5. (18 pts) Consider the check matrix Hs7 below for the (7, 4) Hamming code disc

Question

5. (18 pts) Consider the check matrix Hs7 below for the (7, 4) Hamming code discussed in class. 0 1 0 1 1 1 0 Let [ci c2 c3 m4 ms me m2] be a generic code word. What is the equation for c2 (check bit 2)? What is the error detecting capability of this code? Suppose that [1 1 001 01] is received. What is the weight of this received word? Is this a correct code word? What data would the receiver decide was sent? Suppose that [1 10 0 1 1 0] is received. Is this a correct code word? What transmitted code word would the receiver decide was sent? a. b. c. d.

Explanation / Answer

1.

for(i=0; i< 3 ;I++

{

    arr[i][1]=arr[i][3]^arr[i][4]^arr[i][5]^arr[i][6];

}

2)

-Easy to encode and decode data at both sender and receiver end.Easy to implement.

-but there is also disadvantage. Cannot correct burst errors and redundant bits are also sent with the data therefore it requires more bandwidth to send the data.

3)

[1 1 0 0 1 0 1] waight is 4.min weight is 4 so right word.

4)

[1 1 00 1 1 0] - waight is 4.

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