基于AVX512指令集扩展的线性网络编码伽罗瓦域算法
Galois Field Arithmetics for Linear Network Coding using AVX512 Instruction Set Extensions
摘要：
线性网络编码需要在伽罗瓦域上进行算术运算，更具体地说是在有限扩展域上。虽然GF（2）上的编码简化为简单的XOR运算，但是由于线性依赖性的高机会以及因此冗余的编码分组，该字段对于随机线性网络编码的实际应用不是优选的。在诸如GF（16）和GF（256）的较大字段上的编码不具有该问题，但是明显较慢。处理器的SIMD向量扩展，例如基于x86的系统上的AVX2或基于ARM的设备上的NEON，提供了将性能提高几个数量级的潜力。在本文中，我们提出了不同的算法和伽罗瓦域的基础上AVX512指令集扩展的实现，并将其集成到有限域库libmoepgf。我们将新实现的性能与基于AVX2的参考实现进行了比较，显示出吞吐量的显着增加。此外，我们还提供了各种不同平台提供的最佳编码性能的调查。
英文摘要：
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.
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