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Informational properties of networks under communication constraints

Periodic Reporting for period 2 - InfoNet (Informational properties of networks under communication constraints)

Période du rapport: 2022-04-01 au 2023-09-30

In our contemporary information era, there's a virtual explosion of data being generated every single day. From smartphones to self-driving cars, from online shopping to social media, and from remote sensing satellites to complex biomedical research - the sources and volume of data are vast and continually expanding. Every day we create, share, and store an astronomical amount of information. But this ever-growing flood of data presents new and fundamental challenges in how we manipulate, store, transmit, and retrieve this data efficiently and reliably.

These challenges are at the forefront of information science and technology and have significant implications for nearly every sector of our economy and society. They are the driving force behind the development of sophisticated data encoding and decoding strategies, which ensure that our information can be efficiently and securely handled.

This project is positioned at the center of this exciting and vital domain. It aims to research and develop new methods for coding theory, a cornerstone of modern data communication and storage systems. The goal is to push the boundaries of how we can ensure reliable, efficient, and secure data transmission, even in situations where parts of the system might fail or operate under constraints.

Here are the primary objectives of the project:

Better Data Storage: The project aims to improve the way we store data across a network. This means creating systems that can take in information, figure out the best place to store it, and then do so in a way that's extra secure and reliable.

Fixing Errors More Efficiently: Another goal is to get better at spotting when data has been lost or changed and recovering it. This is like having a detective in the network that can solve the mystery of what went wrong and fix it.

Dealing with 'Bad' Nodes: Just like in any community, there might be a few 'bad apples' in a network – nodes that cause disruptions. The project aims to better understand these 'bad apples' and create strategies to handle them, ensuring they can't do too much damage.

Making Sense of Limited Information: Sometimes, parts of a network (nodes) can only send a little bit of information at a time due to limitations in power or communication. This project will look into ways to still understand what's going on, even when we only have a little bit of information to work with.

Making Theory Useful: Finally, the project will also work on ways to apply these new ideas and techniques to real-world networks to make them more efficient and reliable.

In summary, this project is addressing some of the most pressing challenges that have arisen in the wake of the data explosion in the information era. The project team seeks to enhance our capabilities in data management, contributing to a future where information is harnessed more effectively and securely.
Improving Data Storage and Fixing Errors: Our main focus was on Reed Solomon codes, which is a special family of codes used often in data storage to keep information safe and secure. Here's what we found out:

Better Recovery from a Single Erasure: Imagine you had a book and suddenly a page went missing; that's an erasure. We found a better way to "find" that missing page and restore it, making our data storage even more reliable.

Fighting Against Insertions and Deletions: Sometimes, errors might sneak in and either add extra stuff that doesn't belong (insertions) or remove parts of the data (deletions). This is a tough problem in data storage, but we made significant progress in fighting against these types of errors.

Improving the Singleton Bound for List Decoding: In data storage, "decoding" is the process of reading the information stored in codes. The "Singleton Bound" is a limit on how many errors we can spot and fix when we're decoding. We managed to improve this limit when using a method called "list decoding," which helps us make better sense of the data even when there are a lot of errors.

Securing Your File Access with Private Information Retrieval: Imagine you wanted to pull a book off a library shelf, but you didn't want anyone to know which book you took. That's the challenge we're tackling but in a digital space called private information retrieval.

Our goal was to understand the PIR capacity or the maximum rate at which a user can privately retrieve information, within a system where each file (or 'book') is stored on two distinct servers according to a certain network layout, which we represent with a graph.

Here's what we achieved:

Better Understanding Through Graph Properties: By studying the characteristics and structure of the graph, we were able to provide bounds on the PIR capacity. These bounds give us an idea on the minimum and maximum capacity for private file retrieval across many types of networks. For certain types of graphs, we were able to provide even more precise bounds. This means that in specific scenarios, we have a more exact understanding of how much data we can privately retrieve.

In simpler terms, we have improved our data storage, protection, and retrieval methods, thereby enhancing the reliability and efficiency of our systems, leading to better data management practices.
Expected Results Until the End of the Project:

Further Development in Dealing with Malicious Nodes: We plan to continue our work on adversarial nodes, focusing on dynamic environments where network conditions and node behavior can change rapidly. We aim to establish more robust strategies to swiftly adapt to these changes and maintain network integrity and data accessibility.

Deeper Analysis of Network Types: With our ongoing research on deterministic and random networks, we anticipate a deeper understanding of how different network types can optimize data storage and recovery. This should lead to more sophisticated network design strategies and data-handling procedures.

Improving Decoding Mechanisms: We aim to refine our decoding techniques further, with the goal of enhancing the efficiency of data recovery from partial information. This will involve innovative algorithm development.

Real-World Applications: We plan to focus also on real-world applications of our findings by implementing our research in practical settings such as cloud storage, sensor networks, and the Internet of Things. Our team is working on creating simple yet effective algorithms that the industry can easily adopt, providing practical and cutting-edge solutions.

In summary, this project is poised to make significant contributions to data storage and recovery in network environments, pushing the boundaries of current understanding and delivering practical solutions to real-world challenges.
Servers in a server farm