Coding for Fading Channels with Imperfect CSI at the Transmitter and Quantized Feedback

The classical Schalkwijk-Kailath (SK) scheme for the additive Gaussian noise channel with noiseless feedback is highly efficient since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. However, how to extend the SK scheme to channel models with memory has yet to be solved. In this paper, we first investigate how to design SK-type scheme for the 2-path quasi-static fading channel with noiseless feedback. By viewing the signal of the second path as a relay and adopting an amplify-and-forward (AF) relay strategy, we show that the interference path signal can help to enhance the transmission rate. Besides this, for arbitrary multi-path fading channel with feedback, we also present an SK-type scheme for such a model, which transforms the time domain channel into a frequency domain MIMO channel.