[Slides] [Video 1] [Video 2]
Anwitaman Datta (Nanyang Technological University), Frédérique Elise Oggier (Nanyang Technological University)
Erasure coding provides a mechanism to store data redundantly for fault-tolerance in a cost-effective manner. Recently, there has been a renewed interest in designing new erasure coding techniques with different desirable properties, including good repairability and degraded read performance, or efficient redundancy generation processes. Very often, these novel techniques exploit the computational resources available 'in the network', i.e., leverage on storage units which are not passive entities supporting only read/write of data, but also can carry out some computations. This article accompanies an identically titled tutorial at the IEEE International Symposium on Network Coding (NetCod 2013), and portrays a big picture of some of the important processes within distributed storage systems, where erasure codes designed by explicitly taking into account the nuances of distributed storage systems can provide significant performance boosts.
Network Coding and Security
Christina Fragouli (EPFL)
In network coding, we no longer use a network by artificially creating end-to-end connections; instead, information is allowed to mix throughout the network. This has interesting implications to security: end-to-end schemes may no longer be applicable or secure; new types of adversaries are possible; and we can take advantage of the network structure itself for securing the information. We present in this talk a short overview of basic results and research directions in this area.
Index Coding: Algorithms and Relation to Network Coding
[Slides 1] [Slides 2] [Video 2]
Alex Sprintson (Texas A&M University) , Michael Langberg (The Open University of Israel)
Index Coding is a central problem in wireless network coding which focuses on the scenario of broadcasting with side information. In this two-part tutorial we will present recent progress in the area of Index Coding. In the first part, we will focus on algorithmic aspects of Index Coding, including various algorithms for code design, the limitations of such algorithms, and lower and upper bounds on the capacity region of Index Coding instances based on linear programming (LP) techniques. In the second part of the tutorial, we will discuss the equivalence between Index Coding and Network Coding, the implications of the equivalence, and some open problems in this context.
Bobak Nazer (Boston University)
This talk overviews a new strategy, compute-and-forward, that exploits the interference property of the wireless channel to achieve higher end-to-end rates in a network. The key idea is that users should decode linear combinations of the transmitted messages over an appropriate finite field. This is a departure from classical information-theoretic frameworks which tend to either to decode interfering messages in their entirety or treat them as noise. Structured codes (such linear or lattice codes) ensure that these linear combinations can be decoded reliably, often at far higher rates than the messages individually. Historically, codes with linear/lattice structure have been studied as a stepping stone to practical constructions. Our recent work has employed compute-and-forward as a building block for coding theorems which lead to new achievability results in network information theory. Using examples drawn from Gaussian multiple-access, broadcast, and interference channels, we will highlight recent advances and open questions.
Topological Interference Management through Index Coding
Syed Jafar (UC Irvine)
The topological interference management (TIM) problem for wireless networks is introduced as the setting where the channel state information at the transmitters is limited to the network topology. It is shown that TIM is essentially related to the index coding problem, and the two are equivalent under linear solutions. An interference alignment perspective is then used to explore the index coding and TIM problems, to solve several interesting classes of these problems, and to identify the simplest instances of index coding problems where non-Shannon inequalities are necessary.
Quantum Network Coding -- How can network coding be applied to quantum information?
Harumichi Nishimura (Nagoya University)
Nowadays, network coding has been a very successful topic in information theory including many applications such as wireless networks while one of the simplest benefits is the efficient transmission in networks by allowing us to encode the transmitted information at every intermediate node. Since quantum information is much more expensive for communication than classical information, it was natural that this benefit made quantum researchers motivate the study of "quantum network coding." This paper reports the current status of quantum network coding. At present, quantum network coding mostly means sending quantum information (rather than classical information) in a quantum network. Since quantum information cannot be cloned (the quantum no-cloning theorem), multiple unicast networks have been well-studied (in several settings). We present some of the known possibilities and limitations, and future works of quantum network coding, focusing on multiple unicast networks.