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, and their outputs match those of the previous algorithms across all tested parameters. 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：本文研究信道编码中不等差错保护的一种变体，其中消息比特串被划分为有限数量的数据块，优化目标为各数据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性能和有限码长性能：一种基于功率域叠加（PDS），另一种基于正交资源分配（ORA），后者亦称为时分复用。推导了最优传输数据块数量的上界，给出了计算两种方案最优功率分配与时间分割的算法。同时提供了计算局部最优功率分配与时间分割的简化算法，其输出在所有测试参数下均与前述算法结果一致。研究结果表明：PDS方案优于ORA方案，但在渐近与有限码长两种机制下性能差异均小于2%（图4-6）。对于PDS和ORA方案，数值结果进一步表明：当n=1000时，渐近性能与有限码长性能的差距上界约为10%；当n=5000时，该差距上界约为3%（图7-10）。