Performance Limits of Lattice Reduction over Imaginary Quadratic Fields with Applications to Compute-and-Forward
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In this work, we first examine both Hermite's constant and Minkowski's theorems in complex lattices, then investigate the proper design of a complex lattice reduction algorithm, which can be used to search the linear combination coefficients in compute-and-forward (C&F). In particular, we show that in the algebraic Lenstra-Lenstra-Lovász (A-LLL) reduction, to satisfy Lovász's condition requires the ring to be Euclidean. We also reveal the impact of chosen rings on the performance bounds of A-LLL.
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