  This paper characterizes the latency of the simplified
successive-cancellation (SSC) decoding scheme for polar codes under hardware
resource constraints. In particular, when the number of processing elements $P$
that can perform SSC decoding operations in parallel is limited, as is the case
in practice, the latency of SSC decoding is
$O\left(N^{1-1/\mu}+\frac{N}{P}\log_2\log_2\frac{N}{P}\right)$, where $N$ is
the block length of the code and $\mu$ is the scaling exponent of the channel.
Three direct consequences of this bound are presented. First, in a
fully-parallel implementation where $P=\frac{N}{2}$, the latency of SSC
decoding is $O\left(N^{1-1/\mu}\right)$, which is sublinear in the block
length. This recovers a result from our earlier work. Second, in a fully-serial
implementation where $P=1$, the latency of SSC decoding scales as
$O\left(N\log_2\log_2 N\right)$. The multiplicative constant is also
calculated: we show that the latency of SSC decoding when $P=1$ is given by
$\left(2+o(1)\right) N\log_2\log_2 N$. Third, in a semi-parallel
implementation, the smallest $P$ that gives the same latency as that of the
fully-parallel implementation is $P=N^{1/\mu}$. The tightness of our bound on
SSC decoding latency and the applicability of the foregoing results is
validated through extensive simulations.
