Information Rates for Channels with Fading, Side Information and Adaptive Codewords

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN). One variation is based on reverse channel models that give the largest rates but are challenging to optimize. A second variation is for receivers unaware of the CSIT where adaptive symbols achieve capacity. The GMI is then based on forward models with inputs that are linear functions of the adaptive symbol's entries. For scalar channels, the maximum GMI is achieved by a conventional codebook, and where the amplitude and phase of each channel symbol are modified based on the CSIT. A third variation partitions the channel output alphabet and has a different auxiliary model for each subset of the partition. The partitioning helps to determine the capacity scaling at high signal to noise ratios. A class of power control policies is described for partial CSIR, including a truncated minimum mean square error policy for full CSIT. Several examples for fading channels with AWGN illustrate the theory, with a focus on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions based on mutual information and directed information.