Noisy Index Coding with PSK and QAM

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 $2^N$- PSK constellation. By transmitting the index coded bits in this way, there is an $N/2$ - fold reduction in the bandwidth consumed. Also, receivers with side information satisfying certain conditions get coding gain relative to a receiver with no side information. This coding gain is due to proper utilization of their side information and hence is called "PSK side information coding gain (PSK-SICG)". A necessary and sufficient condition for a receiver to get PSK-SICG is presented. 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. We go on to show that instead of transmitting the $N$ index coded bits as a signal from $2^N$- PSK, we can as well transmit them as a signal from $2^N$- QAM and all the results including the necessary and sufficient condition to get coding gain holds. We prove that sending the index coded bits as a QAM signal is better than sending them as a PSK signal when the receivers see an effective signal set of eight points or more.