Control approach to computing the feedback capacity for stationary finite dimensional Gaussian channels

We firstly extend the interpretation of feedback communication over stationary finite dimensional Gaussian channels as feedback control systems by showing that, the problem of finding stabilizing feedback controllers with maximal reliable transmission rate over Youla parameters coincides with the problem of finding strictly causal filters to achieve feedback capacity recently derived in [1]. The aforementioned interpretation provides an approach to construct deterministic feedback coding schemes (with double exponential decaying error probability). We next propose an asymptotic capacity-achieving upper bounds, which can be numerically evaluated by solving finite dimensional dual optimizations. From the filters that achieve upper bounds, we derive feasible filters which lead to a sequence of lower bounds. Thus, from the lower bound filters we obtain communication systems that achieve the lower bound rate. Extensive examples show the sequence of lower bounds is asymptotic capacity-achieving as well.Comment: to appear in 2015 Allerto

Secrecy Capacity of Colored Gaussian Noise Channels with Feedback

In this paper, the k-th order autoregressive moving average (ARMA(k)) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that a variant of the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.Comment: 23 pages, 4 figure

Youla Coding and Computation of Gaussian Feedback Capacity

In this paper, we propose an approach to numerically compute the feedback capacity of stationary finite dimensional Gaussian channels and construct (arbitrarily close to) capacity-achieving feedback codes. In particular, we first extend the interpretation of feedback communication over stationary finite dimensional Gaussian channels as feedback control systems by showing that, the problem of finding stabilizing feedback controllers with maximal reliable transmission rate over Youla parameters coincides with the problem of finding strictly causal filters to achieve feedback capacity derived in [2]. This extended interpretation provides an approach to construct deterministic feedback coding schemes with double exponential decaying error probability. We next propose asymptotic capacity-achieving upper bounds, which can be numerically evaluated by solving finite dimensional convex optimizations. From the filters that achieve the upper bounds, we apply the Youla-based interpretation to construct feasible filters, i.e., feedback codes, leading to a sequence of lower bounds. We prove the sequence of lower bounds is asymptotically capacity-achieving.Comment: 35 pages, 5 figures, submitted to IEEE Transactions on Information Theor