To guarantee correction of upto t errors, the minimum Hamming distance dmin in a block code must be.

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UGC NET Computer Science (Paper 2) July 2018 Paper
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  1. t + 1
  2. t − 2
  3. 2t − 1
  4. 2t + 1

Answer (Detailed Solution Below)

Option 4 : 2t + 1
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Concept:

It is one of the concepts in coding for error control. Hamming distance between two words of the same size is the number of differences between the corresponding bits. It can be calculated by applying the XOR operation.

Explanation:

Minimum Hamming distance is the smallest hamming distance between all possible pairs in a set of words. There are three parameters in this: codeword size, data word size, and minimum Hamming distance. When a codeword is corrupted during transmission, the hamming distance between the sent and the received codeword is the number of bits affected by the error.

Points regarding hamming distance:

1) To guarantee the detection of up to s errors in all cases, the minimum hamming distance in a block code must be dmin = s + 1.

2) To guarantee the correction of up to t errors in all cases, the minimum hamming distance in a block code must be dmin = 2t + 1

Example:

A coding scheme has a hamming distance dmin = 4

Then code can detect up to 4 -1 = 3 errors and can correct up to 1 error.
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