Codes in the Sum-Rank Metric: Fundamentals and Applications

By Frank R. Kschischang, Mohannad Shehadeh, Umberto Martínez-Peñas

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.

• Format: Paperback
• Language: English
• ISBN: 1638280304
• ISBN13: 9781638280309
• Release Date: May 2022
• Publisher: Now Publishers
• Length: 234 Pages
• Weight: 0.73 lbs.
• Dimensions: 0.5" x 6.1" x 9.2"