This reprint synthesizes peer-reviewed research papers that explore advances in information theory, coding techniques, and their interdisciplinary applications. The topics covered include error-correcting codes, data compression, cryptographic protocols, and the theoretical foundations of communication systems. The works highlight both theoretical innovations and practical implementations, offering insights for researchers in mathematics, computer science, and engineering. This reprint serves as a curated reference for scholars and practitioners seeking to deepen their understanding of how information theory shapes modern technologies, from secure communications to efficient data storage. By compiling these studies in a single volume, it provides a cohesive overview of the current challenges in the field and their potential solutions.