Operational Duality Between Lossy Compression and Channel Coding

Gupta, Ankit; Verdú, S.

doi:10.1109/tit.2011.2136910

Cited by 25 publications

(27 citation statements)

References 16 publications

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“…On the other hand, operational duality provides a way to construct a solution (a code) for the primal problem using a solution for the dual problem. Operational duality was explored in [23] for lossy compression and channel coding problems, showing that a certain channel decoder can be used as a lossy compressor. The duality used in the OSRB is an operational one.…”

Section: Related Previous Workmentioning

confidence: 99%

“…Part (3) of the proof: Eliminating the shared randomness F : Using Definition 1, equation (26) guarantees existence of a fixed binning with the corresponding pmf p such that if we replace P with p in (23) and denote the resulting pmf withp, thenp(m, f, x n , y n ,ŷ n ) ≈ p(m, f, x n , y n )1{ŷ n = y n } := p(m, f, x n , y n ,ŷ n ). Using the second item of part one of Lemma 4, we havep(…”

Section: Lossy Source Codingmentioning

confidence: 99%

See 1 more Smart Citation

Achievability Proof via Output Statistics of Random Binning

Yassaee

Aref

Gohari

2014

IEEE Trans. Inform. Theory

134

200

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This paper introduces a new and ubiquitous framework for establishing achievability results in network information theory (NIT) problems. The framework uses random binning arguments and is based on a duality between channel and source coding problems. Further, the framework uses pmf approximation arguments instead of counting and typicality. This allows for proving coordination and strong secrecy problems where certain statistical conditions on the distribution of random variables need to be satisfied. These statistical conditions include independence between messages and eavesdropper's observations in secrecy problems and closeness to a certain distribution (usually, i.i.d. distribution) in coordination problems. One important feature of the framework is to enable one to add an eavesdropper and obtain a result on the secrecy rates "for free."We make a case for generality of the framework by studying examples in the variety of settings containing channel coding, lossy source coding, joint source-channel coding, coordination, strong secrecy, feedback and relaying. In particular, by investigating the framework for the lossy source coding problem over broadcast channel, it is shown that the new framework provides a simple alternative scheme to hybrid coding scheme. Also, new results on secrecy rate region (under strong secrecy criterion) of wiretap broadcast channel and wiretap relay channel are derived. In a set of accompanied papers, we have shown the usefulness of the framework to establish achievability results for coordination problems including interactive channel simulation, coordination via relay and channel simulation via another channel.

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Section: Related Previous Workmentioning

confidence: 99%

Section: Lossy Source Codingmentioning

confidence: 99%

Achievability Proof via Output Statistics of Random Binning

Yassaee

Aref

Gohari

2014

IEEE Trans. Inform. Theory

134

200

View full text Add to dashboard Cite

show abstract

“…one based on the construction of codes with finite n. , which deals with a more general setting using the language of hypergraphs. We restate that proof, in the case of permutations and type classes, with a slight strengthening to yield both statements 5 .…”

Section: Discussionmentioning

confidence: 83%

“…Here, the subscript s indicates source coding. The (average) probability of error P e (C) for a code C is defined in (5). These quantities are associated to the error exponents, e s (n, R) := − 1 n log P ⋆ e,s (n, R), sc s (n, R) := − 1 n log(1 − P ⋆ e,s (n, R)).…”

Section: The Information-theoretic Tasksmentioning

confidence: 99%

Duality between source coding with quantum side information and c-q channel coding

Cheng

Hanson

Datta

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we establish an interesting duality between two different quantum informationprocessing tasks, namely, classical source coding with quantum side information, and channel coding over c-q channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an optimal coding strategy for one task can be used to construct an optimal coding strategy for the other task. Along the way, we derive a bound on the error exponent for c-q channel coding with constant composition codes which might be of independent interest.

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“…Duality here is an operational duality [17] in which the solution for the dual problem is converted to a solution for the original problem.…”

Section: Achievabilitymentioning

confidence: 99%

A new wiretap channel model and its strong secrecy capacity

Nafea

Yener

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation.The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the new wiretap channel model by the secrecy capacity when the tapped subset is randomly chosen by nature.

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Operational Duality Between Lossy Compression and Channel Coding

Cited by 25 publications

References 16 publications

Achievability Proof via Output Statistics of Random Binning

Achievability Proof via Output Statistics of Random Binning

Duality between source coding with quantum side information and c-q channel coding

A new wiretap channel model and its strong secrecy capacity

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