Results 1  10
of
10
Deterministic Network Model Revisited: An Algebraic Network Coding Approach
, 2010
"... The capacity of multiuser networks has been a longstanding problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature of wirele ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
The capacity of multiuser networks has been a longstanding problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. We show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Médard. We prove that the ADT network problem can be captured by a single matrix, and show that the mincut of an ADT network is the rank of this matrix; thus, eliminating the need to optimize over exponential number of cuts between two nodes to compute the mincut of an ADT network. We extend the capacity characterization for ADT networks to a more general set of connections, including single unicast/multicast connection and nonmulticast connections such as multiple multicast, disjoint multicast, and twolevel multicast. We also provide sufficiency conditions for achievability in ADT networks for any general connection set. In addition, we show that random linear network coding, a randomized distributed algorithm for network code construction, achieves the capacity for the connections listed above. Furthermore, we extend the ADT networks to those with random erasures and cycles (thus, allowing bidirectional links). In addition, we propose an efficient linear code construction for the deterministic wireless multicast relay network model. Note that Avestimehr et al.’s proposed code construction is not guaranteed to be efficient and may potentially involve an infinite block length. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, for a layered network, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent.
Boundedcontention coding for wireless networks
 in the high SNR regime,” in Distributed Computing
, 2012
"... Abstract Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Abstract Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called BoundedContention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters. BCC enables deterministic local broadcast in a network with n nodes and at most a transmitters with information of bits each within O(a log n + a ) bits of communication with fullduplex radios, and O((a log n + a )(log n)) bits, with high probability, with halfduplex radios. When combined with random linear network coding, BCC gives global broadcast within O((D + a + log n)(a log n + )) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worstcase adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network.
Vector Network Coding Algorithms
 IEEE ISIT
"... Abstract—We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L × L coding matrices that ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract—We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L × L coding matrices that play a similar role as coding coefſcients in scalar coding. Our algorithms for scalar network jointly optimize the employed ſeld size while selecting the coding coefſcients. Similarly, for vector coding, our algorithms optimize the length L while designing the coding matrices. These algorithms apply both for regular network graphs as well as linear deterministic networks. I.
Cooperative Interference Management in Wireless Networks
"... All rights reserved. ..."
(Show Context)
Stabilizability over Deterministic Relay Networks
, 2013
"... We consider the problem of linear system stabilization using a set of decentralized controllers that communicate with the plant’s sensors over a network that employs linear network coding. Our analysis is built upon an existing algebraic description of deterministic relay networks, which is able t ..."
Abstract
 Add to MetaCart
(Show Context)
We consider the problem of linear system stabilization using a set of decentralized controllers that communicate with the plant’s sensors over a network that employs linear network coding. Our analysis is built upon an existing algebraic description of deterministic relay networks, which is able to model broadcast transmissions and multiple access channel constraints. Since these networks can be described as linear timeinvariant systems with specific transfer functions, this network representation allows us to reason about the control system and network (and their interaction) using a common mathematical framework. In this paper we characterize algebraic and topological stabilizability conditions for a wide class of these networks. Our analysis shows that the (algebraic) structure of a network required for stabilization of a dynamical plant can be related to the plant’s dynamics; in particular, we prove that the geometric multiplicities of the plant’s unstable eigenvalues play a key role in the ability to stabilize the system over such networks.
permission. Structured Codes in Information Theory: MIMO and Network Applications
"... All rights reserved. ..."
A Deterministic Polynomial–Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks
"... We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the wellknown multicast network coding scheme of Jaggi et al. to linear deterministic relay networks and is based on the notion of flow for a ..."
Abstract
 Add to MetaCart
(Show Context)
We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the wellknown multicast network coding scheme of Jaggi et al. to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial–time versions of our algorithm and show that for a network with g destinations, our deterministic algorithm can achieve the capacity in dlog(g + 1)e uses of the network. 1
1Two Unicast Information Flows over Linear Deterministic Networks
"... We investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each sourcedestination pair is constrained to be 1, it is obvious that the triangular rate region {(R1, R2) : R1, R2 ≥ 0, R1+R2 ≤ 1} can be achie ..."
Abstract
 Add to MetaCart
We investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each sourcedestination pair is constrained to be 1, it is obvious that the triangular rate region {(R1, R2) : R1, R2 ≥ 0, R1+R2 ≤ 1} can be achieved, and that one cannot achieve beyond the square rate region {(R1, R2) : R1, R2 ≥ 0, R1 ≤ 1, R2 ≤ 1}. Analogous to the work by Wang and Shroff for wired networks [1], we provide the necessary and sufficient conditions for the capacity region to be the triangular region and the necessary and sufficient conditions for it to be the square region. Moreover, we completely characterize the capacity region and conclude that there are exactly three more possible capacity regions of this class of networks, in contrast to the result in wired networks where only the triangular and square rate regions are possible. Our achievability scheme is based on linear coding over an extension field with at most four nodes performing special linear coding operations, namely interference neutralization and zero forcing, while all other nodes perform random linear coding. I.
1Network Coding meets Decentralized Control: Network Linearization and CapacityStabilizablilty Equivalence
"... We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear timeinvariant systems by appropriately restricting channels and coding schemes of network coding to be linear timeinvariant, and the plant and controllers of decentralized control to ..."
Abstract
 Add to MetaCart
(Show Context)
We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear timeinvariant systems by appropriately restricting channels and coding schemes of network coding to be linear timeinvariant, and the plant and controllers of decentralized control to be linear timeinvariant as well. First, we apply linear system theory to network coding. This gives a novel way of converting an arbitrary relay network to an equivalent acyclic singlehop relay network, which we call Network Linearization. Based on network linearization, we prove that the fundamental design limit, mincut, is achievable by a linear timeinvariant networkcoding scheme regardless of the network topology. Then, we use the networkcoding to view decentralized linear systems. We argue that linear timeinvariant controllers in a decentralized linear system “communicate ” via linear network coding to stabilize the plant. To justify this argument, we give an algorithm to “externalize ” the implicit communication between the controllers that we believe must be occurring to stabilize the plant. Based on this, we show that the stabilizability condition for decentralized linear systems comes from an underlying communication limit, which can be described by the algebraic mincutmaxflow theorem. With this reinterpretation in hand, we also consider stabilizability over LTI networks to emphasize the connection with network coding. In particular, in broadcast and unicast problems, unintended messages at the receivers will be modeled as secrecy constraints. I.
Algebraic Techniques for Linear Deterministic Networks
"... Abstract—We here summarize some recent advances in the study of linear deterministic networks, recently proposed as approximations for wireless channels. This work started by extending the algebraic framework developed for multicasting over graphs in [1] to include operations over matrices and to ad ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—We here summarize some recent advances in the study of linear deterministic networks, recently proposed as approximations for wireless channels. This work started by extending the algebraic framework developed for multicasting over graphs in [1] to include operations over matrices and to admit both graphs and linear deterministic networks as special cases. Our algorithms build on this generalized framework, and provide as special cases unicast and multicast algorithms for deterministic networks, as well as network code designs using structured matrices. I.