The channel conditions vary over time in wireless communications. In order to transmit information efficiently, digital wireless communication systems choose the modulation scheme and coding adaptively. This framework is called the adaptive modulation and coding (AMC). The key problem of the framework is how to design the switching strategy. In this paper, we discuss the practical strategy for AMC by comparing the channel capacity, achievable rates with common modulation schemes, and the actual rates with AMC. The channel capacity is defined for a combination of the noisy channel and the constraint on the information source. The noisy channel we assume in this paper is the discrete-time complex-valued additive white Gaussian noise channel (AWGNC). For the constraint, we focus on the peak power instead of the average power since a practical communication transmitter often suffers from the peak power. We compare the capacity and achievable rates with practical modulation schemes. Furthermore, we simulate AMC and evaluate the actual rates numerically.