On the capacity of the erasure multiple relay channel

This paper considers a simple wireless network - the multiple relay channel (MRC) - wherein a single source communicates with a single destination with the aid of M parallel relays. The links between the communicating nodes are non-interfering and subject to erasures. The capacity of this network is derived under the assumption that the destination has access to perfect side information on the erasure locations at the relays. This is done by first establishing an upper bound on the capacity by enumerating bounds on information transfer across various cut-sets and solving for the highest achievable rate using tools from linear programming; subsequently, it is shown that this rate can be achieved using low-complexity capacity-achieving codes designed for the point-to-point erasure channel, e.g., low-density parity-check codes. The paper concludes with a discussion of specific examples of MRCs.