$28.$ Compare the maximum data rate of a noiseless $4-$kHz channel using

$($a$)$ Analog encoding $($e$.$g$.,$ QPSK$)$ with $2$ bits per sample.

$($b$)$ The T$1$ PCM system.

$29.$ If a T$1$ carrier system slips and loses track of where it is$,$ it tries to resynchronize using

the first bit in each frame. How many frames will have to be inspected on average to

resynchronize with a probability of $0\mathrm{.}001$ of being wrong?

$32.$ How long will it take to transmit a $1-$GB file from one VSAT to another using a hub

as shown in Figure $2-17?$ Assume that the uplink is $1$ Mbps$,$ the downlink is $7$ Mbps$,$

and circuit switching is used with $1\mathrm{.}2$ sec circuit setup time.

$35.$ To accommodate lower data rates than STS$-1,$ SONET has a system of virtual tributaries

$($VTs$).$ A VT is a partial payload that can be inserted into an STS$-1$ frame and

combined with other partial payloads to fill the data frame. VT$1\mathrm{.}5$ uses $3$ columns,

VT$2$ uses $4$ columns, VT$3$ uses $6$ columns, and VT$6$ uses $12$ columns of an STS$-1$

frame. Which VT can accommodate

$($a$)$ A DS$-1$ service $(1\mathrm{.}544$ Mbps$)?$

$($b$)$ European CEPT$-1$ service $(2\mathrm{.}048$ Mbps$)?$

$($c$)$ A DS$-2$ service $(6\mathrm{.}312$ Mbps$)?$

$37.$ Three packet$-$switching networks each contain n nodes. The first network has a star

topology with a central switch, the second is a $($bidirectional$)$ ring, and the third is

fully interconnected, with a wire from every node to every other node. What are the

best$-,$ average$-,$ and worst$-$case transmission paths in hops?

$44.$ Suppose that A$,$ B$,$ and C are simultaneously transmitting $0$ bits, using a CDMA system

with the chip sequences of Fig. $2-28($a$).$ What is the resulting chip sequence?

$49.$ A cable company decides to provide Internet access over cable in a neighborhood consisting

of $5000$ houses. The company uses a coaxial cable and spectrum allocation allowing

$100$ Mbps downstream bandwidth per cable. To attract customers, the company

decides to guarantee at least $2$ Mbps downstream bandwidth to each house at any

time. Describe what the cable company needs to do to provide this guarantee.

$50.$ Using the spectral allocation shown in Fig. $2-52$ and the information given in the text,

how many Mbps does a cable system allocate to upstream and how many to downstream?Compare the maximum data rate of a noiseless $4-kHz$ channel using

$($a$)$ Analog encoding $($e$.$g$.,$ QPSK$)$ with $2$ bits per sample.

$($b$)$ The T$1$ PCM system.

If a T$1$ carrier system slips and loses track of where it is$,$ it tries to resynchronize using

the first bit in each frame. How many frames will have to be inspected on average to

resynchronize with a probability of $0\mathrm{.}001$ of being wrong?

How long will it take to transmit a $1-$GB file from one VSAT to another using a hub

as shown in Figure $2-17?$ Assume that the uplink is $1$ Mbos, the downlink is $7$ Mbos,

and circuit switching is used with $1\mathrm{.}2$ sec circuit setup time.

To accommodate lower data rates than STS$-1,$ SONET has a system of virtual tributaries

$($VTs$).$ A VT is a partial payload that can be inserted into an STS$-1$ frame and

combined with other partial payloads to fill the data frame. VT$1\mathrm{.}5$ uses $3$ columns,

VT$2$ uses $4$ columns, VT$3$ uses $6$ columns, and VT$6$ uses $12$ columns of an STS$-1$

frame. Which VT can accommodate

$($a$)$ A DS$-1$ service $(1\mathrm{.}544$ Mbos$)?$

$($b$)$ European CEPT$-1$ service $(2\mathrm{.}048$ Mbps$)?$

$($c$)$ A DS$-2$ service $(6\mathrm{.}312$ MbDs$)?$

Three packet$-$switching networks each contain n nodes. The first network has a star

topology with a central switch, the second is a $($bidirectional$)$ ring, and the third is

fully interconnected, with a wire from every node to every other node. What are the

best$-,$ average$-,$ and worst$-$case transmission paths in hops?

Suppose that A$,$ B$,$ and C are simultaneously transmitting $0$ bits, using a CDMA system

with the chip sequences of Fig. $2-28($a$).$ What is the resulting chip sequence?

A cable company decides to provide Internet access over cable in a neighborhood consisting

of $5000$ houses. The company uses a coaxial cable and spectrum allocation allowing

$100$ Mbesdownstream bandwidth per cable. To attract customers, the company

decides to guarantee at least $2$ Mbps$,$ downstream bandwidth to each house at any

time. Describe what the cable company needs to do to provide this guarantee.

Using the spectral allocation shown in Fig. $2-52$ and the information given in the text,

how many Mbpar, does a cable system allocate to upstream and how many to downstream?