Weighted Unequal Error Protection over a Rayleigh Fading Channel

Abstract

We study a variant of unequal error protection in channel coding, where the message bit string is divided into a finite number of blocks and the maximization objective is a weighted sum of per-block decoding success probabilities. The channel model is quasi-static Rayleigh fading with channel state information available to the receiver but unavailable to the transmitter. We analyze the asymptotic and finite blocklength performance of two achievability schemes, one based on power-domain superposition (PDS) and another based on orthogonal resource allocation (ORA), also known as time-sharing. Upper bounds on the optimal number of blocks to transmit are derived. Algorithms to compute the optimal power and time splits for the two schemes are given. Simplified algorithms to compute locally optimal power and time splits are also given. Our results show that PDS outperforms ORA, but the performance differential is less than 2% in both the asymptotic and finite blocklength regimes (Figures 4 - 6). For both PDS and ORA, numerical results also upper bound the gap between the asymptotic and finite blocklength performance by approximately 10% for n = 1000 and 3% for n = 5000 (Figures 7 - 10).