Question
Download Solution PDFThe minimum distance required for a linear block code to achieve a guaranteed correction of up to 5 errors is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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.
Formula:
To guarantee the correction of up to s errors in all cases, the hamming distance in a block code must be d ≥ 2s + 1
Let hamming distance be minimum
∴ dmin = 2s + 1
Calculation
number of errors = s = 5.
∴ dmin = 2(5) + 1 = 11
Important Point:
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 sent and the received codeword is the number of bits affected by the error.
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