Abstract. Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum point in a finite number of steps is described. The optimum value is shown to be monotone with respect to a partial order on the constraint parameters. Moreover, the optimum value is convex with respect to these parameters. Examples motivated by optimizations for communication systems are used to illustrate the algorithm.

The 3-user discrete memoryless interference channel is considered in this paper. We provide a new inner bound (achievable rate region) to the capacity region for this channel. This inner bound is based on a new class of code ensembles based on asymptotically good nested linear codes. This achievable region is strictly superior to the straightforward extension of Han-Kobayashi rate region from the case of twousers to three-users. This rate region is characterized using single-letter information quantities. We consider examples to illustrate the rate region.

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We consider the problem of communication over a three user discrete memoryless interference channel (3−IC).The current known coding techniques for communicating over an arbitrary 3−IC are based on message splitting, superposition coding and binning using independent and identically distributed (iid) random codebooks. In this work, we propose a new ensemble of codes -partitioned coset codes (PCC) -that possess an appropriate mix of empirical and algebraic closure properties. We develop coding techniques that exploit algebraic closure property of PCC to enable interference alignment over general 3−IC. We analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete 3−IC. Additive and non-additive examples are identified for which the derived achievable rate region is the capacity, and moreover, strictly larger than current known largest achievable rate regions based on iid random codebooks.

Abstract-The problem of computing sum of sources over a multiple access channel (MAC) is considered. Building on the technique of linear computation coding (LCC) proposed by Nazer and Gastpar [1], we employ the ensemble of nested coset codes to derive a new set of sufficient conditions for computing sum of sources over an arbitrary MAC. The optimality of nested coset codes [2] enables this technique outperform LCC even for linear MAC with a structural match. Examples of non-additive MAC for which the technique proposed herein outperforms separation and systematic based computation are also presented. Finally, this technique is enhanced by incorporating separation based strategy, leading to a new set of sufficient conditions for computing sum over a MAC.