Finite-Length Analysis of Frameless ALOHA With Multi-User Detection

In this letter, we present a finite-length analysis of frameless ALOHA for a k multi-user detection scenario, i.e., assuming the receiver can resolve collisions of size k or smaller. The analysis is obtained via a dynamical programming approach, and employed to optimize the scheme's performance. We also assess the optimized performance as a function of k. Finally, we verify the presented results through Monte Carlo simulations.