Publication

On degraded two-message set broadcast

Christina Fragouli, Suhas Diggavi, Vinod Malathidevi Prabhakaran, Shirin Saeedi Bidokhti
2009
Conference Papers

Abstract

We consider the two message set problem, where a source broadcasts a common message W1 to an arbitrary set of receivers U and a private message W2 to a subset of the receivers P ⊆U . Transmissions occur over linear deterministic channels. For the case where at most two receivers do not require the private message, we give an exact characterization of the capacity region, where achievability is through linear coding.

Official source

https://infoscience.epfl.ch/entities/publication/f45d28b0-90bf-4306-8767-9018f34fc065

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Christina Fragouli, Suhas Diggavi, Vinod Malathidevi Prabhakaran, Shirin Saeedi Bidokhti
2009
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/f45d28b0-90bf-4306-8767-9018f34fc065

About this result

Related concepts (19)

Split exact sequence

In mathematics, a split exact sequence is a short exact sequence in which the middle term is built out of the two outer terms in the simplest possible way. A short exact sequence of abelian groups or of modules over a fixed ring, or more generally of objects in an is called split exact if it is isomorphic to the exact sequence where the middle term is the direct sum of the outer ones: The requirement that the sequence is isomorphic means that there is an isomorphism such that the composite is the natural inclusion and such that the composite equals b.

Pure submodule

In mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly well-behaved piece of a module. Pure modules are complementary to flat modules and generalize Prüfer's notion of pure subgroups. While flat modules are those modules which leave short exact sequences exact after tensoring, a pure submodule defines a short exact sequence (known as a pure exact sequence) that remains exact after tensoring with any module.

Flat module

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact. Flatness was introduced by in his paper Géometrie Algébrique et Géométrie Analytique.

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