Question

A DMS has an alphabet of eight letters xi,i=1,2,…,8, with probabilities 0.25,0.20,0.15,0.12, 0.10,0.08,0.05, and 0.05 .

1. Use the Huffman encoding procedure to determine a binary code for the source output.

Answer 1

To generate a Huffman code for a discrete memoryless source, one must list the symbols and their probabilities, repeatedly combine the least probable symbols, and trace back from the tree's root to determine the code for each symbol.

Step-by-step explanation:

Huffman Encoding Procedure

The question involves using the Huffman encoding procedure to create a binary code for a discrete memoryless source (DMS) with a specific probability distribution. Although the exact details of how the Huffman tree should be constructed based on the given probabilities are not provided, the procedure involves the following steps:

1. 
   
3. Start by listing the source symbols and their probabilities.
4. 
   
6. Combine the two symbols with the lowest probabilities into a set, assign binary digits (0 and 1) to them, and then sum their probabilities.
7. 
   
9. Repeat step 2 with the new set of probabilities until you have just one symbol with a probability of 1, representing the entire set.
10. 
    
12. Trace back from the top of the tree to the leaves to determine the Huffman code for each original symbol.

The Huffman code will be a prefix code where no code is a prefix of any other, guaranteeing the uniqueness of each symbol when decoding.