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Most existing contention access schemes are inherently unstable resulting in exponentially deteriorating throughput under increased traffic loads. In this paper, we propose a wide-sense stable (WSS) efficient hexanary-feedback contention access (HFCA) scheme, capable of providing signaling traffic high performance while retaining maximal throughput for wireless access networks. HFCA performs incremental contention resolution, managing a small subset of users at a time via a two-phase process. In the first phase, a group of users is probabilistically admitted, with a negligible probability of the group size greater than five. In the second phase, all users in the group are efficiently resolved. The two-phase process is augmented with hexanary feedback control facilitated by a probability density function (pdf)-based multiuser estimator (PMER) implemented at the physical layer. Basically, PMER measures the exact number of transmitting users (zero to five) in a contention slot by matching the envelope-phase pdf's histograms of received signals to a preconstructed pdf's library. To formally justify the performance of HFCA, we present throughput and stability analysis in which HFCA is shown WSS and the strict-sense stability condition is derived. Finally, analytic and simulation results delineate that, HFCA is highly robust against estimation discrepancy. Significantly, HFCA achieves high performance with respect to maximum stable and saturated throughputs, access delay, and blocking probability.