Performance Bounds for Linear Codes in Multi-Rate Superposition Schemes

We consider unequal error-protection schemes obtained by means of two-level superposition coding. The performance over additive white Gaussian noise channels is investigated for optimal maximum-likelihood decoding as well as for a suboptimal decoding strategy based on interference cancellation. Assuming that linear codes are used, we evaluate, for both strategies, analytical approximations of the word-error rate, based on the union bound. As in the case of turbo codes and turbo-coded modulations, the derivation exploits the concept of uniform interleaving, and the bounds are in excellent agreement with the simulation results obtained using iterative decoding. The analytical expressions are useful for code design and for the selection of decoding strategies providing a suitable performance/complexity tradeoff.