Error Performance Analysis of the Symbol-Decision SC Polar Decoder

TL;DR

This paper demonstrates that symbol-decision successive cancellation decoding for polar codes outperforms bit-decision decoding in FER performance, especially with larger symbol sizes, supported by theoretical proofs and simulations.

Contribution

It proves that symbol-decision SC decoding improves FER over bit-decision decoding for polar codes and shows larger symbols yield better performance.

Findings

Symbol-decision SC decoding outperforms bit-decision SC decoding in FER.

Larger symbol sizes lead to better FER performance.

Simulation results confirm theoretical analysis.

Abstract

Polar codes are the first provably capacity-achieving forward error correction codes. To improve decoder throughput, the symbol-decision SC algorithm makes hard-decision for multiple bits at a time. In this paper, we prove that for polar codes, the symbol-decision SC algorithm is better than the bit-decision SC algorithm in terms of the frame error rate (FER) performance because the symbol-decision SC algorithm performs a local maximum likelihood decoding within a symbol. Moreover, the bigger the symbol size, the better the FER performance. Finally, simulation results over both the additive white Gaussian noise channel and the binary erasure channel confirm our theoretical analysis.