Multiple Multicasts with the Help of a Relay - Gunduz,D; Simeone,O; Goldsmith,AJ; Poor,HV; Shamai,S (IEEE Transactions on Information Theory, 2009)
The problem of simultaneous multicasting of multiple messages with the helpof a relay terminal is considered. In particular, a model is studied in which arelay station simultaneously assists two transmitters in multicasting theirindependent messages to two receivers. The relay may also have an independentmessage of its own to multicast. As a first step to address this general model,referred to as the compound multiple access channel with a relay (cMACr), thecapacity region of the multiple access channel with a "cognitive" relay ischaracterized, including the cases of partial and rate-limited cognition. Then,achievable rate regions for the cMACr model are presented based ondecode-and-forward (DF) and compress-and-forward (CF) relaying strategies.Moreover, an outer bound is derived for the special case, called the cMACrwithout cross-reception, in which each transmitter has a direct link to one ofthe receivers while the connection to the other receiver is enabled onlythrough the relay terminal. The capacity region is characterized for a binarymodulo additive cMACr without cross-reception, showing the optimality of binarylinear block codes, thus highlighting the benefits of physical layer networkcoding and structured codes. Results are extended to the Gaussian channel modelas well, providing achievable rate regions for DF and CF, as well as for astructured code design based on lattice codes. It is shown that the performancewith lattice codes approaches the upper bound for increasing power, surpassingthe rates achieved by the considered random coding-based techniques.