Constituent Automorphism Decoding of Reed-Muller Codes

Abstract

Inspired by a state-of-the-art decoder for Reed–Muller (RM) codes called automorphism ensemble (AE) decoding, constituent automorphism (CA) decoding, a new decoding algorithm for RM codes is devised in this thesis. Unlike AE decoders, which only focus on the RM code itself, CA decoders distribute decoding resources to crucial constituent codes, making the decoding process more efficient. This thesis analyzes the complexity of several decoders for RM codes and compares their performance-complexity tradeoffs. Software simulations show that the best CA decoders for high-order (r ≥ 4, m ≥ 7) RM codes achieve a gain with at least 0.2 dB compared with AE decoders of the same complexity.