6.37 Information communication problems  (Page 8/8)

Hdtv

As HDTV (high-definition television) was being developed, the FCC restricted this digital system to use in the samebandwidth (6 MHz) as its analog (AM) counterpart. HDTV video is sampled on a $1035\times 1840$ raster at 30 images per second for each of the three colors. The least-acceptable picture received bytelevision sets located at an analog station's broadcast perimeter has a signal-to-noise ratio of about 10 dB.

1. Using signal-to-noise ratio as the criterion, how many bits per sample must be used to guarantee that ahigh-quality picture, which achieves a signal-to-noise ratio of 20 dB, can be received by any HDTV set withinthe same broadcast region?
2. Assuming the digital television channel has the same characteristics as an analog one, how much compressionmust HDTV systems employ?

Digital cellular telephones

In designing a digital version of a wireless telephone, you must first consider certain fundamentals. First of all, thequality of the received signal, as measured by the signal-to-noise ratio, must be at least as good as thatprovided by wireline telephones (30 dB) and the message bandwidth must be the same as wireline telephone. Thesignal-to-noise ratio of the allocated wirelss channel, which has a 5 kHz bandwidth, measured 100 meters from thetower is 70 dB. The desired range for a cell is 1 km. Can a digital cellphone system be designed according to thesecriteria?

Optimal ethernet random access protocols

Assume a population of $N$ computers want to transmit information on a random access channel. The access algorithm works as follows.

• Before transmitting, flip a coin that has probability $p$ of coming up heads
• If only one of the $N$ computer's coins comes up heads, its transmission occurs successfully, and the others must wait until thattransmission is complete and then resume the algorithm.
• If none or more than one head comes up, the $N$ computers will either remain silent (no heads) or a collision will occur (morethan one head). This unsuccessful transmission situation will be detected by all computers once thesignals have propagated the length of the cable, and the algorithm resumes (return to the beginning).

1. What is the optimal probability to use for flipping the coin? In other words, what should $p$ be to maximize the probability that exactly one computer transmits?
2. What is the probability of one computer transmitting when this optimal value of $p$ is used as the number of computers grows to infinity?
3. Using this optimal probability, what is the average number of coinflips that will be necessary to resolve the access so that one computer successfully transmits?
4. Evaluate this algorithm. Is it realistic? Is it efficient?

Repeaters

Because signals attenuate with distance from the transmitter, repeaters are frequently employed for both analog and digital communication. For example, let's assume that thetransmitter and receiver are $D$  m apart, and a repeater is positioned halfway between them ( [link] ). What the repater does is amplify its received signal to exactly cancel the attenuationencountered along the first leg and to re-transmit the signal to the ultimate receiver. However, the signal therepeater receives contains white noise as well as the transmitted signal. The receiver experiences the same amountof white noise as the repeater.

1. What is the block diagram for this system?
2. For an amplitude-modulation communication system, what is the signal-to-noise ratio of the demodulated signal atthe receiver? Is this better or worse than the signal-to-noise ratio when no repeater is present?
3. For digital communication, we must consider the system's capacity. Is the capacity larger with therepeater system than without it? If so, when; if not, why not?

Designing a speech communication system

We want to examine both analog and digital communication alternatives for a dedicated speech transmission system. Assume the speech signal has a 5 kHz bandwidth.The wireless link between transmitter and receiver is such that 200 watts of power can be received at a pre-assigned carrier frequency. We have some latitude in choosing the transmission bandwidth, but the noise power added by the channel increases with bandwidth with a proportionality constant of 0.1 watt/kHz.

1. Design an analog system for sending speech under this scenario. What is the received signal-to-noise ratio under these design constraints?
2. How many bits must be used in the A/D converter to achieve the same signal-to-noise ratio?
3. Is the bandwidth required by the digital channel to send the samples without error greater or smaller than the analog bandwidth?

Digital vs. analog

You are the Chairman/Chairwoman of the FCC. The frequency band 3 MHz to 3.5 MHz has been allocated for a new “high-quality” AM band.Each station licensed for this band will transmit signals having a bandwidth of 10 kHz, twice the message bandwidth of what current stations can send.

1. How many stations can be allocated to this band and with what carrier frequencies?
2. Looking ahead, conversion to digital transmission is not far in the future. The characteristics of the new digital radio system need to be established and you are the boss!Detail the characteristics of the analog-to-digital converter that must be used to prevent aliasing and ensure a signal-to-noise ratio of 25 dB.
3. Without employing compression, how many digital radio stations could be allocated to the band if each station used BPSK modulation? Evaluate this design approach.