\documentclass[12pt,a4paper]{article}

\usepackage[utf8]{inputenc} \usepackage[margin=2cm]{geometry}
\usepackage{amstext} \usepackage{amsmath} \usepackage{array}
\newcommand{\lra}{\Leftrightarrow}

\title{Howework 3 -- Computer Networking}

\author{Claudio Maggioni}

\begin{document} \maketitle
\section*{Exercise 1}
The EUI-48 MAC address space can have $2^{48} = 281474976710656$ possible addresses. The IPv4 address space has $2^32 = 4294967296$
addresses while IPv6 has = $2^{128} \approx 3,402823669209385 \cdot 10^{38}$ addresses. In practice, some of the addresses in
 these spaces may be reserved for special purposes (e.g.
  \texttt{FF:FF:FF:FF:FF:FF} as the broadcast MAC address or the
   \texttt{127.0.0.0/8} subnet reserved for loopback networks 
    in IPv4) so the number of usable addresses is smaller than
     these figures.

\section*{Exercise 2}
$$D = 1010100000_2 = 512_{10} + 128_{10} + 32_{10} = 672_{10}$$
$$G = 10011_2 = 19_{10}$$
$$r = |G| - 1 = 4$$ 
$$R =D \cdot 2^r \mod G = 10752 \mod 19 = 17$$

\section*{Exercise 3}

For 10 Mbps:

$$t = \frac{100 \cdot 512 b}{10^7\frac{b}{s}} = 5.12 ms$$ 

For 100 Mbps:

$$t = \frac{100 \cdot 512 b}{10^8\frac{b}{s}} = 0.512 ms$$ 

\section*{Exercise 4}
A mechanism that an AP can use to maintain constant reliability (e.g. constant BER) while communicating with a station that is getting farther away from it is to use rate adaptation: once transmission errors are detected through ARQ checks, the AP can switch to a lower transmission rate (akin to TCP's congestion control mechanisms) to counteract interference and lowering signal strength.

The AP may also decide to boost its transmission power if possible, thus increasing signal strength. However, this technique does not provide a linear increase in signal strength since obstacles or powerful interferences may be present.

In alternative, if the station is in a ESS and another AP is present in the same subnet, the station may decide to hop from the first AP to the new AP if the latter has a better RSSI. If the DS uses switches, those should be informed of the change of BSS so as to keep their switching tables updated. 


\end{document}
