Evolutionary Random Walk Aided Stochastic Sphere Encoder for Broadband G.mgfast

The next generation digital subscriber line (DSL) standard G.mgfast introduces far stronger co-channel interference termed as far-end crosstalk (FEXT) than the existing ones. Given perfect transmitter-side channel state information (CSIT), it is well known that the lattice-reduction-aided ${\mathcal{K}}$-best sphere encoder (LR-KBSE) is a near-optimal transmit precoding (TPC) technique compared to the classic (LR-) depth-first sphere encoder (DFSE), albeit having significantly lower complexity than the latter. However, the decision feedback precoding (DFP) structure and the Schnorr-Euchner enumeration procedure, both perceived as state-of-the-art in the literature, are not provably optimal for solving the closest vector problem (CVP) embedded in sphere encoding. As a counterexample, this paper proposes a stochastic sphere encoder (SSE) relying on differential evolution aided random walk over lattices. The parallel processing complexity, memory efficiency and signal to noise ratio (SNR) improvement of the proposed SSE are all shown to be superior to the LR-KBSE for G.mgfast systems.