How Fast Can Dense Codes Achieve the Min-Cut Capacity of Line Networks?

TL;DR

This paper investigates the speed at which dense network codes approach the min-cut capacity in line networks, providing tighter bounds and a clearer understanding of their convergence behavior under various network conditions.

Contribution

It offers new upper bounds on coding delay and average coding delay for dense codes, improving upon existing bounds in generality and tightness.

Findings

Derived tighter upper bounds on coding delay

Analyzed convergence speed of dense codes to capacity

Applicable to networks with losses and different transmission schedules

Abstract

In this paper, we study the coding delay and the average coding delay of random linear network codes (dense codes) over line networks with deterministic regular and Poisson transmission schedules. We consider both lossless networks and networks with Bernoulli losses. The upper bounds derived in this paper, which are in some cases more general, and in some other cases tighter, than the existing bounds, provide a more clear picture of the speed of convergence of dense codes to the min-cut capacity of line networks.