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(N1-1/μ+N/Plog2 log2N/P), where N is the block length of the code and μ is the scaling exponent of the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where P=N/2, the latency of SSC decoding is O(N1-1/μ), 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 log2 log2 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 log2log2 N. Third, in a semi-parallel implementation, the smallest P that gives the same latency as that of the fully-parallel implementation is P=N1/μ. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.