Index Coded PSK Modulation for Prioritized Receivers

A noisy index coding problem (ICP) over additive white Gaussian noise (AWGN) and Rayleigh fading channels is studied. First, a single-input single-output AWGN broadcast channel is considered. For a chosen index code and an arbitrary mapping (of broadcast vectors to phase-shift keying (PSK) signal points), a decision rule for the maximum-likelihood (ML) decoder is derived. The message error performance of a receiver at high signal-to-noise ratio (SNR) is characterized by a parameter called PSK-index coding gain (PSK-ICG). The PSK-ICG of a receiver is determined by a metric called minimum inter-set distance. For a given ICP with an order of priority among the receivers, and a chosen 2
^N
-PSK constellation, an algorithm to find (index code, mapping) pairs, each of which gives the best performance in terms of PSK-ICG of the receivers, is proposed. No other pair of index code (of length N with 2N broadcast vectors) and mapping can give a better PSK-ICG for the highest priority receiver. Also, given that the highest priority receiver achieves its best performance, the next highest priority receiver achieves its maximum gain possible and so on in the specified order of priority. Next, the noisy ICP over a multiple-input multiple-output (MIMO) Rayleigh fading channel is considered. The receivers are equipped with a single antenna and a server with two antennas. To obtain the diversity gain along with the coding gain, a MIMO scheme that employs space-time coding along with index coded PSK modulation is proposed. For a chosen index code, an arbitrary mapping (of broadcast vectors to PSK signal points), and a 2 × 1 MIMO system employing Alamouti code, we derive a decision rule for the ML decoding. We show that for the best coding gain at high SNR, the mapping must maximize the minimum inter-set distance.