Adaptive polar coding with high order modulation for block fading channels

We consider the design of polar codes for block fading channels. The key idea is to combine modulation, fading, and coding in a single entity. This design is based on two facts: (i) for each fading block, symbols with different fading coefficient has different reliability; (ii) for each symbol, different bit levels of a high order modulation observe different noise levels. In other words, the bit channels are partially polarized by modulation and fading. This new viewpoint inspires us to construct polar codes by matching code polarization perfectly with modulation polarization and fading polarization. The resulting codes adapt to the channel quality fluctuation, thus provide better performance than conventional polar BICM schemes and LDPC codes.