Question 5 ========== a) Consider the parity bit protocol with the p\'s, q\'s, a

Question

Question 5
==========

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

Answer is as follows :

a)

We know that the Hamm(code) >= x + 1.

By using the parity bit protocol as per given information with the p's q's and r's give us 3 bit(p,q,r) error detection power. Hence x = 3.

This means that the hamming distance of this protocol is >= x + 1 = 3 + 1 = 4

b)

From above (part a) we find that the hamming distance of a code is x + 1 where x is the x bit error detection power. If we have a CRC protocol that satisfies all of the desirable properties that we discussed in the slide,which were:

By using these peoperties, we can see that the CRC protocol satisfies all error bursts up to an including 2 <= k <= n bursts.

This means that the Hamm(Code) >= x+1 = (n-2) + 1 = n-1

c)

For part a)

We know that the parity bit protocol can detect all 3 or less bit errors, x = 3

since Hamm(code) >= 4. We also know that in order to perform x-bit correction: Hamm(code) >= 2x + 1. Therefore we can only detect single bit errors because 2(1) + 1 = 3.

For part b)

we know that the CRC protocol has Hamm(code) >= n+2 where x = n+1.

In order for Hamm(code) >= 2x+1,

where x <= floor(n/2).

So this is used in error correction

if there is any query or missing part please ask in comments...

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