ELEC 456 - Mobile Communications
Assignment #3 - Due March 12, 1999

 

  1. For a 900 MHz signal, a vehicle speed of 50 km/hr, and a signal r.m.s. power of 1 mW, use the formulas in the notes to estimate the level crossing rates and the average duration of fades (Ez field only) for the following levels: -5 dB and -15 dB.
  2. The Golay (23,12,7) linear block code has 12 information bits, 11 redundant bits, and a minimum Hamming distance of 7. The file golay23.enc contains all 212 valid codewords with the 11 parity bits followed by the 12 information bits. The file golay23.dec contains all 211 syndromes and the corresponding error vectors with the 11-bit syndrome followed by the 23-bit error vector. For this file, the data is given as two hexadecimal words per line, so watch the bit boundaries!
    Compiling g23syn.c and running the executable will generate a syndrome from a codeword.
    a) What is the maximum number of errors that can be corrected?
    b) If the received hexdecimal word is 5177B9, find the syndrome, error vector, decoded codeword, corrected data vector, and the number of errors detected.
    c) Randomly choose a data vector, encode it, and apply two errors. Then, find the syndrome, error vector, decoded codeword, corrected data vector, and the number of bit errors detected.
    d) Repeat part (c) with the same data vector and four errors. Comment on the result.
  3. For the Golay (23,12,7) linear block code, compute the number of:
    a) zero-bit error vectors
    b) one-bit error vectors,
    c) two-bit error vectors, and
    d) three-bit error vectors.
    e) Compare the total of parts (a) through (d) to the total number of syndromes.