  This paper studies noisy index coding problems over single-input
single-output broadcast channels. The codewords from a chosen index code of
length $N$ are transmitted after $2^N$-PSK modulation over an AWGN channel. In
"Index Coded PSK Modulation for prioritized Receivers," the authors showed that
when a length-$N$ index code is transmitted as a $2^N$-PSK symbol, the ML
decoder at a receiver decodes directly to the message bit rather than following
the two-step decoding process of first demodulating the PSK symbol and
equivalently the index-coded bits and then doing index-decoding. In this paper,
we consider unprioritized receivers and follow the two-step decoding process at
the receivers. After estimating the PSK symbol using an ML decoder, at a
receiver, there might be more than one decoding strategy, i.e., a linear
combination of index-coded bits and different subsets of side information bits,
that can be used to estimate the requested message. Thomas et al. in ["Single
Uniprior Index Coding With Min Max Probability of Error Over Fading Channels,"]
showed that for binary-modulated index code transmissions, minimizing the
number of transmissions used to decode a requested message is equivalent to
minimizing the probability of error. This paper shows that this is no longer
the case while employing multi-level modulations. Further, we consider that the
side information available to each receiver is also noisy and derive an
expression for the probability that a requested message bit is estimated
erroneously at a receiver. We also show that the criterion for choosing a
decoding strategy that gives the best probability of error performance at a
receiver changes with the signal-to-noise ratio at which the side information
is broadcast.
