Joint Source-Channel Coding for Quasi-Static Fading Channels with Quantized Feedback

We consider the transmission of a Gaussian source over a single-input multiple-output (SIMO) quasi-static fading channel. The goal is to minimize the expected distortion of the reconstructed signal at the receiver. We consider a delay-limited scenario where channel coding is restricted to a single realization of the channel. Channel state information (CSI) is assumed to be known perfectly at the receiver, and a zero-delay, noiseless, fixed-rate feedback link provides a quantized version of the CSI to the transmitter. An upper bound on the performance is derived and it is shown that for practical values of the channel signal to noise ratio (SNR), this bound can be achieved with a very limited knowledge of the channel quality. We show that unlike the rate maximization problems, temporal power adaptation at the transmitter provides significant gains, and the amount of the gain heavily depends on the bandwidth expansion ratio. For asymptotically high SNRs, we derive the distortion exponent of the system, defined as the slope of the expected distortion with respect to the channel SNR. We show that the distortion exponent of limited feedback is equivalent to that of superposition coding without feedback, so long as the number of quantization levels in the feedback scheme is equal to the number of the layers in the superposition coding scheme. For the finite-SNR regime, we propose an optimal and efficient numerical technique to design the feedback scheme. Numerical results for a Rayleigh fading channel are also presented.