Neural Computation of Capacity Region of Memoryless Multiple Access Channels

TL;DR

This paper introduces a neural network-based numerical framework to accurately compute the achievable rate region of memoryless MACs with continuous alphabets, improving estimation accuracy and efficiency over previous methods.

Contribution

The paper presents a novel neural network approach using variational bounds to estimate the rate region of MACs, providing tighter bounds than existing estimators.

Findings

Tighter rate region estimates at high SNRs compared to MINE-based methods.

Efficient computation of the rate boundary for optical intensity MAC.

Achieved a new, tighter achievable rate boundary than prior work.

Abstract

This paper provides a numerical framework for computing the achievable rate region of memoryless multiple access channel (MAC) with a continuous alphabet from data. In particular, we use recent results on variational lower bounds on mutual information and KL-divergence to compute the boundaries of the rate region of MAC using a set of functions parameterized by neural networks. Our method relies on a variational lower bound on KL-divergence and an upper bound on KL-divergence based on the f-divergence inequalities. Unlike previous work, which computes an estimate on mutual information, which is neither a lower nor an upper bound, our method estimates a lower bound on mutual information. Our numerical results show that the proposed method provides tighter estimates compared to the MINE-based estimator at large SNRs while being computationally more efficient. Finally, we apply the proposed method to the optical intensity MAC and obtain a new achievable rate boundary tighter than prior works.