| In this dissertation, we introduce a relay protocol for multiple-relay networks called parity forwarding. The relay channel is a classic multiuser information theory problem introduced in 1971, modeling a network of three nodes: a source, a destination, and a relay node. The relay has no message of its own and assists the source to communicate to the destination. Of the two main coding techniques for the relay channel, decode-and-forward (DF) and compress-and-forward (CF), our focus is to understand the DF scheme for single- and multiple-relay channels. For the single-relay channel, we present an interpretation of the classic DF strategy from a linear-coding perspective. Identifying binning in the classic DF strategy as parity bit generation, we devise ensembles of low-density parity-check (LDPC) codes, called bilayer LDPC codes, to incorporate the parity bits generated by the relay in the decoding process at the destination. We develop code design techniques and optimize the parameters of the bilayer LDPC code structure to show that bilayer LDPC codes can approach the theoretical DF rate. Inspired by the relation between binning and parity bits, we introduce the parity forwarding protocol to improve on the achievable DF rate in a multiple-relay network. For a two-relay network, we show that the previous multihop DF protocol can be improved if the relays forward parity messages and receivers (relays or the destination) use a joint decoding scheme. Depending on the relation between relay messages and decoded messages at each relay, different parity forwarding protocols are possible. In this thesis, we present a structured characterization of a class of parity forwarding protocols for multiple-relay networks. We propose a tree structure to describe the relations between messages. Using this tree structure, we derive a closed-form expression for the parity forwarding rate in a relay network with an arbitrary number of relays. Finally, examples of new types of degraded multiple-relay networks are presented for which the parity forwarding protocol achieves capacity. |
