GATE EC 2026 Set 1 — Question 63
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Communications → Error Control Coding → Hamming Distance & Codes
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Question
The average bit error rate at the input of a Hamming decoder is .
The probability that the decoder will fail to decode a received word correctly is __.(rounded off to two decimal places)
The probability that the decoder will fail to decode a received word correctly is __.(rounded off to two decimal places)
Correct answer
0.1 to 0.2
Solution
A Hamming code has a block length and can correct up to error.
The decoder fails if there are more than error in the -bit block.
Let be the bit error rate.
The probability of correct decoding is the probability of or error:
The probability of failure is .
Rounding to two decimal places, we get .
The decoder fails if there are more than error in the -bit block.
Let be the bit error rate.
The probability of correct decoding is the probability of or error:
The probability of failure is .
Rounding to two decimal places, we get .
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