a) Consider the parity bit protocol with the p\'s, q\'s, and the additional r bi

Question

a) Consider the parity bit protocol with the p's, q's, and the additional r bit. What is the hamming distance of this protocol? Briefly explain why

b) Assume we have a CRC protocol that satisfies all the desirable properties that we described in the slides. What is the hamming distance of this protocol? Briefly explain why.

c) For both a) and b), can these protocols be used for error correction, and if so, how many bits can they correct? (i.e., can they perform x-bit correction, and if so, what is x?)

Explanation / Answer

Question 1

According to the Hamming code it is greater than or equal to the bit detction and plus one.That measn

Hamming code >= x+1

Here for the parity check p and q is the main bit and r is the additonal one .So total 3 .
As per the formula Hamming distance of this protocol is 4.

Question 2

According to the Hamming code it is greater than or equal to the bit detction and plus one.That measn

Hamming code >= x+1

And for the CRC protocol satisfying the properties like double bit error or single bit errom and so then it will give a burst factor in 2<= h <=n where h is the error burst bits.

So for this the Hamming code distance will be

Hamming code >= n-1

Question 3

X is the total bit error detection power

For part a

Hamming code can correct 2x+1 bits

so it will be 2*3+1= 7 bits

For part b

It cannot be used for bit correction.

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