Page 368 - Satellite Communications, Fourth Edition

348 Chapter Eleven

11.19. For the signal in Prob. 11.18, calculate the new value of bit error
probability if FEC is applied at a code rate of 3/4, given that the carrier power
remains unchanged.
11.20. Derive Eq. (11.11).

11.21. Explain what is meant by coding gain as applied to error correcting
coding. When FEC coding is used on a digital link, a coding gain of 3 dB is
achieved for the same BER as the uncoded case. What decibel reduction in
transmitted carrier power does this imply?

11.22. A certain (15, 11) block code is capable of correcting one error at most.
Given that this is a perfect code (see Sec. 11.8), plot, on the same set of axes,
the BER for the coded and uncoded cases for an [E b /N 0 ] range of 2 to 12 dB.
6
Calculate the coding gain at a BER of 10 .
11.23. State briefly the difference between hard and soft decision decoding.
Following the description given in Sec. 11.9, determine the output produced by
(a) hard decision and (b) soft decision decoding when the sampled signal from
the demodulator is 0.4 V, 0.85 V, and 0.4 V for triple redundancy coding.

11.24. From Fig. 11.10 find the minimum [E b /N 0 ] as determined by the
Shannon limit curve. Explain the significance of this.

11.25. For equiprobable bit transmission a received bit level is 0.55V. Assuming
this is normalized where 1V represents a certainty of the bit being a 1, calculate
the LLR.

11.26. Referring to Eq. (11.26), identify the parity equations which contain code
bit c 7 .

11.27. Complete the Tanner graph of Fig. 11.13 for all the parity equations
given in Eq. 11.26.

1
11.28. For the parity equation for row 5, (Eq. 11.26) the probabilities are: p 5
1
1
0.7, p 8 0.6, p 14 0.3. Calculate the estimated probability p 2 .
11.29. Research the literature and write brief comparative notes on the use of
turbo codes and LDPC codes in satellite communications.
11.30. A (31, 6) block code is used in an ARQ scheme. Determine the upper
bound on the probability of bit error.

References

Berrou, C., A. Glavieux, and P. Thitmajshima. 1993. “Near Shannon Limit error-correcting
coding: Turbo codes.” Proc. of the IEEE Int. Conf. Commun., Switzerland, at
www-elec.enst-bretagne.fr/equipe/berrou/Near%20Shannon%20Limit%20Error.pdf