Compound Multiple Access Channel with Common Message and Intersymbol Interference

TL;DR

This paper derives the capacity region for a two-user Gaussian compound MAC with common message and intersymbol interference by transforming it into parallel channels via DFT, enabling explicit capacity characterization.

Contribution

It introduces a method to convert the channel with ISI into an equivalent memoryless model, facilitating capacity analysis for complex multi-user channels.

Findings

Capacity region characterized for the Gaussian compound MAC with ISI.

Method to decompose channels into independent parallel channels using DFT.

Capacity region derived for the strong interference channel with common message and ISI.

Abstract

In this paper, we characterize the capacity region for the two-user linear Gaussian compound Multiple Access Channel with common message (MACC) and with intersymbol interference (ISI) under an input power constraint. The region is obtained by converting the channel to its equivalent memoryless one by defining an n-block memoryless circular Gaussian compound MACC model and applying the discrete Fourier transform (DFT) to decompose the n-block channel into a set of independent parallel channels whose capacities can be found easily. Indeed, the capacity region of the original Gaussian compound MACC equals that of the n-block circular Gaussian compound MACC in the limit of infinite block length. Then by using the obtained capacity region, we derive the capacity region of the strong interference channel with common message and ISI.