  We study Low-Density Parity-Check (LDPC) codes with iterative decoding on
block-fading (BF) Relay Channels. We consider two users that employ coded
cooperation, a variant of decode-and-forward with a smaller outage probability
than the latter. An outage probability analysis for discrete constellations
shows that full diversity can be achieved only when the coding rate does not
exceed a maximum value that depends on the level of cooperation. We derive a
new code structure by extending the previously published full-diversity
root-LDPC code, designed for the BF point-to-point channel, to exhibit a
rate-compatibility property which is necessary for coded cooperation. We
estimate the asymptotic performance through a new density evolution analysis
and the word error rate performance is determined for finite length codes. We
show that our code construction exhibits near-outage limit performance for all
block lengths and for a range of coding rates up to 0.5, which is the highest
possible coding rate for two cooperating users.
