Coded multicasting and coded computing for wireless edge processing

Abstract

In this dissertation, we studied coded multicasting and coded computing for wireless edge processing systems. Coded multicasting (or Index coding) is a method, which serves users’ requests simultaneously via exclusive-or (XOR) operation leveraging the stored information at users. Since index coding can be interpreted as a kind of source coding, we reveal that the optimal index code should be dependent on the channel conditions, not simply on the number of transmissions. Then, we find the optimal index code and the optimal time allocation that minimizes the overall outage probability of the users. We found the optimal index code based on majorization theory and the Hasse diagram. On the other hand, coded computing is a method to allocate redundant computed tasks, to combat the bottleneck of distributed computing. First, from the structural insight of the Strassen algorithm and the aid of frame quantization theory, we propose a novel straggler mitigation scheme, which guarantees moderate performance even for the limited number of nodes. Second, we elaborate on how to distribute and reconstruct the matrix multiplication using the group theory and representation theory. Moreover, we derive the condition for perfectly reconstructing the original solution from the local computation results of the worker nodes.