Galois Field Arithmetics for Linear Network Coding using AVX512 Instruction Set Extensions

Linear network coding requires arithmetic operations over Galois fields, more specifically over finite extension fields. While coding over GF(2) reduces to simple XOR operations, this field is less preferred for practical applications of random linear network coding due to high chances of linear dependencies and therefore redundant coded packets. Coding over larger fields such as GF(16) and GF(256) does not have that issue, but is significantly slower. SIMD vector extensions of processors such as AVX2 on x86-based systems or NEON on ARM-based devices offer the potential to increase performance by orders of magnitude. In this paper we present an implementation of different algorithms and Galois fields based on the AVX512 instruction set extension and integrate it into the finite field library libmoepgf. We compare the performance of the new implementation to the reference implementation based on AVX2, showing a significant increase in throughput. In addition, we provide a survey of the best possible coding performance offered by a variety of different platforms.