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 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 $O(N^{1-1/\mu })$ , 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 $O(N\log _{2}\log _{2} N)$ . 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.