  Let $\mathsf{N}_{\rm d}\left[X\right]=\frac{1}{2\pi {\rm e}}{\rm
e}^{2\mathsf{H}\left[X\right]}$ denote the entropy power of the discrete random
variable $X$ where $\mathsf{H}\left[X\right]$ denotes the discrete entropy of
$X$. In this paper, we show that for two independent discrete random variables
$X$ and $Y$, the entropy power inequality $\mathsf{N}_{\rm
d}\left[X\right]+\mathsf{N}_{\rm d}\left[Y\right]\leq 2 \mathsf{N}_{\rm
d}\left[X+Y\right]$ holds and it can be tight. The basic idea behind the proof
is to perturb the discrete random variables using suitably designed continuous
random variables. Then, the continuous entropy power inequality is applied to
the sum of the perturbed random variables and the resulting lower bound is
optimized.
