  Polar code visibly approaches channel capacity in practice and is thereby a
constituent code of the 5G standard. Compared to low-density parity-check code,
however, the performance of short-length polar code has rooms for improvement
that could hinder its adoption by a wider class of applications. As part of the
program that addresses the performance issue at short length, it is crucial to
understand how fast binary memoryless symmetric channels polarize. A number,
called scaling exponent, was defined to measure the speed of polarization and
several estimates of the scaling exponent were given in literature. As of 2022,
the tightest overestimate is 4.714 made by Mondelli, Hassani, and Urbanke in
2015. We lower the overestimate to 4.63.
