21.5. Optimal Prefix Codes

Try these first

1. 1.

   Define a prefix code in your own words?

   Hint

   Think about how Morse code could lead to confusion.

2. 2.

   What encoding method assigns shorter codes to more frequent letters?

   Hint

   Check what Huffman coding does!

3. 3.

   What is a prefix code?

   • A code where one code is a prefix of another
   • A code where no code is a prefix of another
   • A fixed-length coding mechanism

   Hint

   Think about how Morse code functions.

4. 4.

   True or False: Huffman coding is an optimal method for generating prefix codes.

   • True
   • False

   Hint

   Remember what we discussed about minimizing the average code length.

5. 5.

   Given the frequencies of letters {A: 0.5, B: 0.25, C: 0.15, D: 0.10}, design an optimal prefix coding tree and determine the expected length of encoding.

   Hint

   Use Huffman coding principles to design your tree.

6. 6.

   Design a variable-length encoding system for vowels in English based on their frequencies. Show your complete coding tree.

   Hint

   Remember to prioritize based on how often they are used.