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

Abstract

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.