Network Coding and Subspace Designs

Description

This book, written by experts from universities and major research laboratories, addresses the hot topic of network coding, a powerful scheme for information transmission in networks that yields near-optimal throughput. It introduces readers to this striking new approach to network coding, in which the network is not simply viewed as a mechanism for delivering packets, but rather an algebraic structure named the subspace, which these packets span. This leads to a new kind of coding theory, employing what are called subspace codes. The book presents selected, highly relevant advanced research output on: Subspace Codes and Rank Metric Codes; Finite Geometries and Subspace Designs; Application of Network Coding; Codes for Distributed Storage Systems. The outcomes reflect research conducted within the framework of the European COST Action IC1104: Random Network Coding and Designs over GF(q). Taken together, they offer communications engineers, R&D engineers, researchers and graduate students in Mathematics, Computer Science, and Electrical Engineering a comprehensive reference guide to the construction of optimal network codes, as well as efficient encoding and decoding schemes for a given network code. Front Matter ....Pages i-xiv Front Matter ....Pages 1-1 Codes Endowed with the Rank Metric (Elisa Gorla, Alberto Ravagnani)....Pages 3-23 Constructions of Constant Dimension Codes (Anna-Lena Horlemann-Trautmann, Joachim Rosenthal)....Pages 25-42 Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes (Kamil Otal, Ferruh Özbudak)....Pages 43-66 Generalizing Subspace Codes to Flag Codes Using Group Actions (Dirk Liebhold, Gabriele Nebe, María Ángeles Vázquez-Castro)....Pages 67-89 Multi-shot Network Coding (Diego Napp, Filipa Santana)....Pages 91-104 Front Matter ....Pages 105-105 Geometrical Aspects of Subspace Codes (Antonio Cossidente, Francesco Pavese, Leo Storme)....Pages 107-129 Partial Spreads and Vector Space Partitions (Thomas Honold, Michael Kiermaier, Sascha Kurz)....Pages 131-170 q-Analogs of Designs: Subspace Designs (Michael Braun, Michael Kiermaier, Alfred Wassermann)....Pages 171-211 Computational Methods in Subspace Designs (Michael Braun, Michael Kiermaier, Alfred Wassermann)....Pages 213-244 Front Matter ....Pages 245-245 Index Coding, Network Coding and Broadcast with Side-Information (Eimear Byrne, Marco Calderini)....Pages 247-293 Implementation of Network Coding in Wireless Systems (Semiha Tedik Basaran, Ali Reza Heidarpour, Selahattin Gokceli, Gunes Karabulut Kurt, Murat Uysal, Ibrahim Altunbas)....Pages 295-317 Opportunistic Network Coding (Kemal Alic, Ales Svigelj)....Pages 319-338 Coded Random Access (Čedomir Stefanović, Dejan Vukobratović)....Pages 339-359 Front Matter ....Pages 361-361 An Overview of Coding for Distributed Storage Systems (Shiqiu Liu, Frédérique Oggier)....Pages 363-383 Matroid Theory and Storage Codes: Bounds and Constructions (Ragnar Freij-Hollanti, Camilla Hollanti, Thomas Westerbäck)....Pages 385-425 Batch and PIR Codes and Their Connections to Locally Repairable Codes (Vitaly Skachek)....Pages 427-442