Successive Cancellation Automorphism List Decoding of Polar Codes

TL;DR

The paper introduces SCAL decoding, a novel automorphism-based method for polar codes that enhances error correction by adapting to channel conditions, outperforming traditional SCL and AED methods in efficiency and performance.

Contribution

It presents the SCAL decoding technique, integrating automorphisms into SCL decoding to improve error correction and efficiency in polar code decoding.

Findings

SCAL achieves near ML performance with fewer decoder cores.

ASIC implementation shows SCAL outperforms AED in energy and power efficiency.

SCL decoders with SCAL are more area-efficient than AED.

Abstract

The discovery of suitable automorphisms of polar codes gained a lot of attention by applying them in Automorphism Ensemble Decoding (AED) to improve the error-correction performance, especially for short block lengths. This paper introduces Successive Cancellation Automorphism List (SCAL) decoding of polar codes as a novel application of automorphisms in advanced Successive Cancellation List (SCL) decoding. Initialized with L permutations sampled from the automorphism group, a superposition of different noise realizations and path splitting takes place inside the decoder. In this way, the SCAL decoder automatically adapts to the channel conditions and outperforms the error-correction performance of conventional SCL decoding and AED. For a polar code of length 128, SCAL performs near Maximum Likelihood (ML) decoding with L=8, in contrast to M=16 needed decoder cores in AED. Application-Specific Integrated Circuit (ASIC) implementations in a 12 nm technology show that high-throughput, pipelined SCAL decoders outperform AED in terms of energy efficiency and power density, and SCL decoders additionally in area efficiency.