SAZD: A Low Computational Load Coded Distributed Computing Framework for IoT Systems

Coded distributed computing (CDC) can overcome the problem that the computation of matrix multiplication with an extremely huge dimension cannot be executed in a single Internet-of-Things (IoT) node. All the encoding of existing CDC schemes are based on the linear combination (LC) to generate independent computation tasks, which introduces a heavy computational load, including a significant volume of expensive multiplications (compared with inexpensive additions) and even more expensive divisions to the encoding and decoding phases. Note that the number of elementwise multiplications of the LC operation during the encoding phase is <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> times that of the original computation task, where <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> denotes the number of worker nodes. In this article, to avoid expensive multiplications introduced by LC, a fresh new CDC framework based on shift-and-addition (SA) over the real field is proposed. In addition, to avoid the expensive matrix inverse operation (divisions) in the decoding phase, zigzag decoding (ZD) is incorporated. The proposed scheme, which combines SA and ZD and is hence named SAZD-based CDC, avoids expensive multiplications and divisions in both the encoding and decoding phases. It targets the following simultaneous objectives: an arbitrary <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> out of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> generated computation tasks is independent and can recover the original computation tasks with the ZD algorithm, and the shift distance is small so as to cause a light additional computational load in the computation phase. Both analysis and practical study show that compared to the LC-based CDC, the SAZD-based CDC significantly reduces the computational load.