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Keywords
(11)
Directed Acyclic Graph
Global Optimization
Networked Systems
Optimal Design
Polynomial Time Algorithm
Scalar Quantization
Multiple Description
Multiple Description Scalar Quantizer
Multi Resolution
Shortest Path Problem
wyner ziv
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Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems
Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems,10.1109/TIT.2007.911170,IEEE Transactions on Information Th
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Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems
(
Citations: 18
)
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Dan Muresan
,
Michelle Effros
We propose a polynomialtime algorithm for optimal scalar quantizer design on discretealphabet sources. Special cases of the proposed approach yield opti mal design algorithms for fixedrate and entropyconstrained scalar quantizers, multiresolution scalar quantizers, multiple description scalar quantizers, and WynerZiv scalar quantizers. The algorithm guarantees globally optimal solu tions for fixedrate and entropyconstrained scalar quantizers and constrained optima for the other coding scenarios. We derive the algorithm by demonstrat ing the connection between scalar quantization, histogram segmentation, and the
shortest path problem
in a certain directed acyclic graph.
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 54, no. 1, pp. 344366, 2008
DOI:
10.1109/TIT.2007.911170
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Citation Context
(11)
...The case of scalar source codes for the WZ problem was handled in several papers, e.g., [3] and [
4
]...
Avraham Reani
,
et al.
Efficient OnLine Schemes for Encoding Individual Sequences With Side ...
...Globally optimal solutions for the MRSQ design problem under the cell convexity constraint were proposed in [19], [24], [3], [4], and [
20
] using combinatorial approaches...
...In [9] and [
20
], an example of finite alphabet source with mean squared error (MSE) distortion, was given for which the optimal MRSQ with two refinement stages must have nonconvex cells (in other words, noncontiguous cells)...
...For general distributions, Effros and Muresan proved in [9] and [
20
] that convexity of cells in the highest resolution partition does not prevent from optimality when the distortion measure is the squared distance...
Sorina Dumitrescu
.
Fast Encoder Optimization for MultiResolution Scalar Quantizer Design
...in several papers, e.g. [
7
] and [8]. In contrast to our case, these schemes operate under...
Avraham Reani
,
et al.
Efficient Online Schemes for Encoding Individual Sequences with Side ...
...The main design methods can be classified into two types: generalized Lloyd algorithms [4], [12], [17], [26], [27], and combinatorial algorithms [5]‐[8], [16], [22], [
23
]...
...These algorithms ensure globally optimal solution under the above convexity constraint. Specifically, in [22], [
23
] the...
Sorina Dumitrescu
,
et al.
On properties of locally optimal multiple description scalar quantizer...
...Under broad assumptions on the distortion measure, design under the codecell contiguity requirement guarantees a globally optimal code in the SQ case; unfortunately, the optimal MRSQ, MDSQ, and WZSQ with contiguous codecells may achieve performances worse than those of the corresponding optimal codes with noncontiguous codecells [
5
]...
...possible in an acyclic graph).In the partial RD graph used for optimal ECSQ design, the vertex labels give the topological order of the vertices.In general, ordering the vertices requires O(V + E) steps [
5
]...
...We focus our description on variablerate MDSQ design with M =2 (i. e. , 2DSQ) for simplicity.The generalizations to fixedrate coding, M> 2, MRSQ, and other examples of MDSQs with restricted packetloss scenarios are extensions of the variablerate M = 2 solution, as described briefly at the end of this work and in full in [
5
]...
...Due to space considerations, we here exclude a variety of algorithm extensions described in [
5
].Those extensions include fixed and variablerate MDSQs for M ≥ 2. These codes require an increase in design complexity, but complexity in both cases remains polynomial.In fixedrate MDSQ design, the complexity increase arises from the need to constrain the partition sizes, which requires inclusion of the current partition size in the vertex ...
...The above MDSQ discussion assumes that all packet loss scenarios occur with nonzero probability.A variety of codes, including MRSQ, can be described as MDSQs with restricted allowed packet loss scenarios.In [
5
], we modify the general MDSQ design algorithm for use with arbitrary scenario sets.The discussion treats both an optimized design algorithm for the highly structured packetloss framework of MRSQ and a general algorithm for arbitrary ...
...The final extension described in [
5
] treats the problem of fixed and variablerate...
Dan Muresan
,
et al.
Quantization as Histogram Segmentation: Optimal Scalar Quantizer Desig...
References
(34)
Design of absolutely optimal quantizers for a wide class of distortion measures
(
Citations: 30
)
DHIRAJ K. SHARMA
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 24, no. 6, pp. 693702, 1978
Quantizer monotonicities and globally optimal scalar quantizer design
(
Citations: 23
)
Xiaolin Wu
,
Kaizhong Zhang
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 39, no. 3, pp. 10491053, 1993
Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems
(
Citations: 18
)
Dan Muresan
,
Michelle Effros
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 54, no. 1, pp. 344366, 2008
On Optimal Multiresolution Scalar Quantization
(
Citations: 6
)
Xiaolin Wu
,
Sorina Dumitrescu
Conference:
Data Compression Conference  DCC
, pp. 322331, 2002
Source coding for a simple network
(
Citations: 56
)
R. M. Gray
,
A. D. Wyner
Published in 1974.
Sort by:
Citations
(18)
Efficient OnLine Schemes for Encoding Individual Sequences With Side Information at the Decoder
Avraham Reani
,
Neri Merhav
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 57, no. 10, pp. 68606876, 2011
Fast Encoder Optimization for MultiResolution Scalar Quantizer Design
Sorina Dumitrescu
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 57, no. 3, pp. 15201529, 2011
Efficient Online Schemes for Encoding Individual Sequences with Side Information at the Decoder
(
Citations: 3
)
Avraham Reani
,
Neri Merhav
Journal:
Computing Research Repository  CORR
, vol. abs/0908.1, 2009
On properties of locally optimal multiple description scalar quantizers with convex cells
(
Citations: 1
)
Sorina Dumitrescu
,
Xiaolin Wu
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 55, no. 12, pp. 55915606, 2009
Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems
(
Citations: 18
)
Dan Muresan
,
Michelle Effros
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 54, no. 1, pp. 344366, 2008