Problem $1(5$ points$)$: On simple parity scheme

Assume a frame of $\backslash (\backslash$mathrm$\{$F$\}=50\backslash )$ bits, with bit$-$error$-$rate $($BER$)$ equal to $\backslash (5\backslash$times $10^\{-2\}\backslash ).$

a$)(3$ points$)$ Compute the probability that the frame is received in error.

b$)(2$ points$)$ Compute the average number of erroneous bits in an average frame.

Solution:

Problem $2(10$ points$)$: On Hamming code $(11,7)$:

$($a$)(5$ points$)$ Following the example shown in Figure $6$ in textbook page $206,$ it is required to encode the message: $1100110$ using $\backslash ((11,7)\backslash )$ hamming code. Specify the resulting codeword and show your work.

$($b$)(5$ points$)$ Assume the following received codeword $10000110110$ and it contains a SINGLE bit error. Compute the syndrome and show the original transmitted data.

Problem $3(15$ points$)$:

A CRC is constructed to generate a $4-$bit FCS for an $8-$bit message given by $\backslash (1010\backslash$quad $1100\backslash ).$ The generator polynomial is specified by $\backslash ($ G$($X$)=$X$^\{4\}+$X$+1\backslash ).$

$($a$)(5$ points$)$ Draw the shift register corresponding the generator polynomial $\backslash (\backslash$mathrm$\{$G$\}(\backslash$mathrm$\{$X$\})\backslash ).$

$($b$)(6$ points$)$ Compute the CRC bits using the above data string and generator polynomial using the polynomial division.

$($c$)(4$ points$)$ What is the transmitted frame Tt in bits form and in polynomial form?

Problem $4(10$ points$)$:

A link between a Riyadh ground station and a second one in Dammam through a geostationary satellite at the height of $\backslash ($ h$=36000\backslash$mathrm$\{$~km$\}\backslash ).$ The link uses Sliding Window Protocol with window size $\backslash ($ W$=7\backslash )$ and frame size $\backslash ($ L$=12000\backslash )$ bits with the link transmission rate $\backslash ($ R$=2\backslash$mathrm$\{$Mb$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Assume propagation speed of $\backslash ($ R F $\backslash )$ signal is equal to $\backslash (3\backslash$times $10^\{8\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}\backslash ).$

a$)(6$ points$)$ Compute the link utilization and throughput in frames $\backslash (/\backslash$mathrm$\{$sec$\}\backslash )$ for the given parameters.

b$)(4$ points$)$ It is desired to increase the link throughput to $\backslash (1\backslash$mathrm$\{$Mb$\}/\backslash$mathrm$\{$s$\}\backslash )$ by increasing the window size $($i$.$e$.$ the link transmission rate $\backslash ($ R$=2\backslash$mathrm$\{$Mb$\}/\backslash$mathrm$\{$s$\}\backslash )$ and frame size $\backslash ($ L $\backslash )$ are NOT changed$).$ Compute the minimum number of bits needed for the sequence numbers.

Problem $5(10$ points$)$: A $100-$byte IP packet is transmitted over local loop using ADSL protocol stack. How many ATM cells will be transmitted? Specify$/$describe the contents of each of these ATM cells.

Hint: Utilize the AAL$5$ frame structure given in Figure $27$ on textbook page $250.$ The default PPP protocol field is $2$ bytes in size.