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IEEE Transactions on Information Theory
Article . 1997 . Peer-reviewed
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Publications at Bielefeld University
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On interactive communication

Authors: Ahlswede, Rudolf; Cai, Ning; Zhang, Zhen;

On interactive communication

Abstract

Summary: Almost two decades ago Ahlswede introduced an abstract correlated source \(({\mathcal V}\times{\mathcal W},{\mathcal S})\) with outputs \((v,w)\in{\mathcal S}\subset{\mathcal V}\times{\mathcal W}\), where persons \(P_{\mathcal V}\) and \(P_{\mathcal W}\) observe \(v\) and \(w\), respectively. More recently, Orlitsky considered the minimal number \(C_m\) of bits to be transmitted in \(m\) rounds to ``inform \(P_{\mathcal W}\) about \(v\) over one channel.'' He showed that \(C_2\leq 4C_\infty+3\) and that in general \(C_2\nsim C_\infty\). We give a simple example for \(C_3\nsim C_\infty\). However, for the new model ``inform \(P_{\mathcal W}\) over two channels,'' four rounds are optimal for this example -- a result we conjecture in general. If both \(P_{\mathcal V}\) and \(P_{\mathcal W}\) are to be informed over two channels about the other outcome, we determine asymptotically the complexities for all sources. In our last model ``inform \(P_{\mathcal V}\) and \(P_{\mathcal W}\) over one channel'' for all sources the total number \(T_2\) of required bits is known asymptotically and \(T_\infty\) is bounded from below in terms of average degrees. There are exact results for several classes of regular sources. An attempt is made to discuss the methods of the subject systematically.

Country
Germany
Keywords

hypergraph covering and, Communication theory, average degree bound, abstract sources, Source coding, Hypergraphs, worst case complexity, hypergraph covering and coloring, communication complexity, coloring

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
12
Average
Top 10%
Average
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