Sublinear Latency for Simplified Successive Cancellation Decoding of Polar Codes

TL;DR

This paper demonstrates that simplified successive cancellation decoding for polar codes achieves sublinear latency, significantly reducing decoding time compared to traditional methods, especially through parallel decoding of certain subcodes.

Contribution

It establishes a theoretical bound on SSC decoding latency, showing it is sublinear in block length, and validates this with numerical results highlighting practical latency improvements.

Findings

Latency of SSC decoding is $O(N^{1-1/})$

Most latency reduction comes from parallel decoding of subcodes

Numerical results confirm the tightness of the theoretical bound

Abstract

This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is $O(N^{1-1/\mu})$, where $N$ is the block length and $\mu$ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate $0$ or $1$.