Coded computation has attracted significant attention because it can eliminate the stragglers' effect effectively. Most existing works of coded computation are designed for linear tasks, such as matrix multiplication. They cannot handle non-linear tasks directly, leading to high computation, transmission and decoding latency. This is not suitable for latency-sensitive services. In this paper, considering a non-linear task in wireless heterogeneous networks, we propose an efficient merged- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> Luby transform (LT) coded computation scheme based on the rateless and sparse LT code. First, we give the merged- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> LT coding strategy to reduce the computation and transmission costs. Then, the maximum degree decoding (MDD) strategy is proposed to speed up the decoding process. Finally, we analyze the latency performance for the whole network by designing the optimal merging parameter and sub-block size. The wireless non-linear merged- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> LT coded computation (WNLMrLTCC) algorithm minimizes the total latency. Theoretical analysis and numerical simulation show that our proposed scheme has significant advantages over the existing ones for non-linear tasks.

Wireless Merged-r LT Coded Computation: A Low-Latency Design for Non-Linear Tasks