The adoption of aggressive frequency reuse schemes along with interference management techniques has become the leading paradigm in satellite communications to increase the spectral efficiency. In general terms, one cannot rely on precoding techniques in the absence of channel phase information. Nevertheless, the availability of channel magnitude information, makes it possible to explore power-based separation of superimposed signals. In this paper, rate splitting (RS) ideas are exploited, whereby the separation of messages into private and public parts serves to improve the performance of successive cancellation decoding (SCD). Numerical results reveal that in some pertinent system scenarios, the proposed schemes achieve a larger rate region than that of orthogonal schemes that do not exploit the interference and other strategies that either do not allow beam cooperation or do not apply RS.

This paper presents a joint typicality framework for encoding and decoding nested linear codes in multiuser networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In particular, it establishes an achievable rate region for computing a linear combination over a discrete memoryless multiple-access channel (MAC). When specialized to the Gaussian MAC, this rate region recovers and improves upon the lattice-based compute-forward rate region of Nazer and Gastpar, thus providing a unified approach for discrete memoryless and Gaussian networks. Furthermore, our framework provides some valuable insights on establishing the optimal decoding rate region for compute-forward by considering joint decoders, progressing beyond most previous works that consider successive cancellation decoding. Specifically, this work establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from K senders. Index Terms Linear codes, joint decoding, compute-forward, multiple-access channel, relay networks I. INTRODUCTION In network information theory, random i.i.d. ensembles serve as the foundation for the vast majority of coding theorems and analytical tools. As elegantly demonstrated by the textbook of El Gamal and Kim [1], the core results of this theory can be unified via a few powerful packing and covering lemmas. However, starting from the many-help-one source coding example of Körner and Marton [2], it has been well-known that there are coding theorems that seem to require random linear ensembles, as opposed to random i.i.d. ensembles. Recent efforts have demonstrated that linear and lattice codes can yield new achievable rates for relay networks [3]-[9],

Abstract-Inspired by the compute-and-forward scheme from Nazer and Gastpar, a novel multiple-access scheme introduced by Zhu and Gastpar makes use of nested lattice codes and sequential decoding of linear combinations of codewords to recover the individual messages. This strategy, coined computeforward multiple access (CFMA), provably achieves points on the dominant face of the multiple-access capacity region while circumventing the need of time sharing or rate splitting. For a two-user multiple-access channel (MAC), we propose a practical procedure to design suitable codes from off-the-shelf LDPC codes and present a sequential belief propagation decoder with complexity comparable with that of point-to-point decoders. We demonstrate the potential of our strategy by comparing several numerical evaluations with theoretical limits.

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