On Coding with Rate-Limited Side Information

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 part, 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 state. A single letter expression for the capacity of the channel is given. In case the CSIT comprises only the rate limited part we show that the capacity suggested in [5] is too optimistic, and suggest a correction as part of our expression for the information capacity. For the general setting, an optimal coding scheme based upon multiplexing of several codebooks is presented. It is proved that the capacity of the channel is the same whether the quantizer’s output is observed causally or noncausally 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. 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.