The Minimal Directed Information Needed to Improve the LQG Cost

Sabag, Oron; Tian, Peida; Kostina, Victoria; Hassibi, Babak

doi:10.1109/cdc42340.2020.9304490

Cited by 11 publications

(8 citation statements)

References 21 publications

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“…While in general the t-step optimization problems ( 20) and ( 21) are challenging to compute, we illustrate in this paper that the normalized limit as t → ∞ is possible to compute in the Gaussian setting. Similar limit results in other communication scenarios were shown in [19], [22], [24], [25], [35]- [38].…”

Section: Berger-tung Bounds With Inter-block Memorysupporting

confidence: 89%

“…Thus, we may apply the result [24, Th. 7] on the causal counterpart of Gaussian Wyner-Ziv rate-distortion function to the process { Xk i } (90) with side information {X i } (91) to write (while stated for the scalar Gaussian source, the same argument applies to n parallel Gaussian sources of the same power, as is the case here; see [25] for the general vector case)…”

Section: X[k]mentioning

confidence: 99%

“…1, is computed in [22]. The causal rate-distortion function of the Gauss-Markov source with a Gaussian side observation available at the decoder (the causal counterpart of the Wyner-Ziv setting) is computed in [24] for the scalar source and in [25] for the vector source. That causal Wyner-Ziv setting can be viewed a special case of our causal CEO problem (2), (3) with two observers, with one of the observers enjoying an infinite rate.…”

Section: Introductionmentioning

confidence: 99%

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The CEO Problem With Inter-Block Memory

Kostina

Hassibi

2021

IEEE Trans. Inform. Theory

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An n-dimensional source with memory is observed by K isolated encoders via parallel channels, who compress their observations to transmit to the decoder via noiseless rate-constrained links while leveraging their memory of the past. At each time instant, the decoder receives K new codewords from the observers, combines them with the past received codewords, and produces a minimum-distortion estimate of the latest block of n source symbols. This scenario extends the classical one-shot CEO problem to multiple rounds of communication with communicators maintaining the memory of the past.We extend the Berger-Tung inner and outer bounds to the scenario with inter-block memory, showing that the minimum asymptotically (as n → ∞) achievable sum rate required to achieve a target distortion is bounded by minimal directed mutual information problems. For the Gauss-Markov source observed via K parallel AWGN channels, we show that the inner bound is tight and solve the corresponding minimal directed mutual information problem, thereby establishing the minimum asymptotically achievable sum rate. Finally, we explicitly bound the rate loss due to a lack of communication among the observers; that bound is attained with equality in the case of identical observation channels.The general coding theorem is proved via a new nonasymptotic bound that uses stochastic likelihood coders and whose asymptotic analysis yields an extension of the Berger-Tung inner bound to the causal setting. The analysis of the Gaussian case is facilitated by reversing the channels of the observers.

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Section: Berger-tung Bounds With Inter-block Memorysupporting

confidence: 89%

Section: X[k]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The CEO Problem With Inter-Block Memory

Kostina

Hassibi

2021

IEEE Trans. Inform. Theory

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“…decoder. Rate distortion formulations were considered in [7], [8], and [9], meanwhile an achievability approach (assuming noiseless SI also available at the encoder) was given in [10]. In this letter we show that, in stark contrast to the case where the SI consists of plant measurements, shared randomness does not effect lower bounds on bitrate…”

Section: A Literature Reviewmentioning

confidence: 95%

“…We consider a setup where the encoder and decoder share common SI in the form of shared randomness. The impact of SI on the communication/LQG cost tradeoff was investigated in [7], [8], [9], and [10]. The SI considered in these works was linear/Gaussian observations of the plant available at the Fig.…”

Section: A Literature Reviewmentioning

confidence: 99%

A Lower-bound for Variable-length Source Coding in LQG Feedback Control

Cuvelier,

Tanaka,

Heath

2022

Preprint

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In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified via the channel bitrate) required to attain a given control performance. We assume that at every time step an encoder can convey a packet containing a variable number of bits over the channel to a decoder at the controller. Our system model provides for the possibility that the encoder and decoder have shared randomness, as is the case in systems using dithered quantizers. We define two extremal prefix-free requirements that may be imposed on the message packets; such constraints are useful in that they allow the decoder, and potentially other agents to uniquely identify the end of a transmission in an online fashion. We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness. We also provide a generalization of the bound that applies if prefix-free requirements are relaxed. We conclude with a ratedistortion formulation.

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Rate of Prefix-free Codes in LQG Control Systems with Side Information

Cuvelier

Tanaka

2021

2021 55th Annual Conference on Information Sciences and Systems (CISS)

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The Minimal Directed Information Needed to Improve the LQG Cost

Cited by 11 publications

References 21 publications

The CEO Problem With Inter-Block Memory

The CEO Problem With Inter-Block Memory

A Lower-bound for Variable-length Source Coding in LQG Feedback Control

Rate of Prefix-free Codes in LQG Control Systems with Side Information

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