2012
DOI: 10.1109/tit.2011.2173708
|View full text |Cite
|
Sign up to set email alerts
|

On Codecell Convexity of Optimal Multiresolution Scalar Quantizers for Continuous Sources

Abstract: Abstract-It has been shown by earlier results that for fixed rate multiresolution scalar quantizers and for mean squared error distortion measure, codecell convexity precludes optimality for certain discrete sources. However it was unknown whether the same phenomenon can occur for any continuous source. In this paper, examples of continuous sources (even with bounded continuous densities) are presented for which optimal fixed rate multiresolution scalar quantizers cannot have only convex codecells, proving tha… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
4
0

Year Published

2014
2014
2022
2022

Publication Types

Select...
3
2

Relationship

0
5

Authors

Journals

citations
Cited by 5 publications
(4 citation statements)
references
References 21 publications
0
4
0
Order By: Relevance
“…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%
See 1 more Smart Citation
“…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%
“…(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%
“…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%