Approximate performance analysis for linear codes in superposition schemes over Gaussian broadcast channels

Unequal error-protection schemes obtained by means of two-level superposition coding are considered. Their performance over Gaussian broadcast channels (GBCs) is investigated with optimal maximum-likelihood decoding as well as with a suboptimal decoding strategy based on interference cancellation. We focus on GBCs without fading and, assuming that linear codes are used, we evaluate, for both decoding strategies, analytical approximations of the word-error rate based on a suitable application of the union bound. As in the case of turbo codes and turbo-coded modulations in schemes without superposition, the derivation of the approximations exploits the concept of uniform interleaving. The analytical expressions obtained are in excellent agreement with the simulation results, and thus provide a useful tool for analysis and design of practical superposition-coding schemes. Unlike the existing design tools, which rely on the assumption of infinite-length superposition codes, the proposed approach allows us to study the effectiveness of finite-length coding schemes with known distance spectrum.