## Probability that the equal-rate capacity and sum-capacity of a MAC coincide (or nearly so): non-asymptotic bounds

### Uri Erez (Tel Aviv University)

**Abstract: **

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication scheme is considered where all users transmit at (just below) the equal-rate capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the transmission scheme. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains an equal-rate point, i.e., that the scheme strictly attains the sum-capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the MAC channel.