“ Hamming(7,4) has same order of error rate as repetition codes”, is there any simple proof?

Mayank Khetan

1

Yes there is.

For repetition code to fail. (Consider the 3-repetition code), either two bits or three bits should be flipped. That amounts to (3C2*f²*(1-f) + 3C3*f³). Which is of order O(f²).

For hammnig code to fail, either two or three bits of the block should be flipped. That amounts to (3C2*f²*(1-f) + 3C3*f³). Which is of order O(f²).

But the transmission rate for 3-repetition code is (1/3), but that for hamming code is (4/7).