Codes In The Sum-Rank Metric: Fundamentals And Applications (Foundations And Trends(R) In Communications And Information)

Hamming distance and rank metric have long been used in coding theory. The sum-rank metric naturally extends these over fields. They have attracted significant attention for their applications in distributed storage systems, multishot network coding, streaming over erasure channels, and multi-antenna wireless communication. In this monograph, the authors provide a tutorial introduction to the theory and applications of sum-rank metric codes over finite fields. At the heart of the monograph is the construction of linearized Reed-Solomon codes, a general construction of maximum sum-rank distance (MSRD) codes with polynomial field sizes. These specialize to classical Reed-Solomon and Gabidulin code constructions in the Hamming and rank metrics, respectively and produce an efficient Welch-Berlekamp decoding algorithm. The authors proceed to develop applications of these codes in distributed storage systems, network coding, and multi-antenna communication before surveying other families of codes in the sum-rank metric, including convolutional codes and subfield subcodes, and recent results in the general theory of codes in the sum-rank metric. This tutorial on the topic provides the reader with a comprehensive introduction to both the theory and practice of this important class of codes used in many storage and communication systems. It will be a valuable resource for students, researchers and practising engineers alike.

• | Author: Umberto Martínez-Peñas|Mohannad Shehadeh|Frank R. Kschischang
• | Publisher: Now Publishers
• | Publication Date: May 31, 2022
• | Number of Pages: 234 pages
• | Language: English
• | Binding: Paperback
• | ISBN-10: 1638280304
• | ISBN-13: 9781638280309