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This paper proposes a new model called \emph{spatial continuum asymmetricchannels} to study the channel capacity region of asymmetric scenarios in whicheither one source transmits to a spatial density of receivers or a density oftransmitters transmit to a unique receiver.This approach is built upon theclassical broadcast channel (BC) and multiple access channel (MAC). For thesake of consistency, the study is limited to Gaussian channels with powerconstraints and is restricted to the asymptotic regime (zero-errorcapacity).The reference scenario comprises one base station (BS) in Tx or Rxmode, a spatial random distribution of nodes (resp. in Rx or Tx mode)characterized by a probability spatial density $u(x)$ and a request for aquantity of information with no delay constraint. This system is modeled as an$\infty-$user asymmetric channel (BC or MAC). To derive the properties of thismodel, a spatial discretization is performed and the equivalence with either aBC or MAC is established. A discretization sequence is then defined to refineinfinitely the approximation. Achievability and capacity results are obtainedin the limit of this sequence. The uniform capacity is then defined as themaximal symmetric achievable rate at which the distributed users cantransmit/receive with no delay constraint.The capacity region is alsoestablished as the set of information distributions that are achievable. Thetightness of these limits and their practical interest are briefly illustratedand discussed.

Spatial Continuum Extensions of Asymmetric Gaussian Channels (Multiple Access and Broadcast)