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arXiv cs/0703052cs.ITmath.IT
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关于循环除代数的单调MIMO格

On the densest MIMO lattices from cyclic division algebras

C. Hollanti, J. Lahtonen, K. Ranto, R. Vehkalahti

摘要:

证明了循环除代数中的最大阶判别式必须最小化,以得到具有指定非零最小行列式的无限可能矩阵格的原因。使用类场理论的结果,一个下界的最大阶的最小判别式与给定的中心和索引(= Tx/Rx天线的数量)的推导。此外,许多例子的司代数实现我们的界限。例如,我们构造一个具有QAM系数的矩阵格,其码字是具有相同最小行列式的著名Golden码的2.5倍。我们描述了一个通用的算法,由于Ivanyos和Ronyai寻找最大的订单内的循环划分代数,并讨论我们的增强这个算法。我们还考虑了一般的方法来寻找循环划分代数的规定指标实现我们的下限。

英文摘要:

It is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant. Using results from class field theory a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas) is derived. Also numerous examples of division algebras achieving our bound are given. E.g. we construct a matrix lattice with QAM coefficients that has 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We describe a general algorithm due to Ivanyos and Ronyai for finding maximal orders within a cyclic division algebra and discuss our enhancements to this algorithm. We also consider general methods for finding cyclic division algebras of a prescribed index achieving our lower bound.

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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