  Polar codes are a class of capacity-achieving error correcting codes that
have been selected for use in enhanced mobile broadband in the 3GPP 5th
generation (5G) wireless standard. Most polar code research examines the
original Arikan polar coding scheme, which is limited in block length to powers
of two. This constraint presents a considerable obstacle since practical
applications call for all code lengths to be readily available. Puncturing and
shortening techniques allow for flexible polar codes, while multi-kernel polar
codes produce native code lengths that are powers of two and/or three. In this
work, we propose a new low complexity coding scheme called asymmetric polar
coding that allows for any arbitrary block length. We present details on the
generator matrix, frozen set design, and decoding schedule. Our scheme offers
flexible polar code lengths with decoding complexity lower than equivalent
state-of-the-art length-compatible approaches under successive cancellation
decoding. Further, asymmetric decoding complexity is directly dependent on the
codeword length rather than the nearest valid polar code length. We compare our
scheme with other length matching techniques, and simulations are presented.
Results show that asymmetric polar codes present similar error correction
performance to the competing schemes, while dividing the number of SC decoding
operations by up to a factor of 2 using the same codeword length
