ellessaahd show whether this bit change is detected. Problem 8: 20 Points A 1024

Question

ellessaahd show whether this bit change is detected. Problem 8: 20 Points A 1024-bit message is sent that contains 992 data bits and 32 CRC bits. CRC is computed using the IEEE 802 standardized, 32- whether the errors during message transmission will be detected by the receiver: (a) There was a single-bit error. (b) There were 2 isolated bit errors. (c) There were 6 isolated bit errors. (d) There were 27 isolated bit errors. (e) There was a 27-bit long burst error (f) There was a 41-bit long burst error. degree CRC polynomial. For each of the following, explain

Explanation / Answer

Crc is a error detecting code commonly used in digital networks

To compute an n-bit binary crc,line the bits representing the input in a row and position the(n+1) bit pattern representing the crc divisor(called polynomial)

we shall encode 14 bits of message with a 3-bit crc wuth polynomial x3+x+1.the polynomial is written in binary as the coefficient has 4 coefficients(1x3+0x2+1x+1)

single bit error:

d(x):dataword to be sent(as a polynomial)

c(x):codeword sent

e(x):error

c(x)+e(x)-codeword sent with error introduced

g(x)-generator polynomial to be used at crc encoder

A single bit error e(x)=xi when is the position of the bit.In a single bit error is caught when e(x)=xi is not divisible by g(x).g(x) has atleast two terms and the coefficients of x0 is not zero.Then e(x) cannot be divided by g(x) and all single bits errors can be caught Esingle=(0,0,0,1,0,0......0)

e(x)=xi

detect double errors:

codeword n bits

Edouble=(0,0,0,1,0,1,....0)

E(x)=xi+xj

e(x)=xi(1+x(j-i))

g(x) is such that it has more than one term and cannot divisible xi

e(x) is divisible by g(x)

detect odd number of errors:

e(x)=(1+x)q(x)

g(x)=(x+1)*p---> detect all single ,double,odd number of errors

here after x all are in powers position

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