In lattice-coded multiple-input multiple-output (MIMO) systems, optimal decoding amounts to solving the closest vector problem (CVP). Embedding is a powerful technique for the approximate CVP, yet its remarkable performance is not well understood. In this paper, we analyze the embedding technique from a bounded distance decoding (BDD) viewpoint. 1/(2γ)-BDD is referred to as a decoder that finds the closest vector when the noise norm is smaller than λ1/{2γ), where λ1 is the minimum distance of the lattice. We prove that the Lenstra, Lenstra and Lovász (LLL) algorithm can achieve 1/{2γ)-BDD for γ ≈ O(2n over 4). This substantially improves the existing result γ = O(2n) for embedding decoding. We also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT).
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机译：在点阵编码的多输入多输出（MIMO）系统中，最佳解码相当于解决最接近的向量问题（CVP）。对于近似CVP，嵌入是一种强大的技术，但其出色的性能尚未得到很好的理解。在本文中，我们从有界距离解码（BDD）的角度分析了嵌入技术。 1 /（2γ）-BDD称为解码器，当噪声范数小于λ 1 / {2γ）时找到最接近的向量，其中λ 1 为晶格的最小距离。我们证明，对于γ≈O（2 n over 4 ），Lenstra，Lenstra和Lovász（LLL）算法可以实现1 / {2γ）-BDD。这实质上改善了用于嵌入解码的现有结果γ= O（2 n ）。我们还证明，就分集复用增益折衷（DMT）而言，正则化格的BDD是最佳的。
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