This paper proposes a novel transmission strategy, referred to as cocktail BPSK, where two independent BPSK symbols are layered with various weights to be transmitted and, capitalizing on the cross power utilization, will be demodulated at the receiver without interference from each other. To evaluate the performance of the proposed scheme, its achievable data rate is formulated over additive white Gaussian noise (AWGN) channels. Based on the theoretical analysis, numerical results are provided for the performance comparisons between the proposed scheme and conventional transmission schemes, which substantiate the validity of the proposed scheme. Specifically, when the signal-to-noise power ratio (SNR) is small, the achievable data rate of the proposed scheme outperforms the channel capacity achieved by Gaussian-distributed inputs.