Almost Universal Codes Achieving Ergodic MIMO Capacity Within a Constant Gap
Almost Universal Codes Achieving Ergodic MIMO Capacity Within a Constant Gap
复制标题
几乎通用的代码在恒定间隙内实现遍历 MIMO 容量
DOI：
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发表时间：
2015
影响因子：
2.5
通讯作者：
Roope Vehkalahti
中科院分区：
文献类型：
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作者：
Laura Luzzi;Roope Vehkalahti
研究了当衰落块数趋于无穷大时，格形码在多天线块衰落信道中的容量问题。提出了一种基于归一化最小行列式的分代数多块空时码设计准则，该准则与高斯信道下的Hermite不变量具有相似的作用。根据最大似然解码，它表明，该标准是足以保证传输速率在一个恒定的间隙从容量确定性信道和遍历衰落信道。此外，如果接收天线的数量大于或等于发射天线的数量，则在朴素格解码下也实现相同的恒定间隙。在独立同分布瑞利衰落的情况下，错误概率指数快速消失。与文献中采用随机格系综的标准方法不同，本文的存在性结果是从数论中得到的。首先，容量的差距取决于所选择的划分代数的判别式，然后，类域理论应用于建立家庭的代数与小判别式。在建设中的关键因素是选择一个序列的司代数的中心是数域与小根判别式。
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.