Odlyzko界的非交换模拟及空时格码的性能界
A non-commutative analogue of the Odlyzko bounds and bounds on performance for space-time lattice codes
摘要：
本文考虑了多个独立瑞利衰落块的空时编码。特别是，我们将集中在格型空时码的编码增益的上限块的数量增长。Bayer等人在2006年曾在单天线情况下考虑过该问题。对他们的工作至关重要的是Odlyzko对代数数域的判别式的界限，因为这为数域代码的归一化编码增益提供了上限。在MIMO环境中，自然码是从定义在数域上的除代数构造的，并且编码增益由相应的（非交换）代数的判别式来测量。在本文中，我们将开发类似的Odlyzko界在这种情况下，并显示这些界限如何限制一个非常一般的家庭的划分代数为基础的空时码的归一化编码增益。这些界限也可以作为基准在实际的代码设计和作为工具来分析性能的渐近边界的独立衰落块的数量增加。
英文摘要：
This paper considers space-time coding over several independently Rayleigh faded blocks. In particular we will concentrate on giving upper bounds for the coding gain of lattice space-time codes as the number of blocks grow. This problem was previously considered in the single antenna case by Bayer et al. in 2006. Crucial to their work was Odlyzko's bound on the discriminant of an algebraic number field, as this provides an upper bound for the normalized coding gain of number field codes. In the MIMO context natural codes are constructed from division algebras defined over number fields and the coding gain is measured by the discriminant of the corresponding (non-commutative) algebra. In this paper we will develop analogues of the Odlyzko bounds in this context and show how these bounds limit the normalized coding gain of a very general family of division algebra based space-time codes. These bounds can also be used as benchmarks in practical code design and as tools to analyze asymptotic bounds of performance as the number of independently faded blocks increases.
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