English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Multiple groupcasting over the broadcast channel (BC) is studied. Inparticular, an inner bound is obtained for the $K$-receiver discrete memoryless(DM) BC for the diamond message set which consists of four groupcast messages:one desired by all receivers, one by all but two receivers, and two moredesired by all but each one of those two receivers. The inner bound is based onrate-splitting and superposition coding and is given in explicit form herein asa union over coding distributions of four-dimensional polytopes. Whenspecialized to the so-called combination network, which is a class ofthree-layer (two-hop) broadcast networks parameterized by $2^K-1$finite-and-arbitrary-capacity noiseless links from the source node in the firstlayer to as many nodes of the second layer, our top-down approach from the DMBC to the combination network yields an explicit inner bound as a singlepolytope via the identification of a single coding distribution. This innerbound consists of inequalities which are then identified to be within the classof a plethora of (indeed, infinitely many) generalized cut-set outer boundsrecently obtained by Salimi et al for broadcast networks. We hence establishthe capacity region of the general $K$-user combination network for the diamondmessage set, and do so in explicit form. Such a result implies a certainstrength of our inner bound for the DM BC in that it (a) produces a hithertounknown capacity region when specialized to the combination network and (b) maycapture many combinatorial aspects of the capacity region of the $K$-receiverDM BC itself (for the diamond message set). Moreover, we further extend thatinner bound by adding binning to it and providing that inner bound also inexplicit form as a union over coding distributions of four-dimensionalpolytopes in the message rates.

Diamond Message Set Groupcasting: From an Inner Bound for the DM Broadcast Channel to the Capacity Region of the Combination Network