Polar Codes are a recently proposed class of linear block error correction codes. They are provably capacity achieving codes over Binary Discrete Memoryless Channels (B-DMC) and have hence garnered a lot of interest from the scientific community. It is also a proposed channel coding method for 5G technology. Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) is a well known design to improve the error correcting performance of underlying channel codes over continuous channels especially Additive White Gaussian Noise (AWGN) channels. The novel idea in this paper, is to combine these powerful error correcting techniques i.e. integrate Polar Codes in a BICM-ID design to produce a high performance Bit-Interleaved Polar Coded Modulation with Iterative Decoding (BIPCM-ID) system. The error correcting performance of such a BIPCM-ID system has been analyzed through simulations over AWGN channel and multiple modulation schemes. Additionally error floor removal has been implemented and system performance has been discussed.