CPS 214 Written Homework 2 - Fall 1997

Due: Wednesday, Oct. 1, 5:30 PM

15 points

  1. How many bits/sec can be sent if 4-level digital signals are used and the signal-to-noise ratio is 40 db?

  2. Does your answer to 1) change change if a 16-level signal is used?

  3. A noiseless 6-MHz channel is sampled every 1 msec. What is the maximum data rate?

  4. Why has the PCM sampling time been set to 125 microseconds?

  5. Is it possible to achieve a data rate of 512 kbps over a {\it noisy} satellite circuit that filters out all frequencies above 68 kHz and below 4 kHz? The channel has a signal-to-noise ratio of 40db.

  6. 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?

  7. Compare the delay in sending an x-bit message over a k-hop path in a circuit-switched network and in a (lightly loaded) packet-switched network. The circuit setup time is s sec, the propagation time is d seconds per hop, the packet size is p bits, and the data rate is b bps. Under what conditions does the packet network have a lower delay?

  8. Suppose that x bits of user data are to be transmitted over a K-hop path in a packet-switched network as a series of packets, each containing p data bits and h header bits, with x << p+h. The bit rate of the lines is b bps and the propagation delay is negligible. What value of p minimizes the total delay?

    Note: correction: the fragment x << p+h above should be x >> p+h

  9. Compute the checksum for the message ``1011011'' using the Generator polynomial ``1101''.

  10. An upper-layer message is split into 10 frames, each of which has an 80% chance of arriving undamaged. If no error control is done by the data link protocol, how many times must the message be sent on average to get the entire thing through?

  11. Consider the following 6-bit codeword of 6 distinct values:

    000000 110100 101010

    001101 110011 111111

    1. What is its Hamming distance?
    2. What is the maximum number of single-bit errors that the code guarantees to detect?
    3. What is the maximum number of single-bit errors that the code guarantees to correct?

  12. If the bit string 011110111110111111110 is bit stuffed, what is the output string?