Performance Bounds of Coded Slotted ALOHA Over Erasure Channels

In this paper, we derive an upper bound on load-threshold of coded slotted ALOHA (CSA) for slot erasure channel (SEC) and that for packet erasure channel (PEC), respectively. In SEC, by exploiting the analogy between Gaussian elimination of solving linear equations and the iterative successive interference-cancellation (SIC) decoding procedure of CSA, we derive the upper performance bound for SEC. Subsequently, in PEC, utilizing density evolution to track the average probability of packet-decoded failure within the SIC decoding process, we obtain the upper bound for PEC. Moreover, we propose a numerical search algorithm of these bounds under a given calculating precision. The numerical results indicate that the asymptotic upper limit on load-threshold of CSA over SEC is always less than that over PEC with any given erasure probability and average transmission rate.