Question

Calculate the following for the data given below:

i) Entropy

ii) Coding redundancy of Binary code

iii) Coding redundancy of Huffman code

Symbol: 1 2 3 4 5 6
Huffman code: 0 10 110 1110 11110 111111
Binary code: 000 001 010 011 100 101
Probability: 0.4 0.2 0.2 0.1 0.05 0.05

[Given, log 0.05= -4.32] 

01 Dec 2023
Answer :
Word Count : 256

To calculate the entropy, coding redundancy of binary code, and coding redundancy of Huffman code, we can use the following formulas:

i) Entropy (H):
\[ H = - \sum_{i=1}^{n} p_i \cdot \log_2(p_i) \]

ii) Coding Redundancy of Binary Code (R_binary):
\[ R_{\text{binary}} = \frac{1}{2} \sum_{i=1}^{n} p_i \cdot L_{\text{binary},i} \]

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