Linear Codes, Target Function Classes, and Network Computing Capacity

TL;DR

This paper investigates the effectiveness of linear codes in network computing, analyzing capacity bounds and achievability for various target function classes and coding strategies in single-receiver networks.

Contribution

It provides new capacity bounds and achievability results for different target function classes using routing, linear, and nonlinear coding.

Findings

Capacity bounds vary with target function class.

Linear codes are effective for certain function classes.

Nonlinear coding can outperform linear coding in some scenarios.

Abstract

We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over finite fields. Computing capacity bounds and achievability are given with respect to these target function classes for network codes that use routing, linear coding, or nonlinear coding.