Page 367 - Satellite Communications, Fourth Edition

Error Control Coding 347

11.5. Using the generator matrix given in Eq. (11.3) find the codewords for the
datawords (a) [0000]; (b) [1111]; and (c) [0010].

11.6. Using the parity check matrix of Eq. (11.5) find the syndrome for the
codeword (1110100). Comment on this.

11.7. Using the parity check matrix of Eq. (11.5) find the syndrome for the
codeword (1000110). Comment on this.
11.8. A received codeword is 1011000. Determine, using the parity check matrix
of Eq. (11.5) if this is a valid codeword, and if not, write out the error vector on
the assumption that only one error is present.

11.9. Calculate the code rate for a Hamming (31, 26) code.

11.10. Calculate the code rate and the number of errors that can be corrected
with a BCH (63, 36) code.

11.11. An R-S code is byte oriented with k 8. Given that there are eight
redundant symbols, calculate the number of symbol errors that can be corrected.

11.12. Determine the values for N′ and K′ for the shortened R-S codes used in
(a) DirecTV and (b) DVB.

11.13. Describe how convolution coding is achieved. State some of the main
advantages and disadvantages of this type of code compared with block
codes.

11.14. Explain what is meant by interleaving when applied to error control
coding and why this might be used.

11.15. Explain what is meant by concatenated codes and why these might be
used.

11.16. Explain what is meant by a FEC code. FEC coding at a code rate of 3/4
is used in a digital system. Given that the message bit rate is 1.544 Mb/s,
calculate the transmission rate.

11.17. The bit rate for a baseband signal is 1.544 Mb/s, and FEC at a code rate
of 7/8 is applied before the signal is used to modulate the carrier. Given that the
system uses raised-cosine filtering with a rolloff factor of 0.2, determine the
bandwidth required for (a) BPSK, and (b) QPSK.

11.18. A BPSK signal provides an [E b /N 0 ] of 9 dB at the receiver. Calculate the
probability of bit error.