New Search for the Polarization-Adjusted Convolutional Codes with Respect to the AFER-Optimality Criterion
Murad Abdullah, Wai Ho Mow · 2023
Polarization-adjusted convolutional (PAC) codes of short blocklengths over the binary-input additive white Gaussian noise channel have excellent performance. To further improve the performance of the PAC codes, we adopt the asymptotic frame error rate (AFER) optimality criterion, i.e., the primary and secondary criteria are to maximize the minimum Hamming distance and to minimize the error coefficient of the code, respectively.In this paper, we conduct a new optimization search using a graphic processing unit that jointly optimizes the rate profile and the convolutional transform of a PAC code. Our search has discovered many short record-breaking binary linear block codes (representable as PAC codes) which achieve smaller error coefficients at the same best-known minimum distance compared to the best records in the literature. In particular, at a frame error rate of 10−9, an optimized [64, 32] PAC code with a minimum distance of 12 outperforms the best-known counterpart by 0.40 dB and is 1.1 dB away from the Polyanskiy-Poor-Verdú bound.