Coding for distributed storage and computing

Abstract

Over the past few decades, coding has been a viable solution to maintain a desired level of system's reliability by controlling errors or erasures in communication and storage channels. In this thesis, we explore the role of coding that enhances the key performance metrics enabling distributed systems. In the first part, we suggest a design of low-density parity-check (LDPC) codes for distributed storage applications exploiting trade-offs between reliability, repair bandwidth and storage overhead. We establish that the regular LDPC code yields a minimum repair bandwidth for a given code rate. It is further shown that LDPC codes can be designed such that a small loss of repair-bandwidth optimality may be traded for a large improvement in erasure-correction capability and thus the mean-time-to-data-loss (MTTDL). In the second part, we propose a framework wherein the NAND flash memory system is regarded as distributed storage. In this context, NAND elements such as pages and blocks are viewed as distributed nodes. We study potential enhancement of the read access speed in solid-state drives (SSDs) by coding. Our analysis provides a clear picture on the coding-overhead and read-access-time trade-offs given read failures and node failures. Node failures reflect various limitations on the memory element level such as page or block failures. Lastly, we propose a modeling of the clustered structure for distributed computing consisting of intra- and cross-cluster coding, reflecting the practical constraints of the imbalance in speed throughout the computing system. A strong motivation for this model is the need for reducing the high decoding burden of large-scale coded computation. It is seen that resorting to cross-cluster coding to a certain point---related to the overall code rate and the ratio between the speed of intra- and extra-cluster work---greatly enhances latency. Incorporating the decoding burden into the latency analysis, the proposed clustered structure is seen to have further latency advantage over the existing non-clustered coded computing.