Index Coded PSK Modulation for Prioritized Receivers over Rayleigh Fading Channels

Noisy index coding problem over single-input singleoutput (SISO) additive white Gaussian noise (AWGN) broadcast channel has been studied in [6]. Further the performance of high priority receivers has been improved by using rotated PSK constellation in [7] for AWGN broadcast channel. In this work, we consider noisy index coding problem in which the source transmits symbols over a SISO Rayleigh fading broadcast channel. We show that even for transmission over Rayleigh fading channel minimum inter-set distance, as seen by the receiver plays a crucial role in its ML decoding performance unlike classical fading cases. For improving the performance of high priority receivers for a chosen index code of length N we are transmitting N bits over Rayleigh fading channel using a rotated M-PSK (M = 2(N)) constellation where half of the signal points have been rotated in such a way to maximize the minimum inter-set distance. Additionally, we account for the multiplicity of signal pairs along with inter-set distance as a factor to achieve better ML decoding performance for some index coding problems with rotated constellation for prioritized receivers over fading channel.