A general formulation of linear feedback communication systems with solutions

Butman, S.

doi:10.1109/tit.1969.1054302

Cited by 93 publications

(94 citation statements)

References 7 publications

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“…It is well known that noiseless channel output feedback, i.e., error-free observation of the channel output by the transmitter, may increase the channel capacity [11]. Thus, if we denote the feed-forward channel capacity as C and the feedback channel capacity as C fb , then C ≤ C fb .…”

Section: Power-constrained Linear Gaussian Noise Channel Modelmentioning

confidence: 99%

“…We note that the Kalman-Bucy filter developed in this paper estimates the channel intersymbol-interference state S t and takes a different form from the filters used in Schalkwijk [15] or Butman [11] which recursively estimate the transmitted message, but it is closely related. The optimal channel input derived in this paper includes a recursive estimate term (the Kalman innovation) and a novelty term (e t Z t ), thus it could be equivalent to the recursive message estimating and transmitting scheme in [15], [11] only if the optimal value of the novelty term e t Z t is zero, which is an open problem that we leave unresolved. 2) We derive an explicit formula for the maximal information rate achieved by (asymptotically) stationary feedback-dependent sources.…”

Section: Introductionmentioning

confidence: 99%

“…If the optimal KalmanBucy filter for processing the feedback (optimized over both stationary and non-stationary feedback-dependent sources) has a steady state, i.e., if the optimal KalmanBucy filter becomes stationary as n → ∞, the feedback channel capacity exists and equals the maximal information rate for stationary sources. For the case of the first order autoregressive (AR) noise channels, our optimal signaling scheme for achieving the maximal stationary-source information rate turns out to be the same as Butman's code [11].…”

Section: Introductionmentioning

confidence: 99%

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On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

Yang

Kavcic

Tatikonda

2007

IEEE Trans. Inform. Theory

124

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Abstract-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.Index Terms-channel capacity, directed information, dynamic programming, feedback capacity, Gauss-Markov source, information rate, intersymbol interference, Kalman-Bucy filter, linear Gaussian noise channel, noise whitening filter

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Section: Power-constrained Linear Gaussian Noise Channel Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

Yang

Kavcic

Tatikonda

2007

IEEE Trans. Inform. Theory

124

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“…This result has been generalized by Hitsuda and the author [13]. On the other hand it has been known that, if a Gaussian channel (GC) is with a non white noise, the capacity is increased by feedback (see [4,24]). Moreover it was claimed by Ebert [7] and Pinsker that the capacity Cf of a GC with feedback is at most twice of the capacity C of the same channel without feedback:…”

Section: Introductionmentioning

confidence: 94%

Capacity of Mismatched Gaussian Channels With and Without Feedback.

Ihara¹

1989

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“…For memoryless channels, Shannon [1] showed that feedback does not increase the capacity, and Schalkwijk and Kalaith [2] proposed a capacity achieving feedback code. For channels with memory, bounds have been developed for the feedback capacity [3], [4], [5], [6], [7]. In [8], the optimal feedback source distribution is derived in terms of a state-space channel representation and Kalman filtering.…”

Section: Introductionmentioning

confidence: 99%

Delayed Feedback Capacity of Stationary Sources over Linear Gaussian Noise Channels

Yang

Kavcic

2007

2007 IEEE International Symposium on Information Theory

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Abstract-We consider a linear Gaussian noise channel used with delayed feedback. The channel noise is assumed to be a ARMA (autoregressive and/or moving average) process. We reformulate the Gaussian noise channel into an intersymbol interference channel with white noise, and show that the delayed-feedback of the original channel is equivalent to the instantaneous-feedback of the derived channel. By generalizing results previously developed for Gaussian channels with instantaneous feedback and applying them to the derived intersymbol interference channel, we show that conditioned on the delayed feedback, a conditional Gauss-Markov source achieves the feedback capacity and its Markov memory length is determined by the noise spectral order and the feedback delay. A Kalman-Bucy filter is shown to be optimal for processing the feedback. The maximal information rate for stationary sources is derived in terms of channel input power constraint and the steady state solution of the Riccati equation of the Kalman-Bucy filter used in the feedback loop.

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A general formulation of linear feedback communication systems with solutions

Cited by 93 publications

References 7 publications

On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

Capacity of Mismatched Gaussian Channels With and Without Feedback.

Delayed Feedback Capacity of Stationary Sources over Linear Gaussian Noise Channels

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