Computation over Mismatched Channels

TL;DR

This paper investigates the effects of mismatched target and channel functions on distributed computation over multiple-access channels, concluding that separation-based designs are generally optimal when functions are mismatched.

Contribution

It provides an analysis of when joint computation and communication designs outperform separation, showing that for most mismatched functions, separation is optimal.

Findings

Joint design offers significant gains when functions are matched.

For most mismatched functions, separation-based design is optimal.

Mismatch generally reduces the benefits of joint computation and communication.

Abstract

We consider the problem of distributed computation of a target function over a multiple-access channel. If the target and channel functions are matched (i.e., compute the same function), significant performance gains can be obtained by jointly designing the computation and communication tasks. However, in most situations there is mismatch between these two functions. In this work, we analyze the impact of this mismatch on the performance gains achievable with joint computation and communication designs over separation-based designs. We show that for most pairs of target and channel functions there is no such gain, and separation of computation and communication is optimal.