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

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 F_q (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).