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In this article, we investigate two variants of traditional automatic repeat request (ARQ) protocols that exploit the disparity in bit error protection levels of multi-resolution M-ary phase-shift-keying for prioritizing the transport of more ldquocriticalrdquo messages in integrated voice/data and delay-sensitive applications (e.g., audio/video streaming). This cross-layer design can lead to a substantial performance improvement (e.g., better sound/picture quality or enhanced throughput of high priority messages) over non-prioritized transmission especially at low and moderate mean channel signal-to-noise ratio (SNR) values or during network congestion. For instance, our numerical results reveal that the proposed SR-ARQ-I and SR-ARQ-II schemes (beta = 0.4) yield approximately 56% and 163% higher throughput than the traditional selective-repeat ARQ protocol in Rayleigh fading at the mean channel SNR of 19dB. This significant throughput gain is obtained by not discarding the correctly demodulated bits within the erroneously demodulated symbols, and also by reducing the average number of retransmission requests in SR-ARQ-II protocol through better error protection (if possible) for the retransmitted packets. However, there exists a slight throughput penalty in the high SNR regime due to competitive nature of the ldquooptimal reliable signaling raterdquo in an unknown time-varying channel.