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This paper presents a scheme of concatenated non-binary LDPC codes with modulation diversity (MD) based on rate match. The rate design of non-binary LDPC codes and MD is studied when overall rate is unchanged for the communication system. And in the receiver, an iterative method is proposed between decoding and detection. It is shown that the rate-optimized concatenated scheme over a fading channel may lead to a significant gain over the conventional design of non-binary LDPC codes and modulation diversity. And the rate optimized concatenated scheme can achieve 1.5 dB gains when bit error rate is equal to 10-3 with low total rate.