In this paper, we derive lower and upper bounds on the OPTA of a two-user multi-input multi-output (MIMO) causal encoding and causal decoding problem. Each user’s source model is described by a multidimensional Markov source driven by additive i.i.d. noise process subject to three classes of spatio-temporal distortion constraints. To characterize the lower bounds, we use state augmentation techniques and a data processing theorem, which recovers a variant of rate distortion function as an information measure known in the literature as nonanticipatory ϵ-entropy, sequential or nonanticipative RDF. We derive lower bound characterizations for a system driven by an i.i.d. Gaussian noise process, which we solve using the SDP algorithm for all three classes of distortion constraints. We obtain closed form solutions when the system’s noise is possibly non-Gaussian for both users and when only one of the users is described by a source model driven by a Gaussian noise process. To obtain the upper bounds, we use the best linear forward test channel realization that corresponds to the optimal test channel realization when the system is driven by a Gaussian noise process and apply a sequential causal DPCM-based scheme with a feedback loop followed by a scaled ECDQ scheme that leads to upper bounds with certain performance guarantees. Then, we use the linear forward test channel as a benchmark to obtain upper bounds on the OPTA, when the system is driven by an additive i.i.d. non-Gaussian noise process. We support our framework with various simulation studies.

中文翻译：

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时空失真约束下具有记忆的MIMO因果源编码系统的和速率的界限

在本文中，我们推导出了双用户多输入多输出 (MIMO) 因果编码和因果解码问题的 OPTA 的下限和上限。每个用户的源模型由受三类时空失真约束的加性 iid 噪声过程驱动的多维马尔可夫源描述。为了表征下界，我们使用状态增强技术和数据处理定理，将率失真函数的变体恢复为文献中称为非预期 ϵ-entropy、顺序或非预期 RDF 的信息度量。我们推导出由 iid 高斯噪声过程驱动的系统的下界特征，我们使用 SDP 算法解决所有三类失真约束。当系统的噪声对于两个用户都可能是非高斯的，并且只有一个用户被高斯噪声过程驱动的源模型描述时，我们获得了封闭形式的解决方案。为了获得上限，当系统由高斯噪声过程驱动时，我们使用与最佳测试通道实现相对应的最佳线性前向测试通道实现，并应用基于顺序因果 DPCM 的方案，反馈回路后跟缩放ECDQ 方案导致具有某些性能保证的上限。然后，当系统由加性 iid 非高斯噪声过程驱动时，我们使用线性前向测试通道作为基准来获得 OPTA 的上限。我们通过各种模拟研究支持我们的框架。