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Almost Universal Codes Achieving Ergodic MIMO Capacity Within a Constant Gap

机译：在恒定间隙内实现遍历MIMO容量的几乎通用代码

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摘要

This paper addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. A design criterion based on the normalized minimum determinant is proposed for division algebra multi-block space-time codes over fading channels; this plays a similar role to the Hermite invariant for Gaussian channels. Under maximum likelihood decoding, it is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for deterministic channels and ergodic fading channels. Moreover, if the number of receive antennas is greater than or equal to the number of transmit antennas, the same constant gap is achieved under naive lattice decoding as well. In the case of independent identically distributed Rayleigh fading, the error probability vanishes exponentially fast. In contrast to the standard approach in the literature, which employs random lattice ensembles, the existence results in this paper are derived from the number theory. First, the gap to capacity is shown to depend on the discriminant of the chosen division algebra; then, class field theory is applied to build families of algebras with small discriminants. The key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants.
机译：本文讨论了当衰落块的数量趋于无穷大时，在多天线块衰落信道中使用晶格码实现容量的问题。提出了一种基于归一化最小行列式的设计准则，用于衰落信道上的划分代数多块空时码。这与高斯通道的Hermite不变量起着相似的作用。在最大似然解码下，表明该准则足以保证确定性信道和遍历衰落信道的容量在恒定间隙内的传输速率。此外，如果接收天线的数量大于或等于发射天线的数量，则在朴素点阵解码下也获得相同的恒定间隙。在独立的相同分布的瑞利衰落的情况下，错误概率迅速消失。与文献中采用随机晶格集成的标准方法相反，本文的存在结果是从数论中得出的。首先，显示出能力差距取决于所选除法代数的判别式；然后，利用类场论建立具有小判别力的代数族。构造中的关键要素是选择除数序列的序列，其中心是具有小的根判别式的数字字段。

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