  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.
