Connected Mathematics for Next Generation Communication Networks

Dear Colleagues,

Data communication and networking (DCN) systems are of great importance in today’s world. Today, the existence of newly emerged wireless communication systems such as 5G and beyond, Wi-Fi 6/6E, etc., witness the importance of DCN systems. Additionally, their importance will continue to increase with new fields of application, such as IoT, tactile internet, augmented/virtual reality (AR/VR), mixed reality (XR), industrial automation and so on. Such advanced communication systems are continually being introduced to live up to the great variety of applications and desires for new services. This development would have been impossible without the realization of DCN systems, wherein mathematics played a vital supporting role. In fact, mathematics is the foundation of information and communication theory in a DCN system, from the information generated at the sender to that received by the receiver (or even that dropped/destroyed on the way). Mathematics is integral in one way or other. The mathematics of sampling/quantization/encoding is involved in the conversion of user data (audio/video/text) into machine-readable format (bits and bytes). The machine-readable information is packetized into transmittable frames and chunks (usually of a predefined size) using headers and trailers. Packets and frames are of varying lengths, with no frames smaller than 64 octets or greater than 1518 octets (header, data and cyclic redundancy check, etc.).  The role of mathematics does not end at this point: a complex and applied mathematics is involved in the transmission of these bits and bytes (enclosed as frames of packets). Transmission media, such as a wireless system, require the implementation of various mathematical operations, such as the conversion of analog data to digital data, bandwidth allocation, channelization, bit rate selection, measurement if received signal strengths indicator (RSSI), signal to noise ratio (SNR), etc. In short, mathematics has played the role of the pathbreaker in the development of new communication procedures, and it is an essential instrument in the planning and optimization of networks. For example, statistical theories and discrete mathematics are used in information theory; linear algebra, convex optimization and game theory are used in the development of new methods of transmission, and linear, combinatorial, and stochastic optimization are used in planning radio networks. In all these cases, it is the collaboration of applied mathematics and communications engineering that deliver essential contributions to the potential solutions.

Despite this immense contribution, essential foundational issues and challenges exist for the mathematical theories, such as the need to redefine itself according to current needs and requirements. Therefore, in this Special Issue, we focus on those applied mathematical models and methods that can be connected and the specific features of DCN systems that differ from past and present ones. We may deliberate on diverse mathematical approaches for machine intelligence based on stochastic processes, queueing theory, statistics, stochastic geometry, and others.

Dr. Rashid Ali
Prof. Dr. Hyung Seok Kim
Guest Editors

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