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Indoor optical wireless communication (IOWC) is a key technology complementing radio communication in 6G. Typically, the downlink of IOWC is implemented using visible light and uplink is implemented using infrared. Though the downlink of IOWC has been studied well, the uplink of multiple-access IOWC requires further research. In this paper, power allocation strategies in the uplink of IOWC with multiple non-cooperative users is studied. Optimizing power allocation in IOWC that maximize sum-rate with power constraints becomes a non-convex problem. First, this paper proposes an alternating maximization algorithm to compute near optimal power allocation policies for small number of users. Next, a phenomenon of invariance is observed when the number of users in the system is large. Under invariance, the optimal power allocation policy of a user becomes independent of other users, thereby facilitating fast and decentralized computation of power allocation strategies. From simulations, it was observed that the invariance can occur even with five to ten users. For the first time, a rigorous analysis of the invariance phenomenon is provided. An algorithm to compute the optimal power allocation at invariance is proposed; this algorithm is proven to achieve the global maxima in sum-rate without the channel knowledge of other users. [ABSTRACT FROM AUTHOR]