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Approximately optimal wireless broadcasting,” submitted to
 IEEE Trans. Info. Theory
"... Abstract—We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the potential aid of relays and cooperation between destinations. The wireless nature of the medium is captured by the broadcast nature of transmissions as ..."
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Abstract—We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the potential aid of relays and cooperation between destinations. The wireless nature of the medium is captured by the broadcast nature of transmissions as well as the superposition of transmitted signals plus independent Gaussian noise at the received signal at any radio. We propose a scheme that can achieve rate tuples within a constant gap away from the cutset bound, where the constant is independent of channel coefficients and power constraints. First, for a deterministic broadcast network, we propose a new coding scheme, constructed by adopting a“receivercentric ” viewpoint,thatusesquantizeandforward relaying as an inner code concatenated with an outer Marton code for the induced deterministic broadcast channel. This scheme is shown to achieve the cutset bound evaluated with product form distributions. This result is then lifted to the Gaussian network by using a deterministic network called the discrete superposition network as a formal quantization interface. This twostage construction circumvents the difficulty involved in working with a vector nonlinear nonGaussian broadcast channel that arises if we construct a similar scheme directly for the Gaussian network. Index Terms—Broadcast network, broadcastrelay channels, capacity, Marton code, multiuser channels, network information theory, wireless networks.
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 ..."
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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.
BoundedContention Coding for Wireless Networks in the High SNR Regime
, 2012
"... 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 pap ..."
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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 ℓ bits each within O(a log n + aℓ) bits of communication with fullduplex radios, and O((a log n + aℓ)(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 + ℓ)) 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.
Cooperative Interference Management in Wireless Networks
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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 ..."
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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.
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 ..."
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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
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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 ..."
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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 ..."
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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.