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This paper proposes a bit-interleaved coded multilevel modulation for non-orthogonal cooperative transmissions. The proposed system encodes and interleaves multiple layers together, using one encoder and one interleaver, in order to average the performance of multiple layers with unequal error probabilities. The multiple layers are mapped by hierarchical symbol mapping. To improve the performance of the proposed system, the relay transmits the layers with a different hierarchical mapping pattern from the source, which is optimally derived for minimizing mean square error. To mitigate error propagation from the relay, we propose a power scaling scheme based on the error performance of the layers. The detected signals at the relay are scaled before being transmitted to the destination. A corresponding destination structure is also presented, where multiple layers can be decoupled by an iterative equalization with improved soft information. To estimate the performance of the proposed system, we develop a density evolution technique, and show that the predicted performances are consistent with simulated performances. Simulation results indicate that by using the optimal mapping pattern, power scaling, and iterative equalization with improved soft information, the proposed technique achieves both cooperative diversity and coding gains, and thus outperforms conventional cooperative schemes.