  Polar codes are one of the most recent advancements in coding theory and they
have attracted significant interest. While they are provably capacity achieving
over various channels, they have seen limited practical applications.
Unfortunately, the successive nature of successive cancellation based decoders
hinders fine-grained adaptation of the decoding complexity to design
constraints and operating conditions. In this paper, we propose a systematic
method for enabling complexity-performance trade-offs by constructing polar
codes based on an optimization problem which minimizes the complexity under a
suitably defined mutual information based performance constraint. Moreover, a
low-complexity greedy algorithm is proposed in order to solve the optimization
problem efficiently for very large code lengths.
