For Reed-Muller codes of length 2^m, the RPA decoder provably achieves vanishing error probability over the binary symmetric channel for code orders that grow at most like a constant times log m.
A performance comparison of polar codes and Reed-Muller codes,
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An Analysis of RPA Decoding of Reed-Muller Codes Over the BSC
For Reed-Muller codes of length 2^m, the RPA decoder provably achieves vanishing error probability over the binary symmetric channel for code orders that grow at most like a constant times log m.