Long Polar vs. LDPC Codes under Complexity-Constrained Decoding

TL;DR

This paper demonstrates that with limited decoding complexity, long polar codes under simplified successive cancellation decoding outperform LDPC codes, challenging the common belief about their relative performance at large block lengths.

Contribution

The study shows that under fixed complexity constraints, polar codes with SSC decoding outperform LDPC codes, providing a new perspective on their comparative efficiency.

Findings

Polar codes outperform LDPC codes under fixed complexity constraints.

SSC decoding of polar codes has better complexity scaling than $N \,\log{N}$.

Fewer operations are needed for polar codes than a single LDPC BP iteration.

Abstract

The prevailing opinion in industry and academia is that polar codes are competitive for short code lengths, but can no longer keep up with low-density parity-check (LDPC) codes as block length increases. This view is typically based on the assumption that LDPC codes can be decoded with a large number of belief propagation (BP) iterations. However, in practice, the number of iterations may be rather limited due to latency and complexity constraints. In this paper, we show that for a similar number of fixed-point log-likelihood ratio (LLR) operations, long polar codes under successive cancellation (SC) decoding outperform their LDPC counterparts. In particular, simplified successive cancellation (SSC) decoding of polar codes exhibits a better complexity scaling than $N \log{N}$ and requires fewer operations than a single BP iteration of an LDPC code with the same parameters.