Linear feedback rate bounds for regressive channels (Corresp.)

Butman, S.

doi:10.1109/tit.1976.1055548

Cited by 37 publications

(43 citation statements)

References 6 publications

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“…This result was generalized to higher order channels [18]. Proving that Butman's coding scheme (9) achieves the capacity is still an open problem.…”

Section: A Butman's Recursive Feedback Coding Schemementioning

confidence: 97%

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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“…This result was generalized to higher order channels [18]. Proving that Butman's coding scheme (9) achieves the capacity is still an open problem.…”

Section: A Butman's Recursive Feedback Coding Schemementioning

confidence: 97%

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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“…Then, causal encoders and decoders that stabilize the plant (in the sense described above) exist only if CFB log jj: (13) Proof: An outline of the proof follows. Further details can be found in [19,Lemma 3.3].…”

Section: E Channel Capacity Required For Stabilizationmentioning

confidence: 99%

“…As noted in [11], following the structure of [12] also explored in [13], there exists a first-order autoregressive filter relating S k to N k , that generates optimal transmissions [11, (40)]…”

Section: Ma1 Channel Capacity With Feedbackmentioning

confidence: 99%

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Feedback Stabilization Over a First Order Moving Average Gaussian Noise Channel

Middleton

Rojas²,

Freudenberg³

et al. 2009

IEEE Trans. Automat. Contr.

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“…By using the concept of entropy power, a lower bound of the mean square norm of the state vector had been derived. For the case of an autoregressive channel, a linear coding scheme had been applied to ACGN channels to achieve a lower bound on the feedback channel capacity in Butman (1976). The closed-form feedback capacity of the first-order moving average additive Gaussian noise channel had been established in Kim (2006).…”

Section: Introductionmentioning

confidence: 99%

Disturbance attenuation over a first-order moving average Gaussian noise channel

Guan

et al. 2014

International Journal of Systems Science

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In this paper, the problem of disturbance attenuation has been studied for a linear time-invariant feedback control system with a first-order moving average Gaussian noise channel. By applying the concept of entropy power, a lower bound of signal-to-noise ratio has been achieved which is necessary for stabilisation of a system with the limited channel input power constraint. Moreover, the problem of minimising the influence of a stochastic disturbance on the output has also been investigated, and the controller design method has been obtained by using Youla parameterisation and H 2 theory. It is shown that the minimum variance of the system output depends not only on the disturbance variance, noise variance and unstable poles, but also on the non-minimum phase zeros and channel parameter. Finally, the effectiveness of the proposed results is illustrated by a numerical example.

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Linear feedback rate bounds for regressive channels (Corresp.)

Cited by 37 publications

References 6 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

Feedback Stabilization Over a First Order Moving Average Gaussian Noise Channel

Disturbance attenuation over a first-order moving average Gaussian noise channel

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