Source coding with side information and a converse for degraded broadcast channels

Ahlswede, Rudolf; Körner, János

doi:10.1109/tit.1975.1055469

Cited by 364 publications

(340 citation statements)

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“…Note that the same tradeoff also appears in common randomness extraction on a 2-DMS with one-way communication [31], lossless source coding with a helper [15], [16], [17], and a quantity studied by Witsenhausen and Wyner [32]. It is shown in [33] that its slope is given by the chordal slope of the hypercontractivity of Markov operator [34] …”

Section: Necessary Conditional Entropymentioning

confidence: 84%

“…. , |Y|}\(|X |, |Y|); see [16], [19]. 2 1) To see that I XY is convex, for any U 0 , U 1 and λ ∈ [0, 1], let Q ∼ Bern(λ) be independent of X, Y, U 0 , U 1 , and let U = (Q, U Q ).…”

Section: A Proof Of the Converse Of Theoremmentioning

confidence: 99%

“…They can be considered as distances from extreme dependency, as they are equal to zero only under certain conditions of extreme dependency. In addition to providing operational interpretations to these information theoretic quantities, projections of the mutual information region yield the rate regions for many settings involving a 2-DMS, including lossless source coding with causal side information [12], distributed channel synthesis [13], [14], and lossless source coding with a helper [15], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

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Extended Gray-Wyner system with complementary causal side information

Gamal

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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We establish the rate region of an extended Gray-Wyner system for 2-DMS (X, Y ) with two additional decoders having complementary causal side information. This extension is interesting because in addition to the operationally significant extreme points of the Gray-Wyner rate region, which include Wyner's common information, Gács-Körner common information and information bottleneck, the rate region for the extended system also includes the Körner graph entropy, the privacy funnel and excess functional information, as well as three new quantities of potential interest, as extreme points. To simplify the investigation of the 5-dimensional rate region of the extended Gray-Wyner system, we establish an equivalence of this region to a 3-dimensional mutual information region that consists of the set of all triples of the form (I(X; U ), I(Y ; U ), I(X, Y ; U )) for some p U |X,Y . We further show that projections of this mutual information region yield the rate regions for many settings involving a 2-DMS, including lossless source coding with causal side information, distributed channel synthesis, and lossless source coding with a helper. Index TermsGray-Wyner system, side information, complementary delivery, Körner graph entropy, privacy funnel. I. INTRODUCTIONThe lossless Gray-Wyner system [1] is a multi-terminal source coding setting for two discrete memoryless source (2-DMS) (X, Y ) with one encoder and two decoders. This setup draws some of its significance from providing operational interpretation for several information theoretic quantities of interest, namely Wyner's common information [2], the Gács-Körner common information [3], the necessary conditional entropy [4], and the information bottleneck [5].In this paper, we consider an extension of the Gray-Wyner system (henceforth called the EGW system), which includes two new individual descriptions and two decoders with causal side information as depicted in Figure 1. The encoder maps sequences from a 2-DMS (X, Y ) into five indices M i ∈ [1 : 2 nRi ], i = 0, . . . , 4. Decoders 1 and 2 correspond to those of the Gray-Wyner system, that is, decoder 1 recovers X n from (M 0 , M 1 ) and decoder 2 recovers Y n from (M 0 , M 2 ). At time i ∈ [1 : n], decoder 3 recovers X i causally from (M 0 , M 3 , Y i ) and decoder 4 similarly recovers Y i causally from (M 0 , M 4 , X i ). Note that decoders 3 and 4 correspond to those of the complementary delivery setup studied in [6], [7] with causal (instead of noncausal) side information and with two additional private indices M 3 and M 4 . This extended Gray-Wyner system setup is lossless, that is, the decoders recover their respective source sequences with probability of error that vanishes as n approaches infinity. The rate region R of the EGW system is defined in the usual way as the closure of the set of achievable rate tuplesThe first contribution of this paper is to establish the rate region of the EGW system. Moreover, to simplify the study of this rate region and its extreme points, we show that it is equivale...

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Section: Necessary Conditional Entropymentioning

confidence: 84%

“…. , |Y|}\(|X |, |Y|); see [16], [19]. 2 1) To see that I XY is convex, for any U 0 , U 1 and λ ∈ [0, 1], let Q ∼ Bern(λ) be independent of X, Y, U 0 , U 1 , and let U = (Q, U Q ).…”

Section: A Proof Of the Converse Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended Gray-Wyner system with complementary causal side information

Gamal

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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“…We also assume that is acyclic but note that cyclic graphs can be handled using the approach from [2]. Given an -dimensional rate vector Ê ´Ê´ µµ ¾ , a rate-Ê, length-Ò block code for´AE È µ comprises a set of encoding functions ¾ and a set of decoding functions By [1], the network's lossless rate region is…”

Section: Problem Formulation and Notationmentioning

confidence: 99%

“…In Section III, we use the single-letter characterization of [1] to directly prove the concavity of the lossless rate region for the coded side information problem. In Section IV, we consider type A networks (defined in that section) and show that their lossless rate regions are also concave.…”

Section: Introductionmentioning

confidence: 99%

On the Concavity of Rate Regions for Lossless Source Coding in Networks

Effros

2006

2006 IEEE International Symposium on Information Theory

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Abstract-For a family of network source coding problems, we prove that the lossless rate region is concave in the distribution of sources. While the proof of concavity is straightforward for the few examples where a single-letter characterization of the lossless source coding region is known, it is more difficult for the vast majority of networks where the lossless source coding region remains unsolved. The class of networks that we investigate includes both solved and unsolved examples. We further conjecture that the same property applies more widely and sketch an avenue for investigating that conjecture.

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Information Theory and Coding Theory

Berger¹

2005

Encyclopedia of Statistical Sciences

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Source coding with side information and a converse for degraded broadcast channels

Cited by 364 publications

References 7 publications

Extended Gray-Wyner system with complementary causal side information

Extended Gray-Wyner system with complementary causal side information

On the Concavity of Rate Regions for Lossless Source Coding in Networks

Information Theory and Coding Theory

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