# Simple Bounds for the Symmetric Capacity of the Rayleigh Fading Multiple Access Channel

## TL;DR

This paper derives tight bounds on the probability that a simple, feedback-based communication protocol attains the sum capacity in a Rayleigh fading MAC, providing insights into the diversity-multiplexing tradeoff and proposing an effective coding scheme.

## Contribution

It introduces tight bounds on the distribution of the symmetric rate in Rayleigh fading MACs and proposes a practical integer-forcing and space-time precoding scheme.

## Key findings

- Bounds characterize the probability of achieving sum capacity.
- Protocol's performance closely relates to the diversity-multiplexing tradeoff.
- Proposed coding scheme is effective for the considered scenario.

## 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 protocol is considered where all users transmit at (just below) the symmetric 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 protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. Finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.