This paper introduces a novel framework for constructing algebraic lattices based on Construction-D, leveraging nested linear codes and prime ideals from algebraic number fields. We focus on the application of these lattices in block-fading (BF) channels, which are characterized by piecewise-constant fading across blocks of transmitted symbols. This approach results in a semi-systematic generator matrix, providing a structured foundation for high -dimensional lattice design for BF channels. The proposed Construction-D lattices exhibit the full diversity property, making them highly effective for error performance improvement. To address this, we develop an efficient decoding algorithm designed specifically for full-diversity Construction-D lattices. Simulations indicate that the proposed lattices notably enhance error performance compared to full-diversity Construction-A lattices, especially in high-diversity scenarios. Interestingly, the anticipated performance gain from increasing the number of nested code levels was only observed in the two-level case. We believe that this is due to the amplified impact of error propagation during successive cancellation at higher levels. These findings highlight the promise of Construction-D lattices as an effective and practical coding strategy for enhancing communication reliability in BF channels.

This paper presents a novel framework for constructing full-diversity algebraic lattices based on Construction-D, utilizing nested linear codesC1⊂ · · · ⊂Ca⊆ FpNand prime ideals from algebraic number fields of degree n. Focused on block-fading (BF) channels, this approach yields a semi-systematic generator matrix suited for high-dimensional lattice design. The resulting Construction-D lattices achieve full diversity, significantly enhancing error performance. Additionally, we develop a decoding algorithm tailored for these full-diversity lattices, achieving linear complexity relative to the lattice dimension. Simulations indicate that the proposed lattices notably enhance error performance compared to full-diversity Construction-A lattices in diversity-2 cases. Interestingly, unlike AWGN channels, the expected performance enhancement of Construction-D over Construction-A, resulting from an increased number of nested code levels, was observed only in the two-level and diversity-2 cases. This phenomenon is likely due to the compounded error propagation during successive cancellation at higher levels, further amplified by higher diversity orders. The omission of parity-check enforcement at the final code level—aimed at simplifying our decoding—restricts the diversity order from the maximum ofn·dmin(Ca) ton, limiting performance gains. Unraveling the core reasons behind this decoding behavior remains an open challenge. Nevertheless, these findings highlight the promise of full-diversity Construction-D lattices as an effective coding strategy for BF channels.