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Ethernet adopts the well-known binary exponential back-off (BEB) scheme for collision resolution. Operation of the BEB algorithm leads to the last-come-first-served result among competing users (also known as the "capture effect", which allows a few "winning" users to occupy most of the available bandwidth); also, BEB is unstable for every arrival rate greater than 0. Taking advantage of the central control unit (access point or base station) in the wireless network, we propose a novel scheme, fixed collision rate (FCR) back-off algorithm, which repairs the drawbacks of BEB. FCR not only achieves a throughput of 1/e for an extremely busy channel, but also shares the limited bandwidth among competing users in a fairer way. Operation of the FCR scheme relies on estimating the number of users and maintains the collision rate at a constant level. A variety of estimation methods are provided. Simulation results with perfect knowledge of the number of users are obtained to find the performance upper bound of the proposed scheme.