Find average length coding efficiency and variance of the code $P (a_1) = 0.2, P (a_2) = 0.4, P (a_3)= 0.2, P (a_4 ) = 0.1, P (a_5) = 0.1.$ - Mumbai University > EXTC > Sem 7 > Data Compression and Encryption

Marks: 10 M

Year: May 2014

1) Minimum variance

• Entropy $(H ) =_n (log_2 ( 1 / P_n)) \\ H = 2.122 bits/ Symbol$

• Average Length $(L ) = _n . l_n \\ L = 2.2 bits/ Symbol$

• Coding efficiency $(η ) = H /L = 96.45$ %

• Redundancy of the Code $(R) = 1 – η = 3.55$ %

2) Huffman Tree

$a_1 = 0.2 \\ a_2 =0.4 \\ a_3 = 0.2 \\ a_4 = 0.1 \\ a_5 = 0.1 \\ n = 3 bits$

Compression ratio = $N_{BC} / N_{AC} = 30 /22 = 136$ %

Huffman Tree

$a_2 - \gt 1 \\ a_1 - \gt 01 \\ a_3 - \gt 000 \\ a_4 - \gt 0000 \\ a_5 - \gt 0011$

$$\text{Figure 1.2 Huffman Tree}$$

At input : $a_5 , a_1 , a_2 , a_1 , a_3 , a_2 , a_2 , a_3 , a_4 , a_2$

Output at Transmitter: 0011 , 01, 101 ,000, 11 ,000 ,001 ,01

Channel is Noiseless

Output at receiver