An Analytical Model for Perpetual Network Codes in Packet Erasure Channels

Perpetual codes provide a sparse, but structured coding for fast encoding and decoding. In this work, we illustrate that perpetual codes introduce linear dependent packet transmissions in the presence of an erasure channel. We demonstrate that the number of linear dependent packet transmissions is highly dependent on a parameter called the width (\(\omega \)), which represents the number of consecutive non-zero coding coefficient present in each coded packet after a pivot element. We provide a mathematical analysis based on the width of the coding vector for the number of transmitted packets and validate it with simulation results. The simulations show that for \(\omega = 5\), generation size \(g = 256\), and low erasure probability on the link, a destination can receive up to \(70\%\) overhead in average. Moreover, increasing the width, the overhead contracts, and for \(\omega \ge 60\) it becomes negligible.