Approximate Perturbation Aided Lattice Encoding (APPLE) for G.fast and Beyond

G.fast suffers from strong far-end crosstalk at high frequencies in cable binders containing a large number of twisted copper pairs. For the 212-MHz G.fast spectrum, the power penalty incurred by the conventional zero-forcing precoding-based linear vectoring (LV) scheme is far more substantial than it was over the 30-MHz VDSL2 spectrum. In this paper, we propose a novel non-LV (NLV) scheme based on Babai's nearest plane approximation of the closest lattice point problem on the reduced lattice basis. Similar to the conventional Tomlinson-Harashima precoding (THP)-based NLV, the proposed approximate perturbation aided lattice encoding (APPLE) scheme closely approaches the dirty paper coding capacity which provided that the system employs a fully rate-adaptive power allocation policy per tone per pair. However, if the system employs a scalar power policy that is only rate-adaptive with respect to each tone, APPLE becomes capable of achieving a higher throughput per binder than THP. APPLE's transmitter complexity is considerably lower than that of the conventional lattice encoding schemes (e.g., vector perturbation) and comparable to that of THP.