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As the rapid growth of data, many storage systems have used erasure codes instead of replication to reduce the storage cost under the same level of reliability. Maximum-Distance- Separable (MDS) codes have been the most widely adopted, due to their optimal storage efficiency. It is well understood that the application of codes in storage systems, where the data is less frequently accessed. For the...
The energy used to transmit a single bit of data between the devices in sensor networks is equal to the energy for performing hundreds of instructions in those devices. Thus the reduction of the data necessary to transmit, while keeping the same functionality of the employed algorithms is a formidable and challenging scientific task. We describe an algorithm called Small Set of Allowed Coefficients...
This paper considers the multiple-access relay channel in a setting where two source nodes transmit packets to a destination node, both directly and via a relay node, over packet erasure channels. Intra-session network coding is used at the source nodes and inter-session network coding is employed at the relay node to combine the recovered source packets of both source nodes. In this work, we investigate...
Network coding tends to increase not only the end-to-end delay due to unavoidable buffering of packets, but it also increases the inter-packet delay variations (jitter) due to batching. While an increase in delay does not necessarily adversely affect throughput, sudden delay spikes may interfere with TCP’s congestion avoidance mechanism. Such spikes are a common phenomenon in coded packet networks...
In this paper, we investigate a rateless code design for a two-way relay channel (TWRC) where a network coding operation is employed at the relay. Rateless codes are used at both two users and the relay nodes as it can cope with various channel conditions. We propose a hybrid estimate and forward (EF)/decode and forward (DF) protocol with rateless codes for the TWRC. In the proposed scheme, the relay...
Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase in complexity. In this paper, we design a simple IDNC-like graph model for a specific subclass of ONC, by introducing a more generalized definition of its vertices and the notion...
Large Scale distributed storage systems play a vital role in maintaining data across storage locations globally. These systems use replication as the default mechanism for providing fault-tolerance. Recently, erasure codes are being used as a viable alternative to replication, since they provide the same fault-tolerance for reduced storage overhead. However, their performance is unclear in a geographically...
In this paper, we study in-order packet delivery in instantly decodable network coded systems for wireless broad- cast networks. We are interested in applications, in which the successful delivery of a packet depends on the correct reception of this packet and all its preceding packets. We formulate the problem of minimizing the number of undelivered packets to all receivers over all transmissions...
We consider a setting in which a sender wishes to broadcast a block of K data packets to a set of wireless receivers, where each of the receivers already has a subset of the data packets available to it (e.g., from prior transmissions) and wants to obtain the rest of the packets in the block. Our goal is to find a linear network coding scheme that yields the minimum average packet decoding delay (APDD),...
This paper considers the problem of reducing the broadcast delay of wireless networks using instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In D2D-enabled networks, devices help hasten the recovery of the lost packets of devices in their transmission range by sending network coded packets. To solve the problem, the different events occurring at each device are...
Network coding, by right of the concise form and remarkable effect, has been applauded around the world since its emergence especially in the field of wireless communication. However, we find the superiority of network coding may be concealed by the over redundant information in coded packets under certain circumstances. That is, the back-and-forth coding at intermediate nodes makes the old information...
We introduce the “blind index coding” (BIC) problem, which generalizes the classic index coding problem by considering a sender that has some uncertainty about the side information that is available at each receiver. This problem naturally arises in wireless networks in which users obtain their side information through wireless channels with errors that may be unknown to the sender. For the proposed...
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and decoding algorithms. In this paper we consider such cyclic codes. We provide constructions of optimal cyclic codes for which their codewords do not have full length...
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate R ∈ [0, 1]. An efficient interpolation-based decoding algorithm for this code construction is given which allows to correct insertions and deletions up to the normalized radius s (1 − ((1/h + h)/(h − s + 1))R), where h...
Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proven, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove...
The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We show that the column sum rank parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several column distance properties and introduce a new family of convolutional codes that maximize the column...
Consider the problem of reliable multicast over a network in the presence of adversarial errors. In contrast to traditional network error correction codes designed for a given network capacity and a given number of errors, we study an arguably more realistic setting that prior knowledge on the network and adversary parameters is not available. For this setting we propose efficient and throughput-optimal...
We introduce a property that we call Successive Description property for Slepian Wolf coding. We show that Monotone-Chain Polar Codes can be used to construct low-complexity codes that satisfy this property. We discuss applications of this property to network coding problems.
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of transmissions (optimal length) to be made so that all receivers can decode their wanted messages using the transmitted symbols and their respective prior information...
The connection between index coding and matroid theory have been well studied in the recent past. El Rouayheb et al. established a connection between multi linear representation of matroids and wireless index coding. Muralidharan and Rajan showed that a vector linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions...
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