On Codecell Convexity of Optimal Multiresolution Scalar Quantizers for Continuous Sources

Antos, András

doi:10.1109/tit.2011.2173708

Cited by 5 publications

(4 citation statements)

References 21 publications

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“…We also consider the infinite-horizon average cost problem where the objective is to minimize c 0 (x t , u t ) . (2) Our main assumption on the Markov source {x t } is the following. Assumption 1.…”

Section: A Zero-delay Codingmentioning

confidence: 99%

“…On the other hand, it is likely that the convex codecell assumption results in a loss of system optimality in our case. This can be conjectured from the results of [2] where it was shown that in multiresolution quantization, requiring that quantizers have convex codecells may preclude system optimality even for continuous sources. We note that the convex codecell assumption is often made when provably optimal and fast algorithms are sought for the design of multiresolution, multiple description, and Wyner-Ziv quantizers; see, e.g., [27] and [13].…”

Section: Quantizer Actions and Controlled Markov Process Constructionmentioning

confidence: 99%

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On Optimal Zero-Delay Coding of Vector Markov Sources

Linder

Yüksel

2014

IEEE Trans. Inform. Theory

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Abstract-Optimal zero-delay coding (quantization) of a vector-valued Markov source driven by a noise process is considered. Using a stochastic control problem formulation, the existence and structure of optimal quantization policies are studied. For a finite-horizon problem with bounded per-stage distortion measure, the existence of an optimal zero-delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells. The bounded distortion assumption is relaxed to cover cases that include the linear quadratic Gaussian problem. For the infinite horizon problem and a stationary Markov source the optimality of deterministic Markov coding policies is shown. The existence of optimal stationary Markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed.

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Section: A Zero-delay Codingmentioning

confidence: 99%

Section: Quantizer Actions and Controlled Markov Process Constructionmentioning

confidence: 99%

On Optimal Zero-Delay Coding of Vector Markov Sources

Linder

Yüksel

2014

IEEE Trans. Inform. Theory

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“…(ii) The convex codecell restriction may lead to suboptimality in general; however it includes the class of nearest neighbor quantizers studied in [31]. For multiresolution scalar quantizers (MRSQ) and the squared error distortion measure, [35], [36] showed that for discrete and continuous sources (even with bounded continuous densities), optimal fixed rate multiresolution scalar quantizers cannot have only convex codecells, proving that the convex codecells assumption leads to a loss in performance. However, the parametric representation of convex codecell quantizers allowed [37] to establish compactness and desired convergence properties.…”

Section: Denotes the Set Of All Quantization Policies In π Cmentioning

confidence: 99%

Zero-Delay Lossy Coding of Linear Vector Markov Sources: Optimality of Stationary Codes and Near Optimality of Finite Memory Codes

Ghomi¹,

Linder²,

Yüksel³

2021

Preprint

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Optimal zero-delay coding (quantization) of R d -valued linearly generated Markov sources is studied under quadratic distortion. The structure and existence of deterministic and stationary coding policies that are optimal for the infinite horizon average cost (distortion) problem is established. Prior results studying the optimality of zero-delay codes for Markov sources for infinite horizons either considered finite alphabet sources or, for the R dvalued case, only showed the existence of deterministic and non-stationary Markov coding policies or those which are randomized. In addition to existence results, for finite blocklength (horizon) T the performance of an optimal coding policy is shown to approach the infinite time horizon optimum at a rate O( 1 T ). This gives an explicit rate of convergence that quantifies the near-optimality of finite window (finite-memory) codes among all optimal zero-delay codes.

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“…Remark 7 (Optimality of regular MRSQs). Counterexamples for both discrete and continuous PDFs have been devised, for which regular MRSQs are strictly suboptimal [37], [38]. However, none such are known for the case of log-concave input PDFs [39].…”

Section: Definition 5 (Regular Mrsq) a T -Step Mrsq Is Regular If The...mentioning

confidence: 99%

Algorithms for optimal control with fixed-rate feedback

Khina

Nakahira

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimizeperformance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions and sequential Bayesian filtering to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions and rate-limited time-varying noiseless channels. We further extend the framework to event-triggered control by allowing to convey information via an additional "silent symbol", i.e., by avoiding transmitting bits; by constraining the minimal probability of silence we attain a tradeoff between the transmission rate and the control cost for rates below one bit per sample.

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On Codecell Convexity of Optimal Multiresolution Scalar Quantizers for Continuous Sources

Cited by 5 publications

References 21 publications

On Optimal Zero-Delay Coding of Vector Markov Sources

On Optimal Zero-Delay Coding of Vector Markov Sources

Zero-Delay Lossy Coding of Linear Vector Markov Sources: Optimality of Stationary Codes and Near Optimality of Finite Memory Codes

Algorithms for optimal control with fixed-rate feedback

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