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Channel polarisation results are extended to the case of communications over parallel channels, where the channel state information is known to both the encoder and decoder. Given a set of parallel binary-input discrete memoryless channels (B-DMCs), by performing the channel polarising transformation over independent copies of these component channels, we obtain a second set of synthesised binary-input channels. Similar to the single-channel case, we prove that as the size of the transformation goes infinity, some of the resulting channels tend to completely noised, and the others tend to noise-free, where the fraction of the latter approaches the average symmetric capacity of the underlying component channels. For finite-length polar coding over parallel channels, performance is found to be relied heavily on the specific channelmapping scheme. To avoid exhaustive searching, an empirically good scheme that is called equal-capacity partition channel mapping is proposed and numerical results show that the proposed scheme significantly outperforms random mapping. Further, utilising the above results, a polar coding method for arbitrary code length is proposed, which has potential applications in practical systems.