  The automorphism group of a code is the set of permutations of the codeword
symbols that map the whole code onto itself. For polar codes, only a part of
the automorphism group was known, namely the lower-triangular affine group
(LTA), which is solely based upon the partial order of the code's synthetic
channels. Depending on the design, however, polar codes can have a richer set
of automorphisms. In this paper, we extend the LTA to a larger subgroup of the
general affine group (GA), namely the block lower-triangular affine group
(BLTA) and show that it is contained in the automorphism group of polar codes.
Furthermore, we provide a low complexity algorithm for finding this group for a
given information/frozen set and determining its size. Most importantly, we
apply these findings in automorphism-based decoding of polar codes and report a
comparable error-rate performance to that of successive cancellation list (SCL)
decoding with significantly lower complexity.
