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arXiv 0908.2505cs.ITcs.DMmath.ITmath.RA
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关于多用户MIMO格码行列式的衰减性

On the Decay of the Determinants of Multiuser MIMO Lattice Codes

Jyrki Lahtonen, Roope Vehkalahti, Hsiao-feng Lu, Camilla Hollanti, Emanuele Viterbo

摘要:

在最近的工作中,Coronel等人发起了对多用户多输入多输出(MU-MIMO)格型码的分集复用折衷(DMT)性能与作为信号星座图的大小的函数的码矩阵的行列式的衰减速率之间的关系的研究。在这篇文章中,我们陈述了一个简单的一般上界的衰减函数和研究的有前途的代码提出的Badr和Belfiore密切的细节。我们推导出一个下界的基础上,由于刘维经典定理的衰减函数。由此产生的界限也适用于其他代码的基础上代数数论的建设。此外,我们研究了Badr-Belfiore代码中的小行列式的示例序列,并推导出其衰减函数的更严格的上限。该上界具有一定的几何渐近不确定性,因此我们也列出了几个有限数据率的精确界。

英文摘要:

In a recent work, Coronel et al. initiated the study of the relation between the diversity-multiplexing tradeoff (DMT) performance of a multiuser multiple-input multiple-output (MU-MIMO) lattice code and the rate of the decay of the determinants of the code matrix as a function of the size of the signal constellation. In this note, we state a simple general upper bound on the decay function and study the promising code proposed by Badr and Belfiore in close detail. We derive a lower bound to its decay function based on a classical theorem due to Liouville. The resulting bound is applicable also to other codes with constructions based on algebraic number theory. Further, we study an example sequence of small determinants within the Badr-Belfiore code and derive a tighter upper bound to its decay function. The upper bound has certain conjectural asymptotic uncertainties, whence we also list the exact bound for several finite data rates.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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