We propose a composite decode-forward (DF) scheme for the two-way relay channel in the full-duplex mode by combining coherent, independent, and partial relaying strategies. The relay partially decodes each user's information in each block and forwards this information coherently with the source user to the destination user in the next block as in block Markov coding. In addition, the relay independently broadcasts a binning index of both users' decoded information parts in the next block as in independent network coding. Each technique has a different impact on the relay power usage and the rate region. We further consider the independent and partial DF scheme for its more practical channel state information requirements, and derive in closed-form link regimes when this scheme achieves a strictly larger rate region than just time sharing between its constituent techniques, direct transmission, and independent DF relaying, and when it reduces to a simpler scheme. The analytical approach is based on maximizing the weighted composite DF sum rate and comparing with the outermost time-sharing line connecting corner points of rate regions of the constituent techniques. Numerical results demonstrate significant rate gains by performing link adaptation of the composite scheme based on the identified link regimes.

We design novel partial decode-forward (PDF) schemes for the Gaussian two-way relay channel with direct link. Different from pure decode-forward, each user divides its message into two parts and the relay decodes only one part of each. The relay then generates its codeword as a function of the two decoded parts and forwards to the two users. We propose PDF schemes for both the full- and half-duplex modes. In full duplex, the scheme is based on block Markov encoding and forward joint decoding over 2 consecutive blocks. In half duplex, the transmission is divided into 4 phases, in which one user transmits during the first phase, the other during the second phase, both users transmit during the third phase and the relay transmits during the last phase. The relay decodes a part of the messages from both users at the end of phase 3 and each user decodes only at the end of phase 4. Analysis and simulation show that if for one user, the direct link is stronger than the user-to-relay link, while for the other, the direct link is weaker, then PDF can achieve a rate region strictly larger than the time-shared region of pure decode-forward and direct transmission for both full- and half-duplex modes.

We propose two coding schemes combining decode-forward (DF) and noisy network coding (NNC) with different flavors. The first is a combined DF-NNC scheme for the oneway relay channel which includes both DF and NNC as special cases by performing rate splitting, partial block Markov encoding and NNC. The second combines two different DF strategies and layered NNC for the two-way relay channel. One DF strategy performs coherent block Markov encoding at the source at the cost of power splitting at the relay, the other performs independent source and relay encoding but with full relay power, and layered NNC allows a different compression rate for each destination. Analysis and simulation show that both proposed schemes supersede each individual scheme and take full advantage of both DF and NNC.

We consider the full-duplex two-way relay channel with direct link between two users and propose two coding schemes: a partial decode-forward scheme, and a combined decode-forward and compute-forward scheme. Both schemes use rate-splitting and superposition coding at each user and generate codewords for each node independently. When applied to the Gaussian channel, partial decode-forward can strictly increase the rate region over decode-forward, which is opposite to the one-way relay channel. The combined scheme uses superposition coding of both Gaussian and lattice codes to allow the relay to decode the Gaussian parts and compute the lattice parts. This scheme can also achieve new rates and outperform both decode-forward and compute-forward separately. These schemes are steps towards understanding the optimal coding.