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62
Computation over MultipleAccess Channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2007
"... The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure ..."
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Cited by 139 (24 self)
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The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separationbased strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multipleaccess channel with a joint sourcechannel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multipleaccess networks, thus linking them to network coding.
Ubiquitous access to distributed data in largescale sensor networks through decentralized erasure codes
, 2005
"... Consider a largescale wireless sensor network of n nodes, where a fraction k out of n generate data packets of global interest. Assuming that the individual nodes have limited storage and computational capabilities, we address the problem of how to enable ubiquitous access to the distributed data p ..."
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Cited by 90 (7 self)
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Consider a largescale wireless sensor network of n nodes, where a fraction k out of n generate data packets of global interest. Assuming that the individual nodes have limited storage and computational capabilities, we address the problem of how to enable ubiquitous access to the distributed data packets. Specifically, we assume that each node can store at most one data packet, and study the problem of diffusing the data so that by querying any k nodes, it is possible to retrieve all the k data packets of interest (with high probability). We introduce a class of erasure codes and show how to solve this problem efficiently in a completely distributed and robust way. Specifically we show that we can efficiently diffuse the data by “prerouting” only O(ln n) packets per data node to randomly selected storage nodes. By using the proposed scheme, the distributed data becomes available “at the fingertips” of a potential data collector located anywhere in the network.
Information fusion for wireless sensor networks: methods, models, and classifications,”
 Article ID 1267073,
, 2007
"... ..."
On optimal communication cost for gathering correlated data through wireless sensor networks
 in Proc. of ACM MobiCom
"... In many energyconstrained wireless sensor networks, nodes cooperatively forward correlated sensed data to data sinks. In order to reduce the communication cost (e.g. overall energy) used for data collection, previous works have focused on specific coding schemes, such as SlepianWolf Code or Expli ..."
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Cited by 32 (2 self)
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In many energyconstrained wireless sensor networks, nodes cooperatively forward correlated sensed data to data sinks. In order to reduce the communication cost (e.g. overall energy) used for data collection, previous works have focused on specific coding schemes, such as SlepianWolf Code or Explicit Entropy Code. However, the minimum communication cost under arbitrary coding/routing schemes has not yet been characterized. In this paper, we consider the problem of minimizing the total communication cost of a wireless sensor network with a single sink. We prove that the minimum communication cost can be achieved using SlepianWolf Code and Commodity Flow Routing when the link communication cost is a convex function of link data rate. Furthermore, we find it useful to introduce a new metric
On practical design for joint distributed source and network coding
 in NETCOD
, 2005
"... Abstract — We consider the problem of communicating correlated information from two source nodes over a network to multiple destination nodes. This problem involves a joint consideration of distributed source coding (compression) and network coding (information relaying). Although the optimal admiss ..."
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Cited by 29 (1 self)
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Abstract — We consider the problem of communicating correlated information from two source nodes over a network to multiple destination nodes. This problem involves a joint consideration of distributed source coding (compression) and network coding (information relaying). Although the optimal admissible rate region was previously characterized, it was not yet clear how to design practical communication schemes with low complexity. This work provides a partial answer to this question. Specifically, we focus on the case where the two sources are related by a binary symmetric channel (BSC). We propose a general strategy that potentially allows low complexity implementation, and a specific practical design based on the general strategy. The proposed specific practical design is in general suboptimal; but its low complexity and robustness to network dynamics make it suitable for practical implementation. I.
Communicating the sum of sources over a network
 IEEE International Symposium on Information Theory (ISIT
, 2008
"... Abstract — We consider a network (that is capable of network coding) with a set of sources and terminals, where each terminal is interested in recovering the sum of the sources. Considering directed acyclic graphs with unit capacity edges and independent, unitentropy sources, we show the rate regio ..."
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Cited by 23 (2 self)
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Abstract — We consider a network (that is capable of network coding) with a set of sources and terminals, where each terminal is interested in recovering the sum of the sources. Considering directed acyclic graphs with unit capacity edges and independent, unitentropy sources, we show the rate region when (a) there are two sources and n terminals, and (b) n sources and two terminals. In these cases as long as there exists at least one path from each source to each terminal we demonstrate that there exists a valid assignment of coding vectors to the edges such that the terminals can recover the sum of the sources. I.
A Power Efficient Sensing/Communication Scheme: Joint SourceChannelNetwork Coding by Using Compressive Sensing
"... Abstract—We propose a joint sourcechannelnetwork coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of ..."
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Cited by 16 (1 self)
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Abstract—We propose a joint sourcechannelnetwork coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of sources within an allowed distortion level at each receiver. We perform joint sourcechannel coding at each source by randomly projecting source values to a lower dimensional space. We consider sources that satisfy the restricted eigenvalue (RE) condition as well as more general sources for which the randomness of the network allows a mapping to lower dimensional spaces. Our approach relies on using analog random linear network coding. The receiver uses compressive sensing decoders to reconstruct sources. Our key insight is the fact that, compressive sensing and analog network coding both preserve the source characteristics required for compressive sensing decoding. I.
Network coding for multicasting
, 2006
"... In today’s practical networks, endtoend information delivery is performed by routing. Network coding generalizes routing by allowing a node to generate output data by mixing (i.e., computing certain functions of) its received data. Ahlswede et al. determined the multicast capacity in a network of ..."
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Cited by 14 (2 self)
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In today’s practical networks, endtoend information delivery is performed by routing. Network coding generalizes routing by allowing a node to generate output data by mixing (i.e., computing certain functions of) its received data. Ahlswede et al. determined the multicast capacity in a network of lossless links and showed that achieving the multicast capacity requires in general the use of network coding. This thesis presents the following research contributions to the theory and practice of network coding. Constructive network coding We propose and simulate a practical scheme for implementing network coding. We demonstrate its asymptotic optimality by analyzing the connectivity in a continuoustime trellis that models the packet transmissions. Hybrid routing/coding A fundamental theorem by Edmonds established that if all nodes other than the source are destinations, the multicast capacity can be achieved by routing. We constructively prove a theorem that contains Edmonds ’ theorem and Ahlswede et al.’s theorem as special cases. It shows the multicast capacity can still be achieved even if mixing is allowed only on links entering relay nodes.
The single source two terminal network with network coding
 in Proceedings of the 9th Canadian Workshop on Information Theory
, 2005
"... Abstract — We consider a communication network with a single source that has a set of messages and two terminals where each terminal is interested in an arbitrary subset of messages at the source. A tight capacity region for this problem is demonstrated. We show by a simple graphtheoretic procedure ..."
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Cited by 11 (1 self)
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Abstract — We consider a communication network with a single source that has a set of messages and two terminals where each terminal is interested in an arbitrary subset of messages at the source. A tight capacity region for this problem is demonstrated. We show by a simple graphtheoretic procedure that any such problem can be solved by performing network coding on the subset of messages that are requested by both the terminals and that routing is sufficient for transferring the remaining messages. I.