The analytic computability of the Shannon transform for a large class of random matrix channels

TL;DR

This paper introduces a class of algebraic random matrix channels enabling the analytical computation of the limiting Shannon transform, with practical numerical methods and closed-form low SNR series coefficients, validated through simulations.

Contribution

It defines a new class of algebraic random matrix channels and provides methods for their Shannon transform computation, including coefficient enumeration and numerical techniques.

Findings

The Shannon transform can be computed analytically for the class.

Numerical techniques effectively approximate the transform.

Closed-form low SNR series coefficients are often obtainable.

Abstract

We define a class of "algebraic" random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We describe this class, the coefficient enumeration techniques and compare theory with simulations.