Genetic Algorithm-based Polar Code Construction for the AWGN Channel

We propose a new polar code construction framework (i.e., selecting the
frozen bit positions) for the additive white Gaussian noise (AWGN) channel,
tailored to a given decoding algorithm, rather than based on the (not
necessarily optimal) assumption of successive cancellation (SC) decoding. The
proposed framework is based on the Genetic Algorithm (GenAlg), where
populations (i.e., collections) of information sets evolve successively via
evolutionary transformations based on their individual error-rate performance.
These populations converge towards an information set that fits the decoding
behavior. Using our proposed algorithm, we construct a polar code of length
2048 with code rate 0.5, without the CRC-aid, tailored to plain successive
cancellation list (SCL) decoding, achieving the same error-rate performance as
the CRC-aided SCL decoding, and leading to a coding gain of 1 dB at BER of
$10^{-6}$. Further, a belief propagation (BP)-tailored polar code approaches
the SCL error-rate performance without any modifications in the decoding
algorithm itself.