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.