Drill Problem 7'8'1

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Drill Problem 7.8.1

• John Alamia

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Problem

• A given code consists of the codewords 0000000,
  0011110, 0101101, 0111000, 1001100, 1011001,
  1101010, 1110100. If 1011011 is received, what is
  the decoded codeword based on the minimum Hamming
  distance.

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Hamming Distance

• dij w(si Ä sj)
• Also thought of as the number of differences or
  errors
• Minimum Hamming distance between two different
  signals is 1

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Solution

• 0000000 Ä 1011011 5
• 0011110 Ä 1011011 3
• 0101101 Ä 1011011 5
• 0111000 Ä 1011011 4
• 1001100 Ä 1011011 4
• 1011001 Ä 1011011 1
• 1101010 Ä 1011011 3
• 1110100 Ä 1011011 5