Conditions for a Monotonic Channel Capacity

TL;DR

This paper proves that for various memoryless vector channels, including optical and interference channels, the channel capacity generally does not decrease with increased power or cost, under certain conditions.

Contribution

It establishes that channel capacity is nondecreasing with power for static point-to-point and interference channels, generalizing to broader cost functions.

Findings

Channel capacity is nondecreasing with power for static point-to-point channels.

Interference channels with identical interferer distributions also have nondecreasing capacity.

Results extend to capacity as a function of general costs, not just power.

Abstract

Motivated by results in optical communications, where the performance can degrade dramatically if the transmit power is sufficiently increased, the channel capacity is characterized for various kinds of memoryless vector channels. It is proved that for all static point-to-point channels, the channel capacity is a nondecreasing function of power. As a consequence, maximizing the mutual information over all input distributions with a certain power is for such channels equivalent to maximizing it over the larger set of input distributions with upperbounded power. For interference channels such as optical wavelength-division multiplexing systems, the primary channel capacity is always nondecreasing with power if all interferers transmit with identical distributions as the primary user. Also, if all input distributions in an interference channel are optimized jointly, then the achievable sum-rate capacity is again nondecreasing. The results generalizes to the channel capacity as a function of a wide class of costs, not only power.