Index coded PSK modulation

In this paper, noisy index coding problems over AWGN channel are considered. For a given index coding problem and a chosen scalar linear index code of length N, we propose to transmit the N index coded bits as a single signal from a 2-PSK constellation. By transmitting the index coded bits in this way, there is an N/2-fold reduction in the required bandwidth. Also, by transmitting the index coded bits as a PSK signal, receivers with side information satisfying certain conditions get coding gain relative to a receiver with no side information. This coding gain obtained by the receivers is due to proper utilization of their side information and hence is called “PSK side information coding gain (PSK-SICG)”. We state and prove a necessary and sufficient condition for a receiver to get PSK-SICG. An algorithm to map the index coded bits to PSK signal set such that the PSK-SICG obtained is maximized for the receiver with maximum side information is given. Further, we show that if index coded bits are transmitted as a PSK signal, it is not always necessary to minimize the length of index code used as there are index coding problems where use of a longer index code will give a better performance in terms of probability of error.