  We propose index codes, based on multidimensional QAM constellations, for the
Gaussian broadcast channel, where every receiver demands all the messages from
the source. The efficiency with which an index code exploits receiver side
information in this broadcast channel is characterised by a code design metric
called "side information gain". The known index codes for this broadcast
channel enjoy large side information gains, but do not encode all the source
messages at the same rate, and do not admit message sizes that are powers of
two. The index codes proposed in this letter, which are based on linear codes
over integer rings, overcome both these drawbacks and yet provide large values
of side information gain. With the aid of a computer search, we obtain QAM
index codes for encoding up to 5 messages with message sizes 2^m, m <= 6. We
also present the simulated performance of a new 16-QAM index code, concatenated
with an off-the-shelf LDPC code, which is observed to operate within 4.3 dB of
the broadcast channel capacity.
