Author: Debarnab Mitra

Publisher:

Published: 2023

Total Pages: 0

ISBN-13:

Channel coding theory offers advanced mathematical techniques that have proven to be highly effective at improving the reliability of traditional communication systems such as wireless communication, storage in memories, and many more. However, modern data driven applications such as blockchains and quantum communications encounter a new set of challenges resulting in new metrics of concerns, e.g., storage requirements, communication costs, security, data rates, etc., compared to traditional systems. These new metrics necessitate new and specialized channel code designs to improve the performance of these systems. In this dissertation, we aim to mitigate the challenges encountered in certain widely used data-driven applications viz. blockchains and quantum communications by designing specialized channel codes that are tailor-made for each specific application. The first line of the dissertation is focused on specialized Low-Density Parity-Check (LDPC) code design to mitigate challenges present in blockchain systems. These systems are known to suffer from a security vulnerability known as Data Availability (DA) Attacks where system users accept an invalid block with unavailable portions. Existing work focused on utilizing random LDPC codes and 2D Reed-Solomon (2D-RS) codes to mitigate DA attacks. Although effective, these codes are not necessarily optimal for this application, especially for blockchains with small block sizes. For these types of blockchains, we propose a co-design of specialized LDPC codes and code word sampling strategies to result in good system performance in terms of DA detection probability and communication cost. We devise our co-design techniques to tackle adversaries of varying strengths and demonstrate that they result in a higher probability of detection of DA attacks and lower communication cost compared to approaches in earlier literature. The second line of the dissertation is focused on specialized polar code design to mitigate DA attacks in blockchains with large block sizes. Previously used 2D-RS codes and LDPC codes are difficult to apply to blockchains with large block sizes due to their large decoding complexity and coding fraud proof size (2D-RS codes), and intractable code guarantees for large code lengths (LDPC codes). To mitigate DA attacks in blockchains with large block sizes, we propose a novel data structure called Graph Coded Merkle Tree (GCMT): a Merkle tree encoded using the encoding graph of polar codes. Additionally, we propose a specialized polar code design algorithm for the GCMT. We demonstrate that the GCMTbuild using the above specialized polar codes simultaneously performs well in the various performance metrics relevant to DA attacks at large block sizes including DA detection probability, communication cost, tractable code guarantees, and decoding complexity. The third line of the dissertation is focused on an important application in quantum communication known as Quantum Key Distribution (QKD). QKD aims to provide private keys to multiple users at a large key generation rate. LDPC codes have been previously utilized to extract private keys in QKD. However, the existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this dissertation, we propose novel and specialized channel coding techniques to result in high key generation rates in QKD systems. Firstly, we propose a joint code rate and LDPC code design algorithm that is tailored to use the properties of the QKD channel for high key rates. Secondly, we propose an interleaved decoding algorithm to extract the private key from raw quantum data. We demonstrate that the above techniques significantly improve the private key generation rate in QKD systems compared to approaches in earlier literature.