Staged Growth Codes: Intermediate Performance and Overhead Analysis

It is well known that the overhead and error performances of LT codes are primarily determined by the degrees of output symbols. This letter derives a novel relationship using the AND-OR tree analytical technique between the redundancy and release probabilities, and the degree of output symbols in LT codes. Armed with this new relationship, we propose a new class of so-called staged growth codes (SGCs), which can provide the intermediate performance. We investigate the asymptotic performance of the proposed SGCs. In comparison with the conventional growth codes, the SGCs need less feedback messages and the overhead is nearly the same as LT codes when the number of blocks is not too much. Observed from the numerical results, an additional attractive feature of the SGCs in comparison with the growth codes is that the SGCs can provide the often desirable unequal error protection property.