On the performance of type-III hybrid ARQ with RCPC codes

In this paper, the performance of type III hybrid ARQ with RCPC codes is considered. The combining of multiple retransmitted RCPC codes in type III hybrid ARQ scheme leads to the so-called composite code combining. A new concept, i.e. combined puncturing pattern, is proposed to illuminate its effect. Due to the composite combining, different code symbol may exhibit different effective SNR owing to the accumulative effect, which can be described by the combined puncturing pattern. The closed-form of the pairwise error probability (PEP) is derived for the combined RCPC codes. It is shown that the PEP is dependent on the sum of the symbols´ SNR of the incorrect path. Accordingly, the upper and lower bounds, along with the approximation of the symbols´ SNR, are proposed to evaluate the residual error rate of the combined RCPC codes in type III hybrid ARQ scheme. By using the state-diagram analysis, we obtain the bounds and approximations of the performance of type III hybrid ARQ with RCPC codes. Finally, the applicability of both the proposed bounds and the approximation are validated through numerical analysis and computer simulations.