Question

A DMS source has three output symbols with probabilities (0.42, 0.33, 0.25). Determine the Huffman code for this source and find its efficiency.

a. 0: 00, 1: 01, 2: 1
b. 0: 00, 1: 10, 2: 11
c. 0: 0, 1: 10, 2: 11
d. 0: 0, 1: 1, 2: 11

Answer 1

The Huffman code for the given DMS source with output symbols and probabilities (0.42, 0.33, 0.25) is 0: 00, 1: 01, 2: 1, with an efficiency of 1.58.

Step-by-step explanation:

The Huffman code for the given DMS source with output symbols and probabilities (0.42, 0.33, 0.25) can be determined as follows:

1. Arrange the output symbols in ascending order based on their probabilities: (0.25, 0.33, 0.42)
2. Create a binary tree with these symbols as leaves.
3. Assign '0' and '1' to the left and right branches of the tree.
4. The Huffman code for each output symbol is obtained by traversing the tree from the root to the respective symbol. The code for '0' is '00', for '1' is '01', and for '2' is '1'.
5. The efficiency of the Huffman code can be calculated by multiplying the probability of each symbol with its code length and summing them up.

In this case, the efficiency of the Huffman code would be:

Efficiency = (0.25 * 2) + (0.33 * 2) + (0.42 * 1) = 0.5 + 0.66 + 0.42 = 1.58

Therefore, option a. 0: 00, 1: 01, 2: 1, is the correct Huffman code for this source and its efficiency is 1.58.