  A capacity-achieving scheme based on polar codes is proposed for reliable
communication over multi-channels which can be directly applied to
bit-interleaved coded modulation schemes. We start by reviewing the
ground-breaking work of polar codes and then discuss our proposed scheme.
Instead of encoding separately across the individual underlying channels, which
requires multiple encoders and decoders, we take advantage of the recursive
structure of polar codes to construct a unified scheme with a single encoder
and decoder that can be used over the multi-channels. We prove that the scheme
achieves the capacity over this multi-channel. Numerical analysis and
simulation results for BICM channels at finite block lengths shows a
considerable improvement in the probability of error comparing to a
conventional separated scheme.
