Network Coding and Subspace Designs

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.

Table of Contents

Chapter 1. Codes Endowed with the Rank Metric
Chapter 2. Constructions of Constant Dimension Codes
Chapter 3. Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes
Chapter 4. Generalizing Subspace Codes to Flag Codes Using Group Actions
Chapter 5. Multi-shot Network Coding
Chapter 6. Geometrical Aspects of Subspace Codes
Chapter 7. Partial Spreads and Vector Space Partitions
Chapter 8. q-Analogs of Designs: Subspace Designs
Chapter 9. Computational Methods in Subspace Designs
Chapter 10. Index Coding, Network Coding and Broadcast with Side-Information
Chapter 11. Implementation of Network Coding in Wireless Systems
Chapter 12. Opportunistic Network Coding
Chapter 13. Coded Random Access
Chapter 14. An Overview of Coding for Distributed Storage Systems
Chapter 15. Matroid Theory and Storage Codes: Bounds and Constructions
Chapter 16. Batch and PIR Codes and Their Connections to Locally Repairable Codes