Improved Upper Bound for the Capacity of the Random-Access Channel

In this paper we improve the bound of Mikhailov and Tsybakov for the capacity of a synchronous random-access channel with a Poisson input and ternary broadcast feedback (from 0.5874 to 0.5789). A major role is played by a random functional $m_t$, which we call the “mortgage time.” We show that $m_t\leq t$ with probability 1, where $t$ is ordinary time, measured in windows. Addition of $r(t-m_t)$ to the objective function of Mikhailov and Tsybakov, where $r$ is an additional optimization parameter, results in the improved upper bound.