Finite-length performance comparison of network codes using random vs Pascal matrices

TL;DR

This paper compares the finite-length performance of network codes using random matrices versus Pascal matrices, demonstrating that Pascal-based structured codes outperform random codes in throughput and delay for short code lengths.

Contribution

It introduces a novel Pascal matrix-based structured network coding scheme and a methodology to optimize finite-length coding rates for realistic traffic scenarios.

Findings

Pascal matrix codes outperform random codes in throughput.

Structured codes have minimal overhead and meet delay constraints.

Performance advantage is more significant at short code lengths.

Abstract

In this letter, we evaluate the finite-length performance of network coding when using either random or structured encoding matrices. First, we present our novel construction of structured network codes over Fq (q = 2^m) using Pascal matrices. We present their encoding, re-encoding and decoding in matrix notation and derive their packet loss rate. Second, we propose a novel methodology to compute the optimal finite-length coding rate for representative and realistic traffic applications. Finally, our method allows to compare the performance of our codes with the performance of popular random codes. We show that our constructions always have better throughput and minimal overhead, which is more significant for short code lengths. Further, their larger decoding delay fulfils the delay constraints of realistic scenarios (e.g. 5G multihop networks).