Aviv Rosenzweig

We consider an i.i.d. state-dependent channel with partial (rate limited) channel state  information (CSI) at the transmitter (CSIT) and full CSI at the receiver (CSIR). 

The CSIT comprises a non-causal rate limited CSI, which is communicated by a  third party (a genie) over a way-side channel, and may also include outputs of a deterministic scalar quantizer of the channel state.

A single letter expression for the capacity of the channel is given. When the CSIT comprises only a non-causal rate limited part we show that the capacity suggested  by Heegard and El Gamal is too optimistic, and suggest a correction as part of our expression for the information capacity. For the general setting we present an  optimal coding scheme based upon  multiplexing of several codebooks. It is proved that the capacity of the channel is the same whether the quantizer's output is observed causally or non-causally by the encoder, and regardless of the type of  input constraint considered. Using a rate distortion approach we bound the  alphabet's size of the auxiliary RV of the information capacity. Finally, we turn to  the AWGN channel with fading, and show that the determination of the capacity region reduces to finding the optimal genie strategies and the optimal power allocation distribution along the product alphabet of the auxiliary RV and the quantizer's output alphabets. As a special case, we calculate the capacity region of an on-off  channel and suggest sub-optimal genie strategies, which almost fully achieve the  capacity region over a wide range of power and way-side channel rate constraints.

In addition, we show that the optimal power allocation has a water-filling  interpretation. The suggested model can be applied, for example, to an OFDM communication system.