A Weighted Sum Based Construction of PAC Codes

The polarization-adjusted convolutional (PAC) codes concatenate an outer convolutional transform with an inner polar transform to improve the error-correction performance of polar codes. In the short-to-medium codeword length regime, it can approach the normal approximation (NA) bound. However, its optimal rate-profile remains unknown. This letter proposes a new construction for PAC codes based on a weighted sum (WS) metric, which considers both the cutoff rates and the utilizations of the polarized subchannels. In comparison with the existing Reed-Muller (RM) rate-profiles, it can yield a flexible rate. By adjusting the design signal-to-noise ratio (SNR), an appropriate tradeoff between the decoding performance and complexity can be achieved. Simulation results show the designed codes can outperform the ones that are designed by the existing techniques.