The bimodal gaussian (BMG) distribution plays an important role representing the output of many stochastic information sources. In this paper we study the bimodal gaussian distribution as a mixture distribution resulting from mixing both discrete and continuous gaussian random variables (R.V.). This distribution is characterized with the mixture probability model with di erent moment. We argue the entropy of this R.V., consequently, we establish an information theoretic foundation for the recent signaling schemes such as subcarrier index modulation OFDM (SIM-OFDM) and spatial Multiple Input Multiple Output (MIMO) modulation.