Complexity-constrained lattices for communications and signal processing

Research Project, 2026 – 2029

Lattices are regular geometric structures with a wide range of applications in communications and signal processing, from coding and modulation to data compression, pattern recognition, and sampling. The performance of lattice-based applications generally improves with the lattice dimension. Extensive research has been devoted to finding optimal lattices in each dimension, according to various performance criteria. However, the complexity of processing optimal lattices, for example searching for the closest point or shortest vector, also increases with the dimension, which limits their practical usage to low dimensions.Instead of selecting the highest dimension for which the processing complexity of optimal lattices is manageable, which is the mainstream approach, we will in this project explore suboptimal lattices in higher dimensions that enable low-complexity processing algorithms. In other words, we will design lattices and algorithms jointly under a complexity constraint, rather than a sequential design of first lattice (considering only performance) and then algorithms.As proof of concept, we will demonstrate solutions in selected applications where suboptimal lattices outperform optimal lattices in lower dimensions, at comparable processing complexities. In the long term, we envision a paradigm shift in applied lattice theory, paving the way for advances also in lattice applications beyond the scope of this project.