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-rLuby transform (LT) coded computation scheme based on the rateless and sparse LT code. First, we give the merged-rLT 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-rLT 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.

In wireless networks with distributed computing, the computational performance is limited by stragglers. To mitigate the stragglers’ effect, coded computation is adopted through computational redundancy. Moreover, in wireless transmission, transmission errors may occur due to noise, channel fading and so on. Existing works design coded computation and error detection separately. However, this leads to frequent encoding and inefficient allocation. In this paper, we propose a joint computation and transmission coding (JCTC) scheme to design coded computation and error detection jointly. The coded computation is based on Luby transform (LT) code and linear error-detecting codes are applied for the re-transmission mechanism. To achieve the low dynamic encoding, two-layer encoding is adopted. Then, the performances of JCTC scheme are analyzed in terms of latency and computation reliability. Finally, in order to achieve efficient task and redundancy allocation, the wireless LT coded computation with error detection (WLTCC-ED) algorithm is given from both iterative and low-complexity perspectives respectively. Through theoretical analysis and numerical simulation, it shows that our proposed JCTC scheme has significant advantages over separate designs.

In wireless distributed computing, coded computation is adopted through computational redundancy to mitigate the stragglers’ effect. Moreover, transmission errors may occur due to noise, channel fading and so on. Existing works design coded computation and error detection separately. However, this leads to frequent encoding and inefficient allocation. In this paper, we propose a joint computation and transmission coding (JCTC) scheme to design coded computation and error detection jointly. The coded computation is based on Luby transform (LT) code and linear error-detecting codes are applied for the retransmission mechanism. To achieve the low dynamic encoding, two-layer encoding is adopted. Then, the performances of JCTC scheme are analyzed. Finally, in order to achieve efficient task and redundancy allocation, the wireless LT coded computation with error detection (WLTCC-ED) algorithm is given. Through the simulation, it shows that our proposed JCTC scheme has significant advantages over separate designs.