We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.

中文翻译：

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复合 MIMO 信道的语义安全格码

我们考虑复合多输入多输出 (MIMO) 窃听信道，其中假设发射机 (CSIT) 的信道状态信息最少。代码构造是针对各向同性互信息的特殊情况给出的，作为一般情况的保守策略。使用 MIMO 信道的平坦度因子，我们提出了格码，普遍实现复合 MIMO 窃听信道的保密容量，达到与发射天线数量相等的恒定间隙（以 nat 为单位）。所提出的方法从错误概率的角度改进了现有的 MIMO 窃听信道保密编码工作，并建立了信息理论安全性（实际上是语义安全性）。我们还给出了一个代数构造来降低代码设计的复杂性，以及合法接收者的解码复杂度。由于数域和除法代数的代数结构，我们的复合 MIMO 窃听信道的代码构造可以简化为高斯窃听信道的代码构造，增加一些额外的保密容量差距。