Table 12.5 gives a short list of rate 1/2 and rate 3/4 BCH codes. Using the Torrieri bound and an appropriate MATLAB program, plot together on a single set of axes the bit error probability for the rate 1/2 BCH codes having block length n = 7, 15, 31, and 63. Assume PSK modulation with matched-filter detection. Repeat for rate 3/4 BCH codes having block length n = 15,31, 63, and 127. What conclusions can you draw from this exercise?

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Table 12.5 Short List of BCH Codes Rate 1/2 codes Rate 23/4 codes Rate Rate k k п 0.7333 4 0.5714 15 11 0.4667 0.6774 0.7143 0.7795 15 31 21 31 16 3 0.5161 63 45 3 0.4762 0.5039 63 30 127 99 4 0.7490 127 64 10 255 191 511 1023 255 131 18 0.5137 385 14 0.7534 511 259 30 0.5068 768 26 0.7507