  Compress-forward (CF) relays can improve communication rates even when the
relay cannot decode the source signal. Efficient implementation of CF is a
topic of contemporary interest, in part because of its potential impact on
wireless technologies such as cloud-RAN. There exists a gap between the
performance of CF implementations in the high spectral efficiency regime and
the corresponding information theoretic achievable rates. We begin by
re-framing a dilemma causing this gap, and propose an approach for its
mitigation. We utilize trellis coded quantization (TCQ) at the relay together
with multi-level coding at the source and relay, in a manner that facilitates
the calculation of bit LLRs at the destination for joint decoding. The
contributions of this work include designing TCQ for end-to-end relay
performance, since a distortion-minimizing TCQ is suboptimum. The reported
improvements include a 1dB gain over prior results for PSK modulation.
