Dynamic, Decentralized Spatial Code Reuse for OCDMA LiDAR in Robot Swarms

Robots in a LiDAR-equipped swarm mutually interfere when their optical ranging codes collide. Existing mitigations either assign codes statically – requiring $L=N$ distinguishable codes for $N$ robots – or react to detected interference without a scalable, coordinated assignment rule beneath them; prior work explicitly identifies the code-assignment scaling problem as unsolved. We propose a decentralized protocol in which robots dynamically reassign spatial reuse codes based on a live, beacon-maintained interference-neighborhood graph, and prove that the number of codes required grows as $O(\log N\mathrm{/}\log \log N)$ under constant robot density – an unbounded improvement over the $\mathrm{\Theta }(N)$ growth of static assignment. We validate this result under conditions substantially beyond the idealized proof – robot mobility, imperfect beacon-based detection, and reactive reassignment – via Monte Carlo simulation (30 seeds per condition, 95% confidence intervals): the advantage over static assignment widens from roughly $2\times$ at 15 robots to $12\times$ at 120. Against a structurally faithful, fairly constructed model of an existing coordination-free approach, our protocol achieves both substantially greater code-reuse efficiency and 30–40% lower collision risk under an identical, constrained code budget, demonstrating that coordination – not merely reactivity – is what closes the scaling gap.