Topic: Information Theory and Coding
A communication system is designed using the following three 5 bit words as the only valid codewords and uses error correction using hamming distance.
Codeword A: 00000
Codeword B: 01110
Codeword C: 11000
During operation, receiver gets the word 01000. What would the system conclude?
- A. It will correct to codeword A
- B. It will correct to codeword B
- C. It will correct to codeword C
- D. It will be unable to correct the error
Answer: D. It will be unable to correct the error
Explanation: Let's calculate the Hamming distance from the received word (01000) to each valid codeword:
Distance to A (00000) = 1 bit (2nd bit).
Distance to B (01110) = 2 bits (3rd and 4th bits).
Distance to C (11000) = 1 bit (1st bit).
Since the received word is equidistant (distance 1) from both Codeword A and Codeword C, the system cannot unambiguously determine which of the two was originally transmitted. Therefore, it is unable to correct the error.