• a.In error-correcting codes, what is meant by a perfect code?

  (2 marks)

  Illustrate your answer by explaining, with appropriate calculations, whether the following two codes are perfect:

  • i.(31, 26) Hamming code
  • ii.(16, 9) rectangular code

  (6 marks)

• b.A low bit-rate communications link is used to transmit an encoded version of the following message: WOLLONGONG

  If it is assumed that only the symbols/letters of this message are transmitted via the link, rather than all 26 possible symbols/letters, determine the following:

  • i.If a fixed-length code is used, how many bits will be required for each code word?

  (2 marks)

  • ii.By constructing a table similar to that in Activity 2.12, what are the relative frequencies of the symbols in this message?

  (5 marks)

  • iii.Hence, generate the corresponding Huffman coding tree and determine the code words for each symbol.

  (9 marks)

  • iv.What is the entropy and average code word length of the Huffman code?

  (2 marks)

  • v.What is the efficiency of the Huffman code?

  (2 marks)

  • vi.By calculating the corresponding efficiency of the fixed-length code in part i., how does this compare with respect to the Huffman code efficiency in part v.?

  (2 marks)