Journals: On the Computation of the Capacity Region of the Discrete MAC E. Calvo Page, D. Pérez Palomar, J. Rodríguez Fonollosa and J. Vidal ManzanoAbstractThe computation of the channel capacity of discrete memoryless channels is a convex problem that can be efficiently solved using the ArimotoBlahut (AB) iterative algorithm. However, the extension of this algorithm to the computation of capacity regions of multiterminal networks is not straightforward since it gives rise to nonconvex problems. In this context, the AB algorithm has been only successfully extended to the calculation of the sumcapacity of the discrete memoryless multipleaccess channel (DMAC). Thus, the computation of the whole capacity region still requires the use of computationally demanding search methods. In this paper, we first give an alternative reformulation of the capacity region of the DMAC which condenses all the nonconvexities of the problem into a single rankone constraint. Then, we propose efficient methods to compute outer and inner bounds on the capacity region by solving a relaxed version of the problem and projecting its solution onto the original feasible set. Targeting numerical results, we first take a randomization approach. Focusing on analytical results, we study projection via minimum divergence, which amounts to the marginalization of the relaxed solution. In this case we derive sufficient conditions and necessary and sufficient conditions for the bounds to be tight. Furthermore, we are able to show that the class of channels for which the marginalization bounds match exactly the capacity region includes all the twouser binaryinput deterministic DMACs as well as other nondeterministic channels. In general, however, both methods are able to compute very tight bounds as shown for various examples. Full document 
