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Abstract alphabet distortion-rate functions

James G. Dunham
1979 Information and Control  
Two definitions have been given for the distortion-rate function of a sourceuser pair--one involving test channel induced pair probability measures and the other involving general pair probability measures  ...  Examples are given which exhibit some kinds of the possible pathological behavior of the distortionrate function for general source-user pairs.  ...  The operational significance of this rate-distortion function was established by a theorem on block source coding with a fidelity criterion for discrete-time, abstract alphabet, stationary and ergodic  ... 
doi:10.1016/s0019-9958(79)90378-4 fatcat:sd47i2om6vaffgs7ckc7jqt2pa

Causal Rate Distortion Function on Abstract Alphabets: Optimal Reconstruction and Properties [article]

Photios A. Stavrou, Charalambos D. Charalambous, Christos K. Kourtellaris
2012 arXiv   pre-print
A causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and a coding theorem is derived.  ...  The optimal reconstruction kernel is derived, which is causal, and certain properties of the causal rate distortion function are presented.  ...  Information Theoretic Causal Rate Distortion Function This section gives the abstract formulation of R c (D).  ... 
arXiv:1202.0895v1 fatcat:wrgmk56r3ndrpkzm72v4ougrqu

Causal Rate Distortion Function on Abstract Alphabets and Optimal Reconstruction Kernel [article]

Charalambos D. Charalambous, Photios A. Stavrou, Christos K. Kourtellaris
2011 arXiv   pre-print
A Causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and the optimal reconstruction kernel is derived, which consists of a product of causal kernels.  ...  In the process, general abstract spaces are introduced to show existence of the minimizing kernel using weak*-convergence. Certain properties of the causal rate distortion function are presented.  ...  Conclusion The solution of the causal rate distortion function subject to a reproduction kernel which is a product of causal kernels is presented, on abstract alphabets.  ... 
arXiv:1102.3294v1 fatcat:5iphn62drzgixjbldpn7agre6i

Variable-rate source coding theorems for stationary nonergodic sources

M. Effros, P.A. Chou, R.M. Gray
1994 IEEE Transactions on Information Theory  
We also show that the distortion-rate function of a stationary nonergodic source has a decomposition as the average over points of equal slope on the distortion-rate functions of the source's stationary  ...  While a Axed-rate block code cannot achieve arbitrarily closely the distortionrate function on an arbitrary stationary nonergodic source, we show for the case of Polish alphabets that a variable-rate block  ...  show that for any stationary nonergodic finite alphabet source, the distortion-rate function D(R) equals the infimum of the average of the distortion-rate functions of the source's stationary ergodic components  ... 
doi:10.1109/18.340466 fatcat:2b5ysiujznaebi3wkwgi77be4u

Page 5281 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
Given reasonably chosen fixed sets of reproduction letters and/or their probabilities, we de- fine new rate-distortion functions which are coding bounds under these alphabet constraints.  ...  The performance of these codes is evaluated and compared with other quantizers and the rate-distortion function.  ... 

Page 2087 of Mathematical Reviews Vol. 54, Issue 6 [page]

1977 Mathematical Reviews  
The basic tree coding theorem proving that the optimal achievable performance using such systems is given by Shannon’s rate-distortion function was proved by F. Jelinek [same Trans.  ...  Berger, Rate distortion theory, Prentice-Hall, Englewood Cliffs, N.J., 1971; MR 53 #12751].  ... 

Successive Refinement of Abstract Sources [article]

Victoria Kostina, Ertem Tuncel
2018 arXiv   pre-print
In this paper, we derive a parametric characterization of the rate-distortion region for successive refinement of abstract sources.  ...  The rate-distortion region of successive refinement describes the minimum rates required to attain the target distortions at each decoding stage.  ...  Computation of single stage rate-distortion function In the context of finite source and reproduction alphabets, an algorithm for computation of rate-distortion functions was proposed by Blahut [8] .  ... 
arXiv:1707.09567v2 fatcat:6kgqr4ckkfe2vlyy3ooqyhcjpi

Introducing the Perception-Distortion Tradeoff into the Rate-Distortion Theory of General Information Sources

Ryutaroh Matsumoto
2018 IEICE Communications Express  
We introduce their tradeoff into the rate distortion theory of lossy source coding in information theory, and clarify the tradeoff among information rate, distortion and perception for general information  ...  Blau and Michaeli recently introduced a novel concept for inverse problems of signal processing, that is, the perception-distortion tradeoff.  ...  In the rate-distortion theory, we usually assume a reconstruction alphabet different from a source alphabet.  ... 
doi:10.1587/comex.2018xbl0109 fatcat:kzfgkk7xlnfv7cuv72i3fedody

A large deviation theory proof of the abstract alphabet source coding theorem

J.A. Bucklew
1988 IEEE Transactions on Information Theory  
This theorem asserts the existence of a code with distortion less than D + S and with rate less than R,( D ) + S for any S > 0 where R,( D ) is the first-order approximation to the rate-distortion function  ...  Abstract-A modified proof of Berger's abstract alphabet source coding with a fidelity criterion theorem is provided, utilizing a variant of a result from large deviation theory due to Gktner and Ellis.  ... 
doi:10.1109/18.21237 fatcat:r3hmz77mujfrdpyojbvschxtwq

Book review

Oleh J. Tretiak
1974 Information and Control  
The rate distortion function of a finite alphabet memoryless source is defined in Chapter 2, and the problem of calculating this function is carefully discussed.  ...  rate distortion bound.  ... 
doi:10.1016/s0019-9958(74)80025-2 fatcat:haxrvk23b5egpiaqnwucimhxja

Empirical processes and typical sequences

Maxim Raginsky
2010 2010 IEEE International Symposium on Information Theory  
rates in several settings that can be reduced to uniform approximation of general-alphabet memoryless sources with respect to a suitable function class.  ...  This paper proposes a new notion of a typical sequence over an abstract alphabet based on approximation of memoryless sources by empirical distributions, uniformly over a class of measurable "test functions  ...  Define the rate-distortion function R({∆ ρ }) inf Q∈E({∆ρ}) I(Q).  ... 
doi:10.1109/isit.2010.5513601 dblp:conf/isit/Raginsky10 fatcat:hugk2g5izzcpbe2liiovxocgy4

Page 3311 of Mathematical Reviews Vol. , Issue 80H [page]

1980 Mathematical Reviews  
Abstract alphabet distortion-rate functions. Inform. and Control 40 (1979), no. 2, 181-191.  ...  The principal result of this paper is the demonstration that Shan- non’s distortion-rate function for sources with abstract alphabets can be defined either as a minimization over all input/output pair  ... 

Additive successive refinement

E. Tuncel, K. Rose
2003 IEEE Transactions on Information Theory  
These results easily extend to abstract alphabet sources under the condition ( ) for some letter .  ...  Rate-distortion bounds for scalable coding, and conditions under which they coincide with nonscalable bounds, have been extensively studied.  ...  Assume a single-letter distortion measure , i.e., A block code consists of an encoding function which maps the source to index set , and a decoding function A rate-distortion pair is called achievable  ... 
doi:10.1109/tit.2003.814934 fatcat:jmcz6fxc5jczhoiigyldxoqibe

Page 5996 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
given by the rate distortion function R(d).  ...  Summary: “A pair of well-known inequalities due to Shannon provide an upper/lower bound of the rate-distortion function of a real source by the rate-distortion function of the Gaussian source with the  ... 

Page 7236 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
The key concepts of d-bar continuous channels and distortion-rate functions of sources are introduced.  ...  First it is shown that, subject to weak technical re- strictions, the rate-distortion function of an AMS source coincides with that of its stationary mean.  ... 
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