A Fundamental Inequality for Lower-bounding the Error Probability for Classical and Quantum Multiple Access Channels and Its Applications

TL;DR

This paper introduces a new, more general lower bound on error probability for classical and quantum multiple access channels, strengthening existing bounds and aiding in the analysis of channel capacity and converse theorems.

Contribution

The paper generalizes and strengthens the Yagi-Oohama bound, extending it to broader input distributions, encoders, and quantum MACs, with applications in information-spectrum converse problems.

Findings

A new fundamental inequality for error probability bounds.

Extension of bounds to quantum multiple access channels.

Applications to converse problems in information-spectrum settings.

Abstract

In the study of the capacity problem for multiple access channels (MACs), a lower bound on the error probability obtained by Han plays a crucial role in the converse parts of several kinds of channel coding theorems in the information-spectrum framework. Recently, Yagi and Oohama showed a tighter bound than the Han bound by means of Polyanskiy's converse. In this paper, we give a new bound which generalizes and strengthens the Yagi-Oohama bound, and demonstrate that the bound plays a fundamental role in deriving extensions of several known bounds. In particular, the Yagi-Oohama bound is generalized to two different directions; i.e, to general input distributions and to general encoders. In addition we extend these bounds to the quantum MACs and apply them to the converse problems for several information-spectrum settings.