Abstract
This work investigates the general two-user compound Broadcast Channel (BC) in which an encoder wishes to transmit two private messages W1 and W2 to two receivers while being oblivious to the actual channel realizations controlling the communication. The focus is on the characterization of the largest achievable rate region by resorting to more involved encoding and decoding techniques than the usual coding schemes of the standard BC. Involved decoding schemes are first explored, and an achievable rate region is derived based on the principle of Interference Decoding (ID), in which each receiver decodes its intended message and chooses to (non-uniquely) decode, or not, the interfering non-itended message. This decoding scheme is shown to be capacity achieving for a class of non-trivial compound BEC/BSC broadcast channels while the worst-case of Marton’s inner bound—based on No Interference Decoding (NID)—fails to achieve the capacity region. Involved encoding schemes are later investigated, and an achievable rate region is derived based on Multiple Description (MD) coding wherin the encoder transmits a common description as well as multiple dedicated private descriptions to the many possible channel realizations of the users. It turns out that MD coding yields larger inner bounds than the single description scheme—Common Description (CD) coding—for a class of compound Multiple Input Single Output Broadcast Channels (MISO BC).
Highlights
We investigate in this work more involved encoding and decoding techniques than the usual coding schemes that proved to be capacity-achieving for some classes of Broadcast Channel (BC), namely, Interference Decoding (ID) and Multiple Description (MD) coding
We look at the role that Multiple Description (MD) coding can play in the non-ordered compound BC, where the encoder precodes against interference differently for the many channel statistics of each user through private descriptions each tailored to one channel statistic
We prove that MD coding is beneficial as compared with Common Description (CD) coding [3] and we illustrate this for a class of compound Gaussian Multiple Input Single Output Broadcast Channels (MISO BC) under a specificDirtyPaper Coding (DPC) scheme [24]
Summary
T HE two-user Broadcast Channel (BC) –as first introduced by Cover in [1]– consists of an encoder which wishes to. The capacity region of the BC remains an open problem to date, Marton established in [3] an achievable rate region for the general two-user BC based on the notion of random binning and superposition coding, with common and private messages, which is commonly referred to as Marton’s inner bound. This inner bound remains the best hitherto known in literature while the best outer bound on the capacity region of the BC is due to Nair & El Gamal [4]. The coupling between interference and channel uncertainty calls for more involved coding schemes that Marton’s coding scheme, which will be the focus of our contribution
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