Optimal Finite Length Coding Rate of Random Linear Network Coding Schemes

TL;DR

This paper introduces a methodology to determine the optimal finite-length coding rate for various random linear network coding schemes over line networks, balancing throughput and delay.

Contribution

It models the encoding and error processes mathematically and proposes a binary search algorithm to find optimal coding rates for different traffic and erasure conditions.

Findings

Optimal coding rate increases exponentially with blocklength.

Non-capacity achieving schemes trade throughput for delay.

Re-encoding reduces the exponential slope of coding rate growth.

Abstract

In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different coding schemes in matrix notation and corresponding error probabilities. Specifically, we model the finite-length performance for random linear capacity-achieving schemes: non-systematic (RLNC) and systematic (SNC) and non-capacity achieving schemes: SNC with packet scheduling (SNC-S) or sliding window (SWNC). Then, we propose a binary searching algorithm to identify optimal coding rate for given target packet loss rate. We use our proposed method to obtain the region of exponential increase of optimal coding rate and corresponding slopes for representative types of traffic and erasure rates. Our results show the tradeoff for capacity-achieving codes vs non-capacity achieving schemes, since the latter trade throughput with delay, which is reflected in the decrease of the exponential slope with the blocklength. We also show the effect of the number of re-encoding times, which further decreases the slope.