  Physical-layer network coding improves the throughput of the two-way relay
channel by allowing multiple source terminals to transmit simultaneously to the
relay. However, it is generally not feasible to align the phases of the
multiple received signals at the relay, which motivates the exploration of
noncoherent solutions. In this paper, turbo-coded orthogonal multi-tone
frequency-shift keying (FSK) is considered for the two-way relay channel. In
contrast with analog network coding, the system considered is an instance of
digital network coding; i.e., the relay decodes the network codeword and
forwards a re-encoded version. Crucial to noncoherent digital network coding is
the implementation of the relay receiver, which is the primary focus of the
paper. The relay receiver derived in this paper supports any modulation order
that is a power of two, and features the iterative feedback of a priori
information from the turbo channel decoder to the demodulator; i.e., it uses
bit interleaved coded modulation with iterative decoding (BICM-ID). The
performance of the receiver is investigated in Rayeligh fading channels through
error-rate simulations and a capacity analysis. Results show that the BICM-ID
receiver improves energy efficiency by 0.5-0.9 dB compared to a non-iterative
receiver implementation.
