In this paper, we relate a feedback channel with any finite-order autoregressive moving-average (ARMA) Gaussian noises to a variant of the Kalman filter. In light of this, we obtain relatively explicit lower bounds on the feedback capacity for such colored Gaussian noises, and the bounds are seen to be consistent with various existing results in the literature. Meanwhile, this variant of the Kalman filter also leads to explicit recursive coding schemes with clear structures to achieve the lower bounds. In general, our results provide an alternative perspective while pointing to potentially tighter bounds for the feedback capacity problem.

翻译：在本文中,我们将一个反馈渠道与任何定序自动递减移动-平均(ARMA)高斯噪音连接到卡尔曼过滤器的变体中。 有鉴于此,我们对这种有色高斯噪音的反馈能力有了相对明确的较低限制,其范围被认为与文献中的各种现有结果一致。 同时,卡尔曼过滤器的这一变体还导致明确的循环编码计划,其结构明确,以实现较低范围。 一般来说,我们的结果提供了另一种观点,同时指出对反馈能力问题可能存在更严格的限制。