PAC Code Rate-Profile Design Using Search-Constrained Optimization Algorithms

In this paper, we introduce a novel rate-profile design based on search-constrained optimization techniques to assess the performance of polarization-adjusted convolutional (PAC) codes under Fano (sequential) decoding. The results demonstrate that the optimized PAC code offers much reduced computational complexity compared to a construction based on a conventional genetic algorithm without a loss in error-correction performance. We propose an adaptive successive cancellation list decoding algorithm as the fitness function of our algorithm to determine the weight distribution of the rate profiles. The simulation results indicate that, for a PAC(256, 128) code, only 8% of the population requires that their fitness function be evaluated with a large list size. This represents an improvement of almost 92% over a conventional evolutionary algorithm. For a PAC(64, 32) code, this improvement is about 99%. We also consider high-rate PAC(128, 105) and PAC(64, 51) codes, showing superior performance compared to other existing algorithms.