  The compute-and-forward (CAF) scheme has attracted great interests due to its
high band-width efficiency on two-way relay channels. In the CAF scheme, a
relay attempts to decode a linear combination of transmitted messages from
other terminals or relays. It is a crucial issue to study practical
error-correcting codes in order to realize the CAF scheme with low
computational complexity. In this paper, we present an efficient
bit-interleaved coded modulation (BICM) scheme for the CAF scheme with phase
shift keying (PSK) modulations. In particular, we examine the asymptotic
decoding performance of the BICM scheme with low-density parity-check (LDPC)
codes by using the density evolution (DE) method. Based on the asymmetric
nature of the channel model, we utilize the population dynamics method for the
DE equations without the all-zero codeword assumption. The results show that,
for two-way relay channels with QPSK and 8PSK modulations, the LDPC-BICM scheme
provides higher achievable rate compared with an alternative separation
decoding scheme.
