# Signal Shaping for Two-User Gaussian Multiple Access Channels with Computation: Beyond the Cut-Set Bound

## TL;DR

This paper explores optimized signal shaping in a two-user Gaussian MAC with computation, demonstrating that carefully chosen input distributions can surpass the traditional cut-set bound, with practical distributions achieving significant gains.

## Contribution

It introduces a method to optimize input distributions for Gaussian MAC with computation, surpassing the cut-set bound, and analyzes the mutual information behavior in this context.

## Key findings

- Optimized input distributions outperform the cut-set bound.
- Mutual information is non-concave due to computation at the receiver.
- Achieved a 4.0349 dB gain with specific 16-PAM distributions.

## Abstract

In this paper, we investigate the signal shaping in a two-user discrete time memoryless Gaussian multiple-access channel (MAC) with computation. It is shown that by optimizing input probability distribution, the transmission rate per transmitter is beyond the cut-set bound. In contrast with the single-user discrete memoryless channel, the Maxwell-Boltzmann distribution is no longer a good approximation to the optimal input probability distribution for this discrete-time Gaussian MAC with computation. Specifically, we derive and analyze the mutual information for this channel. Because of the computation in the destination, the mutual information is not concave in general on the input probability distribution, and then primal-dual interior-point method is used to solve this non-convex problem. Finally, some good input probability distributions for 16-ary pulse amplitude modulation (PAM) constellation are obtained and achieve $4.0349$ dB gain over the cut-set bound for the target transmission rate $3.0067$ bits/(channel use).