Multilevel Coded Modulation for the Full-Duplex Relay Channel

We investigate coded modulation for full-duplex relay channels, proposing and analyzing a multilevel coding (MLC) framework with capacity approaching performance and practical features. Sufficient conditions are derived under which multilevel coding meets the known achievable rates for decode-and-forward relaying. The effect of a bit additive superposition and the linearity of multilevel code components on the performance of the system are studied. It is shown that linearity of the relay component codes imposes no penalty on rate, however, the linearity of the source-to-relay component codes may impose a performance penalty especially for small modulation constellations. We show that this rate loss occurs because a linearity constraint on codebooks at the source node introduces a new tension between optimality of rate allocation in multilevel coding layers and optimality of source/relay codebook correlations. Motivated by this insight, an alternative modulation labeling is proposed that minimizes the rate loss. The results are extended to multi-antenna relays. Slow fading and fast Rayleigh fading without channel state at the transmitter are also analyzed. The error exponent of the proposed scheme is studied. Finally, the frame- and bit-error rate performance of the proposed scheme is studied via simulations using point-to-point LDPC codes, showing that the proposed MLC relaying has excellent performance.