Polarization-Adjusted Convolutional (PAC) Lattices: Construction and Gaussian Shaping
Junjiang Yu, Линг Лиу, Baoming Bai · 2024
In this paper, we introduce a novel type of lattices called PAC lattices, which are derived from polarization-adjusted convolutional (PAC) codes. The PAC lattices are designed to address the performance degradation observed in polar lattices at short-to-medium block lengths. First, we construct a set of nested PAC codes in accordance with the lattice construction approach of Forney et al., which employs nested linear codes to construct lattices. Second, we integrate PAC channel coding and PAC source coding to achieve non-uniform signaling, which can be used to implement Gaussian shaping and therefore satisfy the power constraint. Numerical results show that the proposed PAC lattices outperform polar lattices at short-to-medium block lengths while maintaining identical encoding and decoding complexity.