CS656 Homework #1, Due March 10th

Total 150 points.

  1. (21pt) Give a one or two sentence description of each of the seven layers of the OSI reference model.

  2. (9pt) Draw the bipolar encoding of 0, 1, 1, 0, 0, 1, 0, 0, and 1. The first one is negative.

  3. Consider a communication medium with bandwidth H=1MHz, S/N = 25dB. and 12 signaling elements. Answer the following questions.
    (a) (8pt) Caculate the maximum data rate of this medium according to Nyquist theorem
    (b) (8pt) Determine the maximum data rate according to Shannon's theorem ?
    (c) (4pt) To the best of our knowledge, what is the maximum data rate of the medium.

  4. (6pt) Give two advantages of digital transmissions over analogue transmissions.

  5. (4pt) What is the primary disadvantage of Manchester encoding compared to NRZ ?

  6. (10pt) Consider a variation of the T1 line, called Tx. A Tx line has 8000 frames per second. Like the T1 line, each frame includes 24 slots plus a delimeter bit at its end. Unlike the T1 line, each slot contains an 8-bit PCM code plus a parity bit. Calculate the data rate of Tx.

  7. (8pt) Give an 8-bit sequence that results in the fastest modulation rate with Manchester encoding (that is, maximum numbers of signal changes).

  8. (7pt) Give an 8-bit sequence that resultsin the slowest modulation rate with delay modulation (smallest numbers of signal changes).

  9. (15pt) Using the generator G(x)=x^7 + x^6 + x^2 + 1 to compute the CRC checksum of 1101000010101. Give T(x) too.
  10. (15pt) Compute the Hamming code of 001010001010

  11. (10pt) A one-bit transmission error occurs to a hamming code. The incorrect code is 0000010000000000. Correct the error and give only the data bits (that is, without check bits).

  12. Consider a coding scheme X where the minimum distance between any pair of valid codewords is 6.
    (a) (3pt) Calculate the number of bit errors X can correct.
    (b) (2pt) Calculate the number of bit errors X can detect.

  13. (20pt) Dr. Y. Huang proposes a 10Base-YH Ethernet standard that supports the network diameter of 5000 meters by cascading 10 500-meters cable segments with 9 repeaters. The signal propagation speed is 2x10^8 meters/second. Per repeater delay is 0.5 microsecond. Minimum frame length is 72 bytes. Determine whether collision detection works with 10Base-YH. Calculations are mandatory.