On K&amp;#x00F6;rner-Marton's sum modulo two problem

Sefidgaran, Milad; Gohari, Amin; Aref, Mohammad Reza

doi:10.1109/iwcit.2015.7140207

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…Two terminal interactive function computation was studied in [18], [19], [21], [22], and [26]. Distributed multi-terminal function computation in a multiple-access network of noiseless links was studied by Körner and Marton [17], Han and Kobayashi [20], Kuzuoka and Watanabe [29], Watanabe [32], and Sefidgaran et al [30]. Function computation in more general graph networks where a single node seeks to compute a function of the inputs at the other nodes was studied by Appuswamy et al [27], Kowshik and Kumar [28], and Sefidgaran and Tchamkerten [31].…”

Section: Introductionmentioning

confidence: 99%

Multiple Access Channel Simulation

Kurri

Ramachandran

Pillai

et al. 2022

IEEE Trans. Inform. Theory

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Section: Introductionmentioning

confidence: 99%

Multiple Access Channel Simulation

Kurri

Ramachandran

Pillai

et al. 2022

IEEE Trans. Inform. Theory

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“…In 1983, Ahlswede and Han [4] used a combination of the schemes of Slepian-Wolf and Körner-Marton to show that it was possible to improve over the convex hull of these schemes. More recent work [5] suggests that the Ahlswede-Han scheme cannot achieve a sum-rate lower than the minimum of the sumrates by Slepian-Wolf and Körner-Marton.…”

Section: Introductionmentioning

confidence: 99%

“…Till recently, there was no better bound than the cut-set bound H(Y |X) + H(X|Y ). In [5], it was shown that when H(X ⊕ Y ) < H(X|Y ) + H(Y |X), the cut-set bound is not tight except for the cases of independent sources or sources with symmetric distribution. Recently, Nair and Wang [6] established a new lower bound on the weighted sum-rate of the transmitters which implied the optimality of the Slepian-Wolf scheme under some previously unknown conditions.…”

Section: Introductionmentioning

confidence: 99%

Zero-Error Sum Modulo Two with a Common Observation

Sefidgaran

Tchamkerten

2021

2020 IEEE Information Theory Workshop (ITW)

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“…Two terminal interactive function computation was studied in [16], [17], [19], [20], [24]. Distributed multi-terminal function computation in a multiple-access network of noiseless links was studied by Körner and Marton [15], Han and Kobayashi [18], Kuzuoka and Watanabe [27], Watanabe [30], and Sefidgaran et al [28]. Function computation in more general graph networks where a single node seeks to compute a function of the inputs at the other nodes was studied by Appuswamy et al [25], Kowshik and Kumar [26], and Sefidgaran and Tchamkerten [29].…”

Section: Introductionmentioning

confidence: 99%

Multiple Access Channel Simulation

Kurri¹,

Ramachandran²,

Pillai³

et al. 2021

Preprint

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We study the problem of simulating a two-user multiple access channel over a multiple access network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links and independent pairwise shared randomness resources between each encoder and the decoder. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the two sources and the side information. We are interested in the rate tuples which permit this simulation. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). General inner and outer bounds on the rate region are derived. For the specific case where the sources at the encoders are conditionally independent given the side-information at the decoder, we completely characterize the rate region. Our bounds recover the existing results on function computation over such multi-terminal networks. We then show through an example that an additional independent source of shared randomness between the encoders strictly improves the communication rate requirements, even if the additional randomness is not available to the decoder. Furthermore, we provide inner and outer bounds for this more general setting with independent pairwise shared randomness resources between all the three possible node pairs.

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On Körner-Marton's sum modulo two problem

Cited by 7 publications

References 12 publications

Multiple Access Channel Simulation

Multiple Access Channel Simulation

Zero-Error Sum Modulo Two with a Common Observation

Multiple Access Channel Simulation

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