  Polar codes are constructed for arbitrary channels by imposing an arbitrary
quasigroup structure on the input alphabet. Just as with "usual" polar codes,
the block error probability under successive cancellation decoding is
$o(2^{-N^{1/2-\epsilon}})$, where $N$ is the block length. Encoding and
decoding for these codes can be implemented with a complexity of $O(N\log N)$.
It is shown that the same technique can be used to construct polar codes for
arbitrary multiple access channels (MAC) by using an appropriate Abelian group
structure. Although the symmetric sum capacity is achieved by this coding
scheme, some points in the symmetric capacity region may not be achieved. In
the case where the channel is a combination of linear channels, we provide a
necessary and sufficient condition characterizing the channels whose symmetric
capacity region is preserved by the polarization process. We also provide a
sufficient condition for having a maximal loss in the dominant face.
