Coded Slotted ALOHA Scheme with Multi-Packet Reception under Erasure Channels

Coded slotted ALOHA (CSA) scheme is a promising grant-free multi-access protocol because it possesses a strong capability of collision resolution. The performance evaluation of the CSA scheme in wireless multi-access system is of great significance and challenge due to various channel characteristics and physical layer technologies. This work investigates the performance of CSA scheme when the access point (AP) is capable of retrieving multiple packets in collided signals and the transmission experiences packet and slot erasures. Specifically, %following an iteration process analysis of the successive interference cancellation during packet recovery, an implicit expression of the decoding failure probability is derived for the general CSA scheme in packet erasure channel by appropriately parameterizing the multi-packet reception capability and channel erasure probability. The implicit expression analysis on the decoding failure probability of the CSA scheme is further extended to slot erasure channels. Based on the obtained results, %characterization on the decoding failure probability of two specific CSA systems, namely, repetition coding- and maximal distance separate (MDS) coding-based CSA systems is also presented. the packet loss ratio, the throughput, and the energy efficiency of the repetition coding-based and maximal distance separate (MDS) coding-based CSA systems are derived in detail. The optimal transmit power that achieves the maximal energy efficiency is presented in closed-form. Simulation results validate the correctness of the theoretical analyses. It shows that %an appropriate UE degree distribution would be useful for suppressing the error floor caused by channel erasures. Using same distributions, the MDS coding can achieve a higher throughput than the repetition coding. With optimized transmit power, the energy efficiency of the system can be improved significantly. © 2023 IEEE