  A method is proposed, referred to as the cocktail BPSK, to use two
independent BPSK streams layered in a parallel transmission through the
additive white Gaussian channel. The critical point of the method is to
translate the interference between the two layered symbols into a problem of
one symbol with two possible amplitudes, whereby we find that the achievable
data rate (ADR) of the first layer equals to the channel capacity at zero
signal-to-noise-ratio limit. By adding the contribution of the second layer, we
find that the total ADR of the two layers can be larger than the channel
capacity. The theoretical proof is done based on the mutual information and the
numerical results are added for the confirmation.
