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We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in applications of networked control systems. Although the work of Schulman and Sahai over the past two decades, and…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
The network coding problem asks whether data throughput in a network can be increased using coding (compared to treating bits as commodities in a flow). While it is well-known that a network coding advantage exists in directed graphs, the…
The {\em repair locality} of a distributed storage code is the maximum number of nodes that ever needs to be contacted during the repair of a failed node. Having small repair locality is desirable, since it is proportional to the number of…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
We discuss secure transmission via an untrusted relay when we have a multiple access phase from two nodes to the relay and broadcast phase from the relay to the two nodes. To realize the security, we construct a code that securely transmits…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
To recover simultaneous multiple failures in erasure coded storage systems, Patrick Lee et al introduce concurrent repair based minimal storage regenerating codes to reduce repair traffic. The architecture of this approach is simpler and…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
The majority of works in distributed storage networks assume a simple network model with a collection of identical storage nodes with the same communication cost between the nodes. In this paper, we consider a realistic multi-rack…
A large number of streaming applications use reliable transport protocols such as TCP to deliver content over the Internet. However, head-of-line blocking due to packet loss recovery can often result in unwanted behavior and poor…
In this paper, we are concerned with the resilience of locally routed network flows with finite link capacities. In this setting, an external inflow is injected to the so-called origin nodes. The total inflow arriving at each node is routed…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
Network coding is famous for significantly improving the throughput of networks. The successful decoding of the network coded data relies on some side information of the original data. In that framework, independent data flows are usually…
In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such…