|| On the Automorphism Group of Polar Codes
||Marvin Geiselhart, Ahmed Elkelesh, Moustafa Ebada, Sebastian Cammerer, Stephan ten Brink, University of Stuttgart, Germany|
||D3-S4-T2: Polar Codes I
||Wednesday, 14 July, 23:00 - 23:20
||Wednesday, 14 July, 23:20 - 23:40
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.