  Automorphism ensemble (AE) decoding for polar codes was proposed by decoding
permuted codewords with successive cancellation (SC) decoders in parallel and
hence has lower latency compared to that of successive cancellation list (SCL)
decoding. However, some automorphisms are SC-invariant, thus are redundant in
AE decoding. In this paper, we find a necessary and sufficient condition
related to the block lower-triangular structure of transformation matrices to
identify SC-invariant automorphisms. Furthermore, we provide an algorithm to
determine the complete SC-invariant affine automorphisms under a specific polar
code construction.
