  We explore the relationship between polar and RM codes and we describe a
coding scheme which improves upon the performance of the standard polar code at
practical block lengths. Our starting point is the experimental observation
that RM codes have a smaller error probability than polar codes under MAP
decoding. This motivates us to introduce a family of codes that "interpolates"
between RM and polar codes, call this family ${\mathcal C}_{\rm inter} =
\{C_{\alpha} : \alpha \in [0, 1]\}$, where $C_{\alpha} \big |_{\alpha = 1}$ is
the original polar code, and $C_{\alpha} \big |_{\alpha = 0}$ is an RM code.
Based on numerical observations, we remark that the error probability under MAP
decoding is an increasing function of $\alpha$. MAP decoding has in general
exponential complexity, but empirically the performance of polar codes at
finite block lengths is boosted by moving along the family ${\mathcal C}_{\rm
inter}$ even under low-complexity decoding schemes such as, for instance,
belief propagation or successive cancellation list decoder. We demonstrate the
performance gain via numerical simulations for transmission over the erasure
channel as well as the Gaussian channel.
