Low overhead vector codes with combination property and zigzag decoding for edge-aided computing in UAV network

Codes that possess combination property (CP) and zigzag decoding (ZD) simultaneously (CP-ZD) has broad application into edge aided distributed systems, including distributed storage, coded distributed computing (CDC), and CDC-structured distributed training. Existing CP-ZD code designs are based on scalar code, where one node stores exactly one encoded packet. The drawback is that the induced overhead is high. In order to significantly reduce the overhead, vector CP-ZD codes are designed, where vector means the number of stored encoded packets in one node is extended from one to multiple. More specifically, in detailed code construction, cyclic shift is proposed, and the shifts are carefully designed for cases that each node stores two, three, and four packets, respectively. Comparisons show that the overhead is reduced significantly.