(a) Consider a real-time communication system operating over an AWGN channel that uses 8-PSK modulation with Gray coding. Select an error-correcting code that provides a decoded bit-error probability of at most 10' when the received Pr/N0 is 70 dB-Hz, and the data rate is 1 Mbit/s. You arc permitted to choose one of the following codes: (24. 12) Extended Golay, or (127. 64) BCH. or (127. 36) BCH. The input-output transfer functions for these codes appear in Figure 6.21. To guide you in making a selection, consider that at PH = 10-2. the transfer functions intercept the abscissa at the following points: the (24, 12) code intercepts at 3 x 10-3, the (127, 64) code intercepts at 1.3 x 104, and the (127. 36) BCH code intercepts at 3 x 10-2.
(b) The general appearance of the code transfer functions may have caused you to form an initial judgement as to which code is the best choice for the stated design requirements. Does your final choice agree with your initial guess? Do the results of part a) surprise you? Explain your results in the context of the two mechanisms at work when using error-correction coding in a real-time communication system. (c) How much coding gain in decibels does your code choice in part a) provide?