  In this letter, we explore the performance limits of short polar codes and
find that the maximum likelihood (ML) performance of a simple CRC-polar
concatenated scheme can approach the finite blocklength capacity. Then, in
order to approach the ML performance with a low average complexity, a CRC-aided
hybrid decoding (CA-HD) algorithm is proposed and its decoding process is
divided into two steps. In the first step, the received sequence is decoded by
the adaptive successive cancellation list (ADSCL) decoding. In the second step,
CRC-aided sphere decoding with a reasonable initial radius is used to decode
the received sequence. To obtain the reasonable radius, the CRC bits of the
survival paths in ADSCL are recalculated and the minimum Euclidean distance
between the survival path and the received sequence is chosen as the initial
radius. The simulation results show that CA-HD can achieve within about
$0.025$dB of the finite blocklength capacity at the block error ratio $10^{-3}$
with code length $128$ and code rate $1/2$.
