Related papers: Linear Codes, Target Function Classes, and Network…
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel…
Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
Link and node failures are two common fundamental problems that affect operational networks. Protection of communication networks against such failures is essential for maintaining network reliability and performance. Network protection…
Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…
In this paper, we investigate function computation problems under different secure conditions over a network with multiple source nodes and a single sink node which desires a function of all source messages without error. A wiretapper has…
Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
Previous work on network coding capacity for random wired and wireless networks have focused on the case where the capacities of links in the network are independent. In this paper, we consider a more realistic model, where wireless…
Random Linear Network Coding (RLNC) is a transmission scheme that opts for linear combinations of the transmitted packets at a subset of the intermediate nodes. This scheme is usually considered when Network Coding (NC) is desired over…
Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…
Redundancy is abundant in Fog networks (i.e., many computing and storage points) and grows linearly with network size. We demonstrate the transformational role of coding in Fog computing for leveraging such redundancy to substantially…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
Nature is rife with networks that are functionally optimized to propagate inputs in order to perform specific tasks. Whether via genetic evolution or dynamic adaptation, many networks create functionality by locally tuning interactions…
Recently, it has been shown that the max flow capacity can be achieved in a multicast network using network coding. In this paper, we propose and analyze a more realistic model for wireless random networks. We prove that the capacity of…