On channels with partial channel state information at the transmitter
We consider an independent and identically distributed (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 two parts, both subject to a rate constraint, and communicated over noiseless way-side channels. The first part is coded CSI, provided by a third party (a genie), and the second part is the output 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 coded part, we show that the capacity previously suggested in the literature 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. In the rest of the correspondence, we focus on the special case where the system employs a stationary quantizer. Using a rate distortion approach we bound the alphabet's size of the auxiliary random variable (RV) of the information capacity. Next, we turn to the additive white Gaussian noise (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. The suggested model can be applied, for example, to an orthogonal frequency-division multiplexing (OFDM) communication system. Here the fading across frequencies comprises the channel state sequence. Coded fading information is provided to the channel encoder via a way-side, rate-limited channel. In addition, since coding operation is expensive, a simpler scheme provides the channel encoder with quantized fading information, e.g., whether each coefficient is above/below a threshold.
scalar quantization power allocation channel with state information fading channels rate distortion with side information rate-limited channel state information