Capacity results for certain wireless relay networks with erasure links

This paper considers two simple wireless network configurations in which the links making up the network do not interfere with one another and the assumed link loss mechanisms are erasures. The first configuration is the M-source multiple access relay channel (MARC), in which M different sources convey information to a single destination with the help of a single relay. The second configuration is the two-fold multi-relay channel (MRC), in which a pair of relays help a single source convey information to a single destination. Cut set bounds are established for these configurations, and linear programming is then employed to formulate closed-form solutions for the capacity regions as a function of the link parameters; moreover, it is shown that easily-implemented capacity-approaching codes such as LDPC or Tornado codes can be used at the link level to achieve any point in the capacity region. For the erasure MARC, the results indicate that the relay should help only those sources that have a weaker direct channel to the destination than the relay itself does - regardless of the quality of the source-to-relay channels. For the erasure MRC, the solution is not as intuitive, but it displays a structure in which the relative quality of the various links determine which relays are used - and, when both are used, which relay is ldquoprimaryrdquo and which is ldquosecondaryrdquo.