: Mr. Nihal Kumar(Ass. Professor)

2. INTRODUCTION
 Huffman coding is a lossless data encoding
algorithm
 This is a method of reducing complex code
into simpler sequences and is common in
video encoding.
 This is a variable length and prefix free
coding.

3. PROCESS
 The source symbols are arranged in order of
decreasing probabilities(frequencies)
 Then the two least probabilities are assigned
to bit 0 & 1.
 Then combine last two symbols and move
the combined symbol as high as possible.
 Repeat the above step until two symbols left.
 Code for each symbol is found by moving
backward

4. CALCULATION
 Length of code
L = 𝑖=1
𝑛
𝑙𝑖 𝑃𝑖
 Entropy
H= 𝑖=1
𝑛
𝑃𝑖 log2
1
𝑃 𝑖
 Efficiency
𝜂 =
𝐻
𝐿

5.  Redundancy
𝛾 = 1 − 𝜂

6. EXAMPLE:
 𝑋 𝜖 {𝐴, 𝐵, 𝐶, 𝐷} with probabilities {
1
2
,
1
4
,
1
8
,
1
8
}
encode using Huffman Coding.
Length
1
2
3
3

7.  Length
L=
1
2
∗ 1 +
1
4
∗ 2 +
1
8
∗ 3 +
1
8
∗ 3
=
14
8
 Entropy
H=
1
2
log2
1
1 2
+
1
4
log2
1
1 4
+
1
8
log2
1
1 8
+
1
8
log2
1
1 8
= 14/8

8.  So efficiency
𝜂 =
𝐻
𝐿
=
14 8
14 8
= 1
Redundancy
𝛾 = 1 − 𝜂
= 0