A BICM-ID system with 3-dimensional rotated BPSK constellation and signal space diversity (SSD) is proposed to combat the effect of Rayleigh fading. A new criterion based on mutual information is proposed to find the optimal rotation matrix, and the labeling that fits well with the outer code is presented. Simulation results show that at BER of 10-5 over a Rayleigh fading channel, with the code length of 192,000 bits and the iteration number of 100, the performance of the proposed system is only about 0.8 dB from the Gaussian-input Shannon limit and exceeds the limit constrained by the traditional QPSK input without rotation or SSD, at the spectrum efficiency of 1 bit/s/Hz.