Broadcast and slepian-wolf multicast over Aref networks

Korada, Satish Babu; Vasudevan, Dinkar

doi:10.1109/isit.2008.4595269

Cited by 6 publications

(7 citation statements)

References 6 publications

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“…) has been sent, if it is a unique tuple such that for each 1 ≤ k ≤ + 1 satisfies the following conditions, [4] )ŷ3(z 3 [5] |x 3 [5] )ŷ3(z 3 [6] |x 3 [6] )ŷ3(z 3 [7] |x 3 [7] ) [2] )ŷ3(z 3 [3] |x 3 [3] )ŷ3(z 3 [4] |x 3 [4] )ŷ3(z 3 [5] |x 3 [5] )ŷ3(z 3 [6] |x 3 [6] )ŷ3(z 3 [7] |x 3 [7] …”

Section: Networkmentioning

confidence: 99%

“…In a recent work [2], this problem was generalized to the problem of lossy multicasting of a source over a broadcast channel with side information. In [3], a necessary and sufficient condition for multicasting a set of correlated sources over acyclic Aref networks [4] was derived. The problem of multicasting correlated sources over networks was also studied in the network coding literature [5], [6].…”

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confidence: 99%

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Slepian–Wolf Coding Over Cooperative Relay Networks

Yassaee

Aref

2011

IEEE Trans. Inform. Theory

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This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A Joint source-Wyner-Ziv encoding/sliding window decoding scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the sub-modular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks.

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Section: Networkmentioning

confidence: 99%

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confidence: 99%

Slepian–Wolf Coding Over Cooperative Relay Networks

Yassaee

Aref

2011

IEEE Trans. Inform. Theory

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“…A typical tractable example of such networks would be a class of acyclic deterministic relay networks with no interference (called the Aref network) in which the concept of "channel capacity" is irrelevant. In this connection, Ratnakar and Kramer [25] have studied Aref networks with a single source and multiple sinks, while Korada and Vasudevan [26] have studied Aref networks with multiple correlated sources and multiple sinks. The network capacity formula as well as the network matching formula obtained by them are in nice correspondence with the formula obtained by Ahlswede et al [1] as well as Theorem 3.1 established in this paper, respectively.…”

Section: Alternative Transmissibility Conditionmentioning

confidence: 99%

“…ACKNOWLEDGMENTS @ The author is very grateful to Prof. Shin'ichi Oishi for providing him with pleasant research facilities during this work. Thanks are also due to Dinkar Vasudevan for bringing reference [26] to the author's attention.…”

Section: G Interference-type Of Network Routingmentioning

confidence: 99%

Polymatroids with network coding

Han

2010

2010 Information Theory and Applications Workshop (ITA)

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The problem of network coding for multicasting a single source to multiple sinks has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they have established the celebrated maxflow mini-cut theorem on non-physical information flow over a network of independent channels. On the other hand, in 1980, Han has studied the case with correlated multiple sources and a single sink from the viewpoint of polymatroidal functions in which a necessary and sufficient condition has been demonstrated for reliable transmission over the network. This paper presents an attempt to unify both cases, which leads to establish a necessary and sufficient condition for reliable transmission over a noisy network for multicasting all the correlated multiple sources to all the multiple sinks. Furthermore, we address also the problem of transmitting "independent" sources over a multiple-access-type of network as well as over a broadcast-type of network, which reveals that the (co-) polymatroidal structures are intrinsically involved in these types of network coding. Several network models with correlated multiple sources have been studied by some people, e.g., by Barros and Servetto [10], Ho, Médard, Effros and Koetter [14], Ho, Médard, Koetter, Karger, Effros, Shi and Leong [15], Ramamoorthy, Jain, Chou and Effros [16]. Among others, [14], [15] and [16] consider (without attention to the converse part) error-free network coding for two (or possibly multiple) stationary memoryless correlated sources with a single (or possibly multiple) sink(s) to study the error exponent problem, where we notice that all the arguments in [14], [15] and [16] can be validated only within the class of stationary memoryless sources of integer bit rates and error-free channels (i.e., the identity mappings) all with one bit capacity (or integer bits capacity, which is allowed by introducing multiple edges); these restrictions are needed solely to invoke "Menger's theorem" in graph theory. The main result in the present paper is quite free from such seemingly severe restrictions, because we can dispense with the use of Menger's theorem.On the other hand, [10] revisits the same model as in Han [3], while [16] mainly focuses on the network with two correlated sources and two sinks to discuss the separation problem of distributed source coding and network coding, where, in addition, cases of two-sources three-sinks, and three-

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“…This idea was explored further in [8] for the compound MAC channel. The characterization of the achievable region for deterministic broadcast-only networks (called Aref networks) was established in [10]. As far as we know, this is the first exploration of lossless distributed source transmission over general relay networks with both broadcast and multiple access signal interactions.…”

Section: Introductionmentioning

confidence: 99%

On source transmission over deterministic relay networks

Mohajer

Tian

Diggavi

2010

IEEE Information Theory Workshop 2010 (ITW 2010)

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Abstract-Lossless transmission of a set of correlated sources over a deterministic relay network is considered for two traffic requirements. In distributed multicast, the set of sources are to be delivered to a set of destinations. The source exchange requires all the nodes with access to sources to be able to reconstruct all other sources observed at other nodes. We develop achievable regions and outer bounds for both these situations. For linear deterministic networks, these bounds coincide, yielding a characterization.

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Broadcast and slepian-wolf multicast over Aref networks

Cited by 6 publications

References 6 publications

Slepian–Wolf Coding Over Cooperative Relay Networks

Slepian–Wolf Coding Over Cooperative Relay Networks

Polymatroids with network coding

On source transmission over deterministic relay networks

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