Joint source-channel coding for quasi-static fading channels with noisy quantized feedback

We consider the transmission of a complex 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. A delay-limited scenario is assumed where channel coding is restricted to a single realization of the channel. Quantized channel state information at the transmitter (CSIT) is obtained using a noisy, fixed-rate feedback link and is used to adjust the transmission rate and power. A channel optimized scaler quantizer (COSQ) is designed to incorporate the effects of the errors in the feedback link. For a high quality feedback channel, the proposed COSQ performs close to the noiseless feedback case, while its performance converges to the no-feedback scenario as the feedback channel quality degrades. We show that noisy feedback does not improve the performance at asymptotically high signal to noise ratios (SNRs). Nevertheless, the numerical results for a Rayleigh fading channel show that noisy feedback provides significant gains for practical values of the SNR.