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).

翻译：我们研究了信道编码中不等差错保护的一种变体形式，其中信息比特串被划分为有限数量的块，最大化目标是各块解码成功概率的加权和。信道模型为准静态瑞利衰落，接收端已知信道状态信息而发送端未知。我们分析了两种可达性方案的渐近和有限块长性能：一种基于功率域叠加（PDS），另一种基于正交资源分配（ORA），也称时分复用。推导了最优传输块数的上界，给出了两种方案的最优功率与时隙分配算法，并提出了计算局部最优功率与时隙分配的简化算法。结果表明PDS性能优于ORA，但在渐近和有限块长两种场景下性能差异均小于2%（图4-6）。对于PDS和ORA，数值结果同时表明：当n=1000时，渐近与有限块长性能差距上界约为10%；当n=5000时，该差距约为3%（图7-10）。