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Classification of Automorphisms for the Decoding of Polar Codes

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Abstract

This paper proposes new polar code design principles for the low-latency automorphism ensemble (AE) decoding. Our proposal permits to design a polar code with the desired automorphism group (if possible) while assuring the decreasing monomial property. Moreover, we prove that some automorphisms are redundant under AE decoding, and we propose a new automorphisms classification based on equivalence classes. Finally, we propose an automorphism selection heuristic based on drawing only one element of each class; we show that this method enhances the block error rate (BLER) performance of short polar codes even with a limited number of automorphisms.
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Dates and versions

hal-03617270 , version 1 (23-03-2022)

Identifiers

  • HAL Id : hal-03617270 , version 1

Cite

Charles Pillet, Valerio Bioglio, Ingmar Land. Classification of Automorphisms for the Decoding of Polar Codes. IEEE International Conference on Communications (ICC), May 2022, Seoul, South Korea. ⟨hal-03617270⟩
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