Capacity Results for Multicasting Nested Message Sets over Combination Networks
Shirin Saeedi Bidokhti, Vinod Prabhakaran, Suhas Diggavi

TL;DR
This paper investigates capacity regions for multicasting nested messages over combination networks, introducing new encoding schemes and proving optimality in certain cases, with implications for broadcast channels.
Contribution
It introduces novel encoding schemes for combination networks, characterizes their capacity regions, and extends the framework to broadcast channels with nested messages.
Findings
Linear superposition coding is optimal for two public receivers.
Block Markov encoding can outperform pre-encoding schemes.
Capacity regions are characterized by feasibility problems.
Abstract
The problem of multicasting two nested messages is studied over a class of networks known as combination networks. A source multicasts two messages, a common and a private message, to several receivers. A subset of the receivers (called the public receivers) only demand the common message and the rest of the receivers (called the private receivers) demand both the common and the private message. Three encoding schemes are discussed that employ linear superposition coding and their optimality is proved in special cases. The standard linear superposition scheme is shown to be optimal for networks with two public receivers and any number of private receivers. When the number of public receivers increases, this scheme stops being optimal. Two improvements are discussed: one using pre-encoding at the source, and one using a block Markov encoding scheme. The rate-regions that are achieved by…
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