On the Partial Ordering of the Discrete Memoryless Channels Arising in Cooperative Sensor Networks

Abstract

We focus on the open problem of the partial ordering of the Discrete Memoryless Channel (DMC) in the context of cooperative sensor networks. In the case of binary DMCs we identify the regions where the binary DMC capacity is a Schur convex (concave) function under the trace channel matrix constraint. Our approach is based upon majorization theory in connection with partial ordering. We are able to give an answer for partial ordering of general symmetric DMCs in connection with binary DMCs. Our results generalize, and extend, the previous work on partial ordering of DMCs and hold promise for efficient sensor network design.