Bandwidth-BER Trade-off with Multi-symbol M-PSK for Index Coding with Prioritized Receivers

Consider single unicast index coding problems with prioritized receivers with transmissions over additive white Gaussian (AWGN) channels. In this setting, if a length-N index-coded vector is transmitted as a 2
^N
-PSK symbol, there will exist some receivers, especially the lower priority ones, that would not see much improvement over the average bit error probability obtained for a 2
^N
-PSK modulated transmission. On the other hand, if we use binary-modulated transmission, which gives the best probability of performance at the receivers, it will result in an N/2 -fold increase in the bandwidth consumed. Hence, in a setting where each receiver has to satisfy some quality of service requirements, we propose multi-symbol PSK-modulated transmission for a bandwidth-performance trade-off where the
$N$
index-coded bits are mapped to complex symbols of multiple smaller-sized constellations. Depending on the available bandwidth, we can choose the number of symbols to which the N-bit index-coded vector should be mapped. In addition to proposing the multi-symbol modulated transmission, we present an algorithm that takes the
$N$
bits of the index-coded vector and maps it to the multiple complex symbols in a way that guarantees that the highest priority receiver sees the best possible performance followed by the second-highest priority receiver and so on. For the special case of single unicast single uniprior index coding problems, we also describe optimal index code selection to ensure that the highest priority receiver sees the best performance.