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 $O\left(N^{1-1/\mu}+ \frac{N}{P}\log_{2}\log_{2}\frac{N}{P}\right)$ , where $N$ is the block length of the code and $\mu$ is the scaling exponent of polar codes for 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 an earlier work. Second, in a fully-serial implementation where $P=1$ , the latency of SSC decoding scales as $O(N\, \log_{2}\log_{2}N)$ . The multiplicative constant is also calculated: we show that the latency of SSC decoding when $P=1$ is given by $(2+o(1))N\, \log_{2}\log_{2}N$ . 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.