Codes With Hierarchical Locality

In this paper, we study the notion of {\em codes with hierarchical locality} that is identified as another approach to local recovery from multiple erasures. The well-known class of {\em codes with locality} is said to possess hierarchical locality with a single level. In a {\em code with two-level hierarchical locality}, every symbol is protected by an inner-most local code, and another middle-level code of larger dimension containing the local code. We first consider codes with two levels of hierarchical locality, derive an upper bound on the minimum distance, and provide optimal code constructions of low field-size under certain parameter sets. Subsequently, we generalize both the bound and the constructions to hierarchical locality of arbitrary levels.Comment: 12 pages, submitted to ISIT 201

Error-Correcting Codes for Networks, Storage and Computation

The advent of the information age has bestowed upon us three challenges related to the way we deal with data. Firstly, there is an unprecedented demand for transmitting data at high rates. Secondly, the massive amounts of data being collected from various sources needs to be stored across time. Thirdly, there is a need to process the data collected and perform computations on it in order to extract meaningful information out of it. The interconnected nature of modern systems designed to perform these tasks has unraveled new difficulties when it comes to ensuring their resilience against sources of performance degradation. In the context of network communication and distributed data storage, system-level noise and adversarial errors have to be combated with efficient error correction schemes. In the case of distributed computation, the heterogeneous nature of computing clusters can potentially diminish the speedups promised by parallel algorithms, calling for schemes that mitigate the effect of slow machines and communication delay. This thesis addresses the problem of designing efficient fault tolerance schemes for the three scenarios just described. In the network communication setting, a family of multiple-source multicast networks that employ linear network coding is considered for which capacity-achieving distributed error-correcting codes, based on classical algebraic constructions, are designed. The codes require no coordination between the source nodes and are end to end: except for the source nodes and the destination node, the operation of the network remains unchanged. In the context of data storage, balanced error-correcting codes are constructed so that the encoding effort required is balanced out across the storage nodes. In particular, it is shown that for a fixed row weight, any cyclic Reed-Solomon code possesses a generator matrix in which the number of nonzeros is the same across the columns. In the balanced and sparsest case, where each row of the generator matrix is a minimum distance codeword, the maximal encoding time over the storage nodes is minimized, a property that is appealing in write-intensive settings. Analogous constructions are presented for a locally recoverable code construction due to Tamo and Barg. Lastly, the problem of mitigating stragglers in a distributed computation setup is addressed, where a function of some dataset is computed in parallel. Using Reed-Solomon coding techniques, a scheme is proposed that allows for the recovery of the function under consideration from the minimum number of machines possible. The only assumption made on the function is that it is additively separable, which renders the scheme useful in distributed gradient descent implementations. Furthermore, a theoretical model for the run time of the scheme is presented. When the return time of the machines is modeled probabilistically, the model can be used to optimally pick the scheme's parameters so that the expected computation time is minimized. The recovery is performed using an algorithm that runs in quadratic time and linear space, a notable improvement compared to state-of-the-art schemes. The unifying theme of the three scenarios is the construction of error-correcting codes whose encoding functions adhere to certain constraints. It is shown that in many cases, these constraints can be satisfied by classical constructions. As a result, the schemes presented are deterministic, operate over small finite fields and can be decoded using efficient algorithms.</p

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Proceedings of IWAMISSE 2018 the International Workshop on Advanced Materials and Innovative Systems in Structural Engineering: Seismic Practices

The International Workshop on Advanced Materials and Innovative Systems in Structural Engineering: Seismic Practices, IWAMISSE 2018, is co-organised by The International Federation for Structural Concrete Turkey Branch, fib-Turkey, and Istanbul Technical University, ITU, on November 16, 2018 at ITU. The International Federation for Structural Concrete, fib, is a not-for-profit association formed by 45 national member groups and approximately 1000 corporate and individual members. The fib’s mission is to develop at an international level the study of scientific and practical matters capable of advancing the technical, economic, aesthetic and environmental performance of concrete construction. Istanbul Technical University (ITU) was established in 1773 and is a state university which defined and continues to update methods of engineering and architecture in Turkey. It provides its students with innovative educational facilities while retaining traditional values, as well as using its strong international contacts to mould young, talented individuals who can compete not only within their country borders but also in the global arena. With its educational facilities, social life and strong institutional contacts, ITU has always been preferred by Turkey’s most distinguished students since its foundation and has achieved justified respect. The workshop covers the topics of advanced materials and innovative systems in structural engineering with a focus on seismic practices as well as other issues related with steel fiber reinforced concrete, anchors/fasteners, precast structures, and recent advances on different types of structural systems such as reinforced concrete, steel, and reinforced masonry structures. This proceeding book contain sixteen papers from ten countries worldwide. We have no doubt that the up-to-date subjects covered during the workshop will be extremely beneficial for the workshop participants both from academia and industry. We would like to thank all authors for their contributions to the workshop as well as the members of the International Scientific Committee for their rigorous work for reviewing the papers. We also gratefully acknowledge the support of the sponsoring companies and we express our sincere thanks to organization committee for their tireless efforts in the overall organization of the workshop. Many thanks go as well to undergraduate and graduate students from ITU for their assistance during all stages of the workshop

Proceedings of the 8th International Conference on Civil Engineering

This open access book is a collection of accepted papers from the 8th International Conference on Civil Engineering (ICCE2021). Researchers and engineers have discussed and presented around three major topics, i.e., construction and structural mechanics, building materials, and transportation and traffic. The content provide new ideas and practical experiences for both scientists and professionals