RESEARCH ON CODE DESIGN FOR CORRECTING SYNCHRONIZATION ERRORS

Abstract

Synchronization errors represent a significant challenge in various communication and storage systems, undermining the reliability and efficiency of data transmission and retrieval processes. These errors occur when the timing or alignment of data becomes distorted during transmission or storage, leading to misinterpretation or loss of information. Addressing synchronization errors is crucial for ensuring data integrity, minimizing data loss, and maximizing system performance. To mitigate the effects of synchronization errors and fortify the resilience of information systems, error correction codes are known as a highly effective approach. Hence, designing synchronization error correction codes is necessary and critical in data transmission and retrieval processes. In information theory, synchronization errors can be manifested in various forms, including deletions, insertions, substitutions, and transpositions of symbols. Consequently, designing synchronization error correction codes means constructing codes that can address deletion, insertion, substitution, and transposition errors. A large body of this thesis is the development of such codes using the number theoretic approach. Specifically, this research delves into the exploration of two novel code designs, each tailored with specific constraints aimed at safeguarding sequences from synchronization errors. The first class of codes involves a binary code aimed at simultaneously rectifying two types of errors while employing techniques such as syndrome and accumulation values. Historically, prior research concentrated on rectifying singular type of errors, such as either a deletion or insertion error. The first proposed code is engineered to counteract the presence of both a deletion and an insertion error within a codeword. To broaden the spectrum of error correction, the second class of codes introduces a nonbinary code designed to rectify different errors, including a single deletion, insertion, substitution, or adjacent transposition errors. This thesis provides insights into the construction of code designs tailored to accommodate various error scenarios based on the specified errors, thereby showcasing the error correction capabilities of these proposed code designs through mathematical analysis. Alongside code designs, this thesis also presents decoding procedures to recover codewords from errors.