Umberto Martinez-Penas,Mohannad Shehadeh,Frank R. Kschischang
Codes in the Sum-Rank Metric: Fundamentals and Applications
Codes in the Sum-Rank Metric: Fundamentals and Applications
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Excellent- More about Codes in the Sum-Rank Metric: Fundamentals and Applications
The authors of this monograph provide a tutorial introduction to the theory and applications of sum-rank metric codes over finite fields. They construct linearized Reed-Solomon codes, which are specialized classical Reed-Solomon and Gabidulin code constructions, and develop applications in distributed storage systems, network coding, and multi-antenna communication. They also survey other families of codes in the sum-rank metric, including convolutional codes and subfield subcodes.
Format: Paperback / softback
Length: 234 pages
Publication date: 30 May 2022
Publisher: now publishers Inc
Coding theory has long relied on the concepts of Hamming distance and rank metric, which have been extended to fields through the sum-rank metric. These metrics have garnered significant interest due to their applications in distributed storage systems, multishot network coding, streaming over erasure channels, and multi-antenna wireless communication. In this comprehensive monograph, the authors offer a tutorial introduction to the theory and applications of sum-rank metric codes over finite fields. At the core of the monograph lies the construction of linearized Reed-Solomon codes, a general method for creating maximum sum-rank distance (MSRD) codes with polynomial field sizes. These codes are specialized versions of classical Reed-Solomon and Gabidulin codes tailored to the Hamming and rank metrics, respectively. They result in an efficient Welch-Berlekamp decoding algorithm.
The authors then proceed to explore the diverse applications of these codes in distributed storage systems, network coding, and multi-antenna communication. They delve into the development of these codes before surveying other families of codes within the sum-rank metric, including convolutional codes and subfield subcodes. Recent advancements in the general theory of codes in the sum-rank metric are also discussed.
This tutorial serves as an invaluable resource for students, researchers, and practicing engineers seeking to gain a deep understanding of this important class of codes employed in numerous storage and communication systems. Its comprehensive coverage and practical insights make it a must-read for anyone interested in this field.
Weight: 335g
Dimension: 234 x 156 (mm)
ISBN-13: 9781638280309
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