A joint exploitation of coding and diversity techniques to achieve efficient, reliable wireless transmission is considered. The system comprises a powerful non-binary low-density parity-check (LDPC) code that will be soft-decoded to supply strong error protection, a quadratic amplitude modulator (QAM) that directly takes in the non-binary LDPC symbols and a modulation diversity operator that will provide power- and bandwidth-efficient diversity gain. By relaxing the rate of the modulation diversity rotation matrices to below 1, we show that a better rate allocation can be arranged between the LDPC codes and the modulation diversity, which brings significant performance gain over previous systems. To facilitate the design and evaluation of the relaxed modulation diversity rotation matrices, based on a set of criteria, three practical design methods are given and their point pairwise error rate are analyzed. With EXIT chart, we investigate the convergence between demodulator and decoder.A rate match method is presented based on EXIT analysis. Through analysis and simulations, we show that our strategies are very effective in combating random fading and strong noise on fading channels.