$6\mathrm{.}2-1$ Two dimensional parity: error detection and correction. Suppose that a packet's payload consists of $10$ eight$-$bit values $($e$.$g$.,$ representing ten ASCII$-$encoded

characters$)$ shown below. $($Here$,$ we have arranged the ten eight$-$bit values as five sixteen$-$bit values$).$ The received data $($including parity$)$ bits are shown. Even parity is used.

One received data bit has been flipped. Which one is it$?($row and column numbering start at $1)$ Use the pulldown boxes to specify the row and column where the flipped bit

appears $($indicates start at $1).[$Note: You can find more examples of problems similar to this here.$]$

received $,0100101000011011|1$

data and $00001110010000011$

$2$D parity $00111110000100010$

bits $1110110000001111,1$

$1001111100011001,1$

$00001001110111010$

In which row has the bit flip occurred?

In which column has the bit flip occurred?

$1\mathrm{.}8$

$9$

$3$

$1$

$2$

$10$

$7\mathrm{.}5$

$8\mathrm{.}7$

$9\mathrm{.}4$

$6\mathrm{.}2-2$ Calculating CRC bits. Consider the Cyclic Redundancy Check $($CRC$)$ algorithm discussed in Section $6\mathrm{.}2\mathrm{.}3$ of the text. Suppose that the $4-$bit generator $($G$)$ is $1001,$ that

the data payload $($D$)$ is $10011101$ and that $r=3.$ What are the values of the $3$ CRC bits? $[$Note: You can find more examples of problems similar to this here.$]$

$010$

$100$

$101$

$011$

$6\mathrm{.}3-4.$ Multiple Access protocols $($d$).$ Consider the figure below, which shows the arrival of $6$ messages for transmission at different multiple access wireless nodes at times

$t=0\mathrm{.}3,1\mathrm{.}7,1\mathrm{.}8,2\mathrm{.}5,4\mathrm{.}2,4\mathrm{.}6.$ Each transmission requires exactly one time unit.

For the CSMA$/$CD protocol $($with collision detection$),$ indicate which packets are successfully transmitted. You should assume that it takes $\mathrm{.}2$ time units for a signal to

propagate from one node to each of the other nodes. You can assume that if a packet experiences a collision or senses the channel busy and that that node will not attempt a

retransmission of that packet until sometime after $t=5.$ If a node senses a collision, it stops transmitting immediately $($although it will still take $\mathrm{.}2$ time units for the last

transmitted bit to propagate to all other nodes$).$ Hint: consider propagation times carefully here. $[$Note: You can find more examples of problems similar to this here.$]$

$1$

$2$

$3$

$4$

$5$

$6$

$6\mathrm{.}3-3.$ Multiple Access protocols $($c$).$ Consider the figure below, which shows the arrival of $6$ messages for transmission at different multiple access wireless nodes at times

$t=0\mathrm{.}3,1\mathrm{.}7,1\mathrm{.}8,2\mathrm{.}5,4\mathrm{.}2,4\mathrm{.}6.$ Each transmission requires exactly one time unit.

For the CSMA protocol $($without collision detection$),$ indicate which packets are successfully transmitted. You should assume that it takes $\mathrm{.}2$ time units for a signal to

propagate from one node to each of the other nodes. You can assume that if a packet experiences a collision or senses the channel busy and that that node will not attempt a

retransmission of that packet until sometime after $t=5.$ Hint: consider propagation times carefully here. $[$Note: You can find more examples of problems similar to this here.$]$

$1$

$2$

$3$

$4$

$5$

$6$