UC San Diego

Random independently and identically distributed code ensembles play a fundamental role in characterizing the limits of communication rates over different network models, with most existing coding schemes built on them. It has been shown in various problems, on the other hand, these conventional random coding schemes are outperformed by \emph{structured} ones that are well-suited to the problem of interest, resulting in strictly better communication rates. This dissertation investigates the benefits of structured codes for a wider class of network models that can be grouped into two parts. In the first part, a special code structure that is built on linearity shared by multiple senders is studied for the two conflicting canonical problems defined over multiple access channels: linear computation of codewords and message communication. For linear computation, the optimal decoding performance of such structured codes is analyzed, which yields strictly larger rates than random coding. For message communication, it is shown that the aforementioned family of structured codes can achieve the optimal tradeoff between communication rates. In the second part, a structured transmission scheme, referred to as caching, is studied to reduce the network load between a server that stores a set of file contents and users that request a file from the server. To cope with the unpredictable nature of file contents and user requests, two new caching problems are formulated. As an answer to these caching problems, a successive refinement approach is proposed to store some partial information about file contents in small increments into the memories of end users. These results motivate further research into the potential of structured codes in network communication.