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While constructing polar codes for successive-cancellation decoding can beimplemented efficiently by sorting the bit-channels, finding optimal polarcodes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL)decoding in an efficient and scalable manner still awaits investigation. Thispaper first maps a polar code to a unique heterogeneous graph called thepolar-code-construction message-passing (PCCMP) graph. Next, a heterogeneousgraph-neural-network-based iterative message-passing (IMP) algorithm isproposed which aims to find a PCCMP graph that corresponds to the polar codewith minimum frame error rate under CA-SCL decoding. This new IMP algorithm'smajor advantage lies in its scalability power. That is, the model complexity isindependent of the blocklength and code rate, and a trained IMP model over ashort polar code can be readily applied to a long polar code's construction.Numerical experiments show that IMP-based polar-code constructions outperformclassical constructions under CA-SCL decoding. In addition, when an IMP modeltrained on a length-128 polar code directly applies to the construction ofpolar codes with different code rates and blocklengths, simulations show thatthese polar code constructions deliver comparable performance to the 5G polarcodes.

Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach