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Cyclic Division Algebras: A Tool for Space-Time Coding provides a tutorial introduction to the algebraic tools involved in the design of codes based on division algebras. The different design criteria involved are illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property and the diversity multiplexing tradeoff. Finally complete mathematical background underlying the construction of the Golden code and the other Perfect Space-Time block codes is given.

Algebraic number theory is gaining an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been developed in the last ten years and many explicit code constructions based on algebraic number theory are now available. Algebraic Number Theory and Code Design for Rayleigh Fading Channels provides an overview of algebraic lattice code designs for...

The most commonly deployed multi-storage device systems are RAID housed in a single computing unit. The idea of distributing data across multiple disks has been naturally extended to multiple storage nodes which are interconnected over a network and are called Networked Distributed Storage Systems (NDSS). The simplest coding techniques based on replication are often used to ensure redundancy in these systems, but given the sheer volume of data that needs to be stored and the overheads of replication, other coding techniques are being developed. Coding Techniques for Repairability in Networked...

This book provides a first course on lattices - mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography.