diff --git a/ex08/kn08.pdf b/ex08/kn08.pdf index 61d96f9..919ed16 100644 --- a/ex08/kn08.pdf +++ b/ex08/kn08.pdf Binary files differ diff --git a/ex08/kn08.tex b/ex08/kn08.tex index 3970564..803f3ce 100644 --- a/ex08/kn08.tex +++ b/ex08/kn08.tex @@ -89,21 +89,84 @@ \vspace{1cm} \Aufgabe{ALOHA, CSMA and CSMA/CD}{5+5+5+5} \begin{enumerate} - \item ALOHA with timeout $2 \cdot t_0$ + \item ALOHA with timeout $2 \cdot t_0$ \item nonpersistent CSMA with timeout $2 \cdot t_0$ \item nonpersistent CSMA/CD with minimum waiting time $t_0$ \item $0.5$-persistent CSMA/CD with slot length $2 \cdot t_0$ \end{enumerate} -\Aufgabe{Code Division Multiple Access(CMDA)}{10+10+10} +\Aufgabe{Code Division Multiple Access(CDMA)}{10+10+10} \begin{enumerate} - \item - \item - \item + \item Generate Walsh-Tables for $n=8$:\\ + \begin{math} + W_1=\begin{pmatrix} + -1 + \end{pmatrix},\ W_2=\begin{pmatrix} + -1 & -1\\ + -1 & 1 + \end{pmatrix},\ W_4=\begin{pmatrix} + -1 & -1 & -1 & -1\\ + -1 & 1 & -1 & 1\\ + -1 & -1 & 1 & 1\\ + -1 & 1 & 1 & -1\\ + \end{pmatrix}\\ + W_8=\begin{pmatrix} + -1 & -1 & -1 & -1&-1 & -1 & -1 & -1\\ + -1 & 1 & -1 & 1&-1 & 1 & -1 & 1\\ + -1 & -1 & 1 & 1&-1 & -1 & 1 & 1\\ + -1 & 1 & 1 & -1&-1 & 1 & 1 & -1\\ + -1 & -1 & -1 &-1&1 & 1 & 1 & 1\\ + -1 & 1 & -1 & 1&1 & -1 & 1 & -1\\ + -1 & -1 & 1 & 1&1 & 1 & -1 & -1\\ + -1 & 1 & 1 & -1&1 & -1 & -1 & 1\\ + \end{pmatrix}=\begin{pmatrix} + c_0&c_1&c_2&c_3&c_4&c_5&c_6&c_7 + \end{pmatrix} + \end{math} + \item $c_2$ is orthogonal to all other chips:\\ + \begin{math} + c_0\cdot c_2=\begin{pmatrix} + -1\\-1\\-1\\-1\\-1\\-1\\-1\\-1 + \end{pmatrix}\cdot\begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1+1-1-1+1+1-1-1=0\\ + c_1\cdot c_2=\begin{pmatrix} + -1\\1\\-1\\1\\-1\\1\\-1\\1 + \end{pmatrix}\cdot \begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1-1-1+1+1-1-1+1=0\\ + c_3\cdot c_2=\begin{pmatrix} + -1\\1\\1\\-1\\-1\\1\\1\\-1 + \end{pmatrix}\cdot \begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1-1+1-1+1-1+1-1=0\\ + c_4\cdot c_2=\begin{pmatrix} + -1\\-1\\-1\\-1\\1\\1\\1\\1 + \end{pmatrix}\cdot\begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1+1-1-1-1-1+1+1=0\\ + c_5\cdot c_2=\begin{pmatrix} + -1\\1\\-1\\1\\1\\-1\\1\\-1 + \end{pmatrix}\cdot \begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1-1-1+1-1+1+1-1=0\\ + c_6\cdot c_2=\begin{pmatrix} + -1\\-1\\1\\1\\1\\1\\-1\\-1 + \end{pmatrix}\cdot\begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1+1+1+1-1-1-1-1=0\\ + c_7\cdot c_2=\begin{pmatrix} + -1\\1\\1\\-1\\1\\-1\\-1\\1 + \end{pmatrix}\cdot\begin{pmatrix} + -1\\-1\\1\\1\\-1\\-1\\1\\1 + \end{pmatrix}=1-1+1-1-1+1-1+1=0\\ + \Rightarrow c_2 + \end{math} is orthogonal to all other chips. + \item \end{enumerate} \Aufgabe{Token Ring}{10+10} \begin{enumerate} \item - \item + \item \end{enumerate} \Aufgabe{Ethernet}{5+5+5+5+5+5} \begin{enumerate}