Data and analytics capabilities have made a leap forward in recent years. The volume of available data has grown exponentially. The huge amount of data needs to be transferred and stored with extremely high reliability. The concept of "coded computing", or a distributed computing paradigm that utilizes coding theory to smartly inject and leverage data/computation redundancy into distributed computing systems, mitigates the fundamental performance bottlenecks for running large-scale data analytics.
In this dissertation, a distributed computing framework, first for input files distributedly stored on the uplink of a cloud radio access network architecture, is studied. It focuses on that decoding at the cloud takes place via network function virtualization on commercial off-the-shelf servers. In order to mitigate the impact of straggling decoders in this platform, a novel coding strategy is proposed, whereby the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors. Transmission of a single frame is considered first, and upper bounds on the resulting frame unavailability probability as a function of the decoding latency are derived by assuming a binary symmetric channel for uplink communications. Then, the analysis is extended to account for random frame arrival times. In this case, the trade-off between an average decoding latency and the frame error rate is studied for two different queuing policies, whereby the servers carry out per-frame decoding or continuous decoding, respectively. Numerical examples demonstrate that the bounds are useful tools for code design and that coding is instrumental in obtaining a desirable compromise between decoding latency and reliability.
In the second part of this dissertation large matrix multiplications are considered which are central to large-scale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold, i.e., the number of workers required to recover the matrix product, and communication load, and the total amount of data to be downloaded from the workers. In addition to exact recovery requirements, security and privacy constraints on the data matrices are imposed, and the recovery threshold as a function of the communication load is studied. First, it is assumed that both matrices contain private information and that workers can collude to eavesdrop on the content of these data matrices. For this problem, a novel class of secure codes is introduced, referred to as secure generalized PolyDot codes, that generalize state-of-the-art non-secure codes for matrix multiplication. Secure generalized PolyDot codes allow a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers while providing perfect secrecy for the two data matrices. Then, a connection between secure matrix multiplication and private information retrieval is studied. It is assumed that one of the data matrices is taken from a public set known to all the workers. In this setup, the identity of the matrix of interest should be kept private from the workers. For this model, a variant of generalized PolyDot codes is presented that can guarantee both secrecy of one matrix and privacy for the identity of the other matrix for the case of no colluding servers.
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