 = 144 = +21.58 dB. Note that different SNR definitions apply to optical telecommunication systems. A standard definition is SNR 2 Q2, which gives SNR 2 +15.5 dB for BER = 10-9. Gaussian channel and Shannon-Hartley theorem Operating SNR = 16.6 dB Coding gain = +5 dB BER = 10-3.5 After Before correction correction BER = 10-9 SNR bit (dB) Figure 14.4 Illustration of the effect of error-correction coding (ECC) on the BER performance (NRZ/OOK), showing a coding gain of +5 dB improving the BER from BER = 10-3.5 to BER = M-ary frequency-shift-keying (M-FSK) format The M-ary frequency-shift-keying (M-FSK) format is based on multi-level frequency modulation, where M is a power of two, and coherent detection. The ISD asso- ciated with M-ary FSK modulation is given by ISD = (21og M)/M. Hence, for M = 2, 4, 8, 16, 32, 64, 128 we have ISD = 1, 1, 0.75, 0.5, 0.31, 0.18, 0.1 (bit/s)/Hz, respectively. The ISD, thus, decreases as the number of modulation levels M increases, which is a drawback specific to this modulation format, which is not bandwidth efficient. The symbol error rate (SER) of M-FSK signals is given by the following approximation (valid for SER < 10-3): (14.24) M-ary phase-shift-keying (M-PSK) format The M-ary phase-shift-keying (M-PSK) format is based on multi-level phase modula- tion. Like M-FSK, it requires coherent detection. The ISD associated with M-ary PSK modulation is given by ISD = log2 M, which shows that it increases with M. Hence, for M = 2, 4, 8, 16, 32, 64, 128 we have ISD = 1, 2, 3, 4, 5, 6, 7 (bit/s)/Hz, respectively. The SER of M-PSK signals is given by: SER = (14.25) 14.1 Gaussian channel M-ary quadrature amplitude modulation (M-QAM) format The M-ary quadrature amplitude modulation (M-QAM) format is based on coherent multi-level amplitude modulation, using the combination of two quadratures. 10 As in the previous case, the ISD associated with M-ary QAM modulation is ISD = log2 M. The SER of M-QAM signals is given by: (14.26) where (SNRbit) represents the average bit SNR. This averaging is requi