Intra-Body Communication (IBC), which employs the human body as the channel to transmit health informatics, is a potential approach for connecting wearable and implantable devices. Undoubtedly, its channel characteristics provide deep insights to select parameters that are beneficial for the physical layer design of the Body Area Network (BAN). Nevertheless, such analysis has not been systematically addressed. To this end, the transfer function from the quasi-static model in the electromagnetic field is considered at first. Then, the linearity of the galvanic coupling IBC channel is verified. Besides, the proper frequency band for data transmission is investigated using the water-filling algorithm. Moreover, the theoretical Bit Error Rate (BER) performances of different modulations are studied. Results revealed that the galvanic coupling IBC channel can be modeled as a linear band-limited Additive White Gaussian Noise (AWGN) channel. Finally, suitable modulations for various scenarios are discussed based on the channel characteristics found. Consequently, this work can further enrich the design of the IBC for medical applications.