increases. Focusing now on M-QAM and M-PSK, we observe from the figure that increasing ISD (though increasing M) requires higher SNRs. The SNR requirement increases far more rapidly with M-PSK. For instance, at SER = 10-3, , the formats 64-PSK and 64-QAM approximately require SNR = 26 dB and SNR = 15 dB, respectively, corresponding to an SNR difference of more than 10 dB. From this analysis, M-QAM appears to be the champion format in combined terms of ISD and SNR requirements. It is noteworthy that as M is increases, the iso-SER curves of M-QAM and M-PSK move closer to the SHT boundary, contrary to M-FSK. The closer any point in these curves get to 14.2 Nonlinear channel the SHT boundary, the more sensitive the system SER is to SNR and signal power. Also, the more complex the error-correction codes to bring the BER to low values. Given constraints in power and noise, in BER requirement after code correction, in code-correction complexity, and, finally, in modulation-format technologies, the difficult task for communications engineers is to find the right tradeoffs between academic and practical engineering solutions. Nonlinear channel Shannon's information theory and all its subsequent developments have always been based on the assumption of channel linearity. The principle of channel linearity can be summarized by two basic conditions: (a) Assuming signal input to the channel with power P, the signal output power is of the form P' = AP, where a is a real constant that is power independent (a < 1 for lossy channels, A = 1 for transparent or lossless channels, and a > 1 for channels with internal amplification or gain); (b) The channel noise N is added linearly to the signal power (additive noise), namely the total output power is of the form P" k P + uN, where u is a real constant that is power independent. Condition (a) implies that the signal can be increased to an arbitrarily high power level, without any changes in the channel's properties, as provided by information theory. Condition (b) implies that the tra