Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes

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 $Oleft(N^{1-1/mu}+frac{N}{P}log_2log_2frac{N}{P}right)$, 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 $Oleft(N^{1-1/mu}right)$, 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 $Oleft(Nlog_2log_2 Nright)$. The multiplicative constant is also calculated: we show that the latency of SSC decoding when $P=1$ is given by $left(2+o(1)right) Nlog_2log_2 N$. 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.