Source coding with distortion side information at the encoder

Martinian, E.; Wornell, Gregory W.; Zamir, Ram

doi:10.1109/dcc.2004.1281462

Cited by 5 publications

(6 citation statements)

References 34 publications

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“…Definition A.5. The system (53) is stablizable in expectation if there exists a control strategy u[·](z) such that for some M < ∞ we have that that lim sup n→∞ E [d n ] < M .…”

Section: E Stability In Expectationmentioning

confidence: 99%

“…The system(53) is stablizable in the zero-error sense if there exists a control strategy u[·](z) such that there exists M < ∞ and N > 0 such that for all n ≥ N , we know P(d n < M ) = 1.…”

mentioning

confidence: 99%

“…Theorem A.4. Consider the system S CF a from (52) and the affiliated system S CF from(53), such that the actuation channels, i.e. the b[n](z) are drawn identically in both cases.…”

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confidence: 99%

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Control Capacity

Ranade

Sahai

2019

IEEE Trans. Inform. Theory

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Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the uncertainty from a system, i.e. stabilize to a known fixed point. We give a computable single-letter characterization of control capacity for memoryless stationary scalar multiplicative actuation channels. Control capacity allows us to answer questions of stabilizability for scalar linear systems: a system with actuation uncertainty is stabilizable if and only if the control capacity is larger than the log of the unstable open-loop eigenvalue.For second-moment senses of stability, we recover the classic uncertainty threshold principle result. However, our definition of control capacity can quantify the stabilizability limits for any moment of stability. Our formulation parallels the notion of Shannon's communication capacity, and thus yields both a strong converse and a way to compute the value of side-information in control. The results in our paper are motivated by bit-level models for control that build on the deterministic models that are widely used to understand information flows in wireless network information theory. 1) Control with communication constraints:Our work is strongly inspired by the family of data-rate theorems [11], [12], [13], [14], [15]. These results quantify the minimum rate required over a noiseless communication channel between the system observation and the controller to stabilize the system 1 . The related notion of anytime capacity considers control over noisy channels and also general notions of η-th moment stability [17]. Elia's work [18] uses the lens of control theory to examine the feedback capacity of channels in a way that is inspired by and extends the work of Schalkwijk and Kailath in [19], [20]. These papers "encode" information into the initial state of the system, and then stabilize it over a noisy channel.All these results allow for encoders-decoder pairs around the unreliable channels, and thus capture a traditional communication model for uncertainty. The main results have the flavor that the appropriate capacity of the bottlenecking communication channel must support a rate R that is greater than a critical rate. This critical rate represents the fundamental rate at which the control system generates uncertainty -it is typically the sum of the logs of the unstable eigenvalues of the system for linear systems. Our paper focuses on extending this aesthetic to capture the impact of physical unreliabilities.The data-rate theorems and anytime results consider the system plant as a "source" of uncertainty. This source must be communicated 2 over the information bottleneck. Our current paper focuses on how control systems can reduce uncertainty about the world by moving the world to a known point as suggested in [21]. We refer to the dissipation of information/uncertainty as the "sink" nature of a control system. This difference is made salient by ...

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“…Definition A.5. The system (53) is stablizable in expectation if there exists a control strategy u[·](z) such that for some M < ∞ we have that that lim sup n→∞ E [d n ] < M .…”

Section: E Stability In Expectationmentioning

confidence: 99%

mentioning

confidence: 99%

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Control Capacity

Ranade

Sahai

2019

IEEE Trans. Inform. Theory

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“…Our first result (generalizing [7]) is that having q only at the encoder and w only at the decoder is asymptotically optimal in high-resolution; see also [1,2] for more general results.…”

Section: Resultsmentioning

confidence: 99%

“…When both types of side information are considered, knowing the former only at the encoder and the latter only at the decoder is often asymptotically as good as complete knowledge of all side information. Potential examples of distortion side information include reliabilities for sensor readings and perceptual effects such as distortion masking, and sensitivity to context [1,2].…”

Section: Introductionmentioning

confidence: 99%