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

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