🤖 AI Summary
This paper addresses the fundamental performance limits of lattice decoders under finite power constraints. We propose a genie-aided decoding framework and jointly optimize the real-valued scaling factor α and Voronoi-region covering-sphere geometry to derive, for the first time, a theoretical word error rate (WER) lower bound applicable to arbitrary lattices—including classical ones such as E₈ and BW₁₆—along with a closed-form high-SNR asymptotic expression. Furthermore, we introduce an efficient WER estimation method based on the effective sphere, significantly improving prediction accuracy: at a target WER of 10⁻⁴, E₈ and BW₁₆ achieve coding gains of 0.5 dB and 0.4 dB, respectively. Finally, integrating α-MMSE scaling, CRC embedding, and polar lattice codes, we design a prototype decoder with blocklength n = 128, experimentally validating the achievability of the derived theoretical bounds in practical constructions.
📝 Abstract
A genie-aided decoder for finite dimensional lattice codes is considered. The decoder may exhaustively search through all possible scaling factors $alpha in {mathbb{R}}$. We show that this decoder can achieve lower word error rate (WER) than the one- shot decoder using αMMSE as a scaling factor. A lower bound on the WER for the decoder is found by considering the covering sphere of the lattice Voronoi region. The proposed decoder and the bound are valid for both power-constrained lattice codes and lattices. If the genie is applied at the decoder, E8 lattice code has 0.5 dB gain and BW16 lattice code has 0.4 dB gain at WER of 10-4 compared with the one-shot decoder using αMMSE. A method for estimating the WER of the decoder is provided by considering the effective sphere of the lattice Voronoi region, which shows an accurate estimate for E8 and BW16 lattice codes. In the case of per-dimension power P → ∞, an asymptotic expression of the bound is given in a closed form. A practical implementation of a simplified decoder is given by considering CRC-embedded n =128 polar code lattice.