Rate splitting and iterative decoding approaches for fading channels with imperfect CSI
As shown by Médard (“The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” May 2000), the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by the Gaussian channel capacity of a virtual channel whose noise variance equals the effective noise variance of the original channel. We demonstrate that, using a simple rate splitting and successive decoding approach with two decoding steps (layers), this capacity lower bound can be strictly improved. We then generalize this observation to an arbitrary number of layers L and determine the limiting expression as L tends to infinity. The resulting bound is shown to be tight with the exact Gaussian-input mutual information for asymptotically perfect CSI. In the context of mismatched decoding, we will explain how this improved bound can be achieved through the use of a successive nearest-neighbor decoding scheme. Further adapations to the case of noncoherent fading (no CSI) and iterative nearest-neighbor decoding are also presented.