  We show that for a relation $f\subseteq \{0,1\}^n\times \mathcal{O}$ and a
function $g:\{0,1\}^{m}\times \{0,1\}^{m} \rightarrow \{0,1\}$ (with $m= O(\log
n)$), $$\mathrm{R}_{1/3}(f\circ g^n) = \Omega\left(\mathrm{R}_{1/3}(f) \cdot
\left(\log\frac{1}{\mathrm{disc}(M_g)} - O(\log n)\right)\right),$$ where
$f\circ g^n$ represents the composition of $f$ and $g^n$, $M_g$ is the sign
matrix for $g$, $\mathrm{disc}(M_g)$ is the discrepancy of $M_g$ under the
uniform distribution and $\mathrm{R}_{1/3}(f)$ ($\mathrm{R}_{1/3}(f\circ g^n)$)
denotes the randomized query complexity of $f$ (randomized communication
complexity of $f\circ g^n$) with worst case error $\frac{1}{3}$.
  In particular, this implies that for a relation $f\subseteq \{0,1\}^n\times
\mathcal{O}$, $$\mathrm{R}_{1/3}(f\circ \mathrm{IP}_m^n) =
\Omega\left(\mathrm{R}_{1/3}(f) \cdot m\right),$$ where
$\mathrm{IP}_m:\{0,1\}^m\times \{0,1\}^m\rightarrow \{0,1\}$ is the Inner
Product (modulo $2$) function and $m= O(\log(n))$.
