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arXiv · 2306.16245

Successive Cancellation Automorphism List Decoding of Polar Codes

Lucas Johannsen·Claus Kestel·Marvin Geiselhart·Timo Vogt·Stephan ten Brink·Norbert Wehn
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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.

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Lucas Johannsen, Claus Kestel, Marvin Geiselhart, Timo Vogt, Stephan ten Brink, Norbert Wehn. 2023-06-28. Successive Cancellation Automorphism List Decoding of Polar Codes. https://arxiv.org/abs/2306.16245

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