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 channels with additive white Gaussian noise (AWGN). One variation is for receivers unaware of the CSIT where adaptive codewords, or Shannon strategies, achieve capacity. The GMI is then based on auxiliary channels with inputs that are linear functions of the adaptive codewords' symbols. For scalar channels, the input that maximizes the GMI is shown to give a conventional codebook but where the amplitude and phase of each symbol is modified based on the CSIT. A second variation partitions the channel output alphabet and has a different auxiliary channel 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 and quadratic waterfilling if the CSIT is known at the receiver. Several examples for fading channels with AWGN illustrate the theory, with a focus on on-off fading and Rayleigh fading. The capacity results are generalized to block fading channels with in-block feedback, including capacity expressions based on mutual information and directed information.