Throughput bound of CDMA unslotted ALOHA with hybrid type II ARQ using rate compatible punctured turbo codes

We derive a throughput bound for CDMA unslotted ALOHA with memory ARQ in general. Since the conventional ´single queue with feedback´ model, customarily employed for an ALOHA system with pure or hybrid type-I ARQ, cannot be applied to this case, we introduce an expanded model, which consists of a network of queues, and apply the Jackson theorem to simplify the analysis. When using code combining, it is very difficult to find the actual probability of packet success. Hence, instead of finding actual values, we evaluate a lower bound on it. Together with the expanded model and the packet success probability bound, we obtain the throughput bound for given composite offered traffic by using an iterative search procedure.