hamming distance

Question

To provide more reliability than the Single Parity Bit technique, a new error-detecting scheme has been proposed. The scheme uses first parity bit for checking all the odd numbered bits and a second parity bit for all the even numbered bits. What is the (minimum) Hamming distance of this code ?

Answer 1

Here we need to know : 

a) Minimum Hamming distance needed to detect 'd' errors  =  d + 1

b) Minimum Hamming distance needed to correct 'd' errors  =  2d + 1

c) A simple parity scheme has one bit error detecting capability

In the modified parity scheme , we can detect two errors as we are using two separate parity bits ; one for checking bits at odd-numbered positions and other at even numbered positions.

Hence number of errors that can be detected   =  2 (corresponding to each parity bit we have one error which can be detected)

Hence minimum hamming distance needed for error detection   =  d + 1   =  2 + 1  = 3

          minimum hamming distance needed for error correction  =  2d + 1   =  2(2) + 1   =   5

Comments

in question, it wasn't mentioned about error correction or detection, so what needs to be assumed ?

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As parity bit is used for error detection , so Hamming distance w.r.t error detection makes more sense.

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Problem 2 a

http://web.eecs.utk.edu/~hqi/teaching/ece453f06/hw/hw3_sol.htm