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

While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit channels, finding optimal polar codes for cyclic-redundancy-check-aided successivecancellation list (CA-SCL) decoding in an efficient and scalable manner still awaits investigation. This paper first maps a polar code to a unique heterogeneous graph called the polar-code-construction message-passing (PCCMP) graph. Next, a heterogeneous graph-neural-network-based iterative messagepassing (IMP) algorithm is proposed which aims to find a PCCMP graph that corresponds to the polar code with minimum frame error rate under CA-SCL decoding. This new IMP algorithm's major advantage lies in its scalability power. That is, the model complexity is independent of the blocklength and code rate, and a trained IMP model over a short polar code can be readily applied to a long polar code's construction. Numerical experiments show that IMP-based polar-code constructions outperform classical constructions under CA-SCL decoding. In addition, when an IMP model trained on a length-128 polar code directly applies to the construction of polar codes with different code rates and blocklengths, simulations show that these polar-code constructions deliver comparable performance to the 5G polar codes. Yun Liao and John M. Cioffi are with the Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA (email: yunliao@stanford.edu; Seyyed Ali Hashemi is with Qualcomm Technologies, Inc., Santa Clara, CA 95051, USA (email: hashemi@qti.qualcomm.com). Hengjie Yang is with Qualcomm Technologies, Inc., San Diego, CA 92121, USA (email: hengjie.yang@ucla.edu).