Ieee Transactions on Information Theory 2 on the Feedback Capacity of Power Constrained Gaussian Noise Channels with Memory
Ieee Transactions on Information Theory 2 on the Feedback Capacity of Power Constrained Gaussian Noise Channels with Memory
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IEEE Transactions on Information Theory 2 on the Feedback Capacitive of Power Constrained Gaussian Noise Channels with Memory
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通讯作者：
S. Tatikonda
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作者：
Shaohua Yang;A. Kavcic;S. Tatikonda
- 对于具有有限阶L的有理噪声功率谱的平稳加性高斯噪声信道，我们在平均信道输入功率约束下得到了反馈容量的两个新结果。首先，我们证明了一个非常简单的反馈相关的高斯-马尔可夫源实现的反馈能力，卡尔曼-布西滤波是最佳的反馈处理。基于这些结果，我们开发了一种新的方法，用于优化信道输入，实现覆盖庞布拉块长度n反馈容量，通过使用动态规划方法，分解成n个顺序相同的优化问题，每个阶段涉及优化O（L 2）变量的计算。其次，我们推导出固定反馈相关源的显式最大信息率。一般来说，估计平稳源的最大信息率只需要通过简单的非线性规划求解几个方程。对于一阶自回归和/或移动平均（阿尔马）噪声信道，这种优化允许一个封闭形式的最大信息速率公式。固定源的最大信息速率是反馈容量的下限，并且如果长期存在的猜想，即固定源实现反馈容量成立，则它等于反馈容量。
— For a stationary additive Gaussian-noise channel with a rational noise power spectrum of a finite-order L, we derive two new results for the feedback capacity under an average channel input power constraint. First, we show that a very simple feedback-dependent Gauss-Markov source achieves the feedback capacity, and that Kalman-Bucy filtering is optimal for processing the feedback. Based on these results, we develop a new method for optimizing the channel inputs for achieving the Cover-Pombra block-length-n feedback capacity by using a dynamic programming approach that decomposes the computation into n sequentially identical optimization problems where each stage involves optimizing O(L 2) variables. Second, we derive the explicit maximal information rate for stationary feedback-dependent sources. In general, evaluating the maximal information rate for stationary sources requires solving only a few equations by simple non-linear programming. For first-order autoregressive and/or moving average (ARMA) noise channels, this optimization admits a closed form maximal information rate formula. The maximal information rate for stationary sources is a lower bound on the feedback capacity, and it equals the feedback capacity if the long-standing conjecture, that stationary sources achieve the feedback capacity, holds.