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16
Restricted isometry property in quantized network coding of sparse messages,” arXiv preprint arXiv:1203.1892
, 2012
"... Abstract—In this paper, we study joint network coding and distributed source coding of internode dependent messages, with the perspective of compressed sensing. Specifically, the theoretical guarantees for robust `1min recovery of an underdetermined set of linear network coded sparse messages are ..."
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Abstract—In this paper, we study joint network coding and distributed source coding of internode dependent messages, with the perspective of compressed sensing. Specifically, the theoretical guarantees for robust `1min recovery of an underdetermined set of linear network coded sparse messages are investigated. We discuss the guarantees for `1min decoding of quantized network coded messages, based on Restricted Isometry Property (RIP) of the resulting measurement matrix. This is done by deriving the relation between tail probability of `2norms and satisfaction of RIP. The obtained relation is then used to compare our designed measurement matrix, with i.i.d. Gaussian measurement matrix, in terms of RIP satisfaction. Finally, we present our numerical evaluations, which shows that the proposed design of network coding coefficients results in a measurement matrix with an RIP behavior, similar to that of i.i.d. Gaussian matrix. Index Terms—Compressed sensing, linear network coding, restricted isometry property, `1min decoding, Gaussian ensembles. I.
Quantized network coding for sparse messages
 CoRR
"... In this paper, we study the data gathering problem in the context of power grids by using a network of sensors, where the sensed data have internode redundancy. Specifically, we propose a new transmission method, called quantized network coding, which performs linear network coding in the infinit ..."
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In this paper, we study the data gathering problem in the context of power grids by using a network of sensors, where the sensed data have internode redundancy. Specifically, we propose a new transmission method, called quantized network coding, which performs linear network coding in the infinite field of real numbers, and quantization to accommodate the finite capacity of edges. By using the concepts in compressed sensing literature, we propose to use `1minimization to decode the quantized network coded packets, especially when the number of received packets at the decoder is less than the size of sensed data (i.e. number of nodes). We also propose an appropriate design for network coding coefficients, based on restricted isometry property, which results in robust `1min decoding. Our numerical analysis show that the proposed quantized network coding scheme with `1min decoding can achieve significant improvements, in terms of compression ratio and delivery delay, compared to conventional packet forwarding. 1
Bayesian quantized network coding via belief propagation,” arXiv preprint arXiv:1209.1679
, 2012
"... Abstract—In this paper, we propose an alternative for routing based packet forwarding, which uses network coding to increase transmission efficiency, in terms of both compression and error resilience. This nonadaptive encoding is called quantized network coding, which involves random linear mappin ..."
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Abstract—In this paper, we propose an alternative for routing based packet forwarding, which uses network coding to increase transmission efficiency, in terms of both compression and error resilience. This nonadaptive encoding is called quantized network coding, which involves random linear mapping in the real field, followed by quantization to cope with the finite capacity of the links. At the gateway node, which collects received quantized network coder packets, minimum mean squared error decoding is performed, by using belief propagation in the factor graph representation. Our simulation results show a significant improvement, in terms of the number of required packets to recover the messages, which can be interpreted as an embedded distributed source coding for correlated messages. Index Terms—Network coding, Bayesian compressed sensing, belief propagation, minimum mean squared error estimation. I.
Empirical RateDistortion Study of Compressive Sensingbased Joint SourceChannel Coding
"... Abstract—In this paper, we present an empirical ratedistortion study of a communication scheme that uses compressive sensing (CS) as joint sourcechannel coding. We investigate the ratedistortion behavior of both pointtopoint and distributed cases. First, we propose an efficient algorithm to find ..."
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Abstract—In this paper, we present an empirical ratedistortion study of a communication scheme that uses compressive sensing (CS) as joint sourcechannel coding. We investigate the ratedistortion behavior of both pointtopoint and distributed cases. First, we propose an efficient algorithm to find the ℓ1regularization parameter that is required by the Least Absolute Shrinkage and Selection Operator which we use as a CS decoder. We then show that, for a pointtopoint channel, the ratedistortion follows two distinct regimes: the first one corresponds to an almost constant distortion, and the second one to a rapid distortion degradation, as a function of rate. This constant distortion increases with both increasing channel noise level and sparsity level, but at a different gradient depending on the distortion measure. In the distributed case, we investigate the ratedistortion behavior when sources have temporal and spatial dependencies. We show that, taking advantage of both spatial and temporal correlations over merely considering the temporal correlation between the signals allows us to achieve an average of a factor of approximately 2.5 × improvement in the ratedistortion behavior of the joint sourcechannel coding scheme. I.
Onestep quantized network coding for near sparse messages,” arXiv preprint arXiv:1210.7399
 2 [d B ] QNC, k/n=0.05 QNC, k/n=0.15 QNC, k/n=0.25 PF (c) 1400 edges, k
, 2012
"... In this paper, mathematical bases for nonadaptive joint source network coding of correlated messages in a Bayesian scenario are studied. Specifically, we introduce onestep Quantized Network Coding (QNC), which is a hybrid combination of network coding and packet forwarding for transmission. Motiv ..."
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In this paper, mathematical bases for nonadaptive joint source network coding of correlated messages in a Bayesian scenario are studied. Specifically, we introduce onestep Quantized Network Coding (QNC), which is a hybrid combination of network coding and packet forwarding for transmission. Motivated by the work on Bayesian compressed sensing, we derive theoretical guarantees on robust recovery in a onestep QNC scenario. Our mathematical derivations for Gaussian messages express the opportunity of distributed compression by using onestep QNC, as a simplified version of QNC scenario. Our simulation results show an improvement in terms of qualitydelay performance over routing based packet forwarding. 1
Article Methods for Distributed Compressed Sensing
, 2013
"... Abstract: Compressed sensing is a thriving research field covering a class of problems where a large sparse signal is reconstructed from a few random measurements. In the presence of several sensor nodes measuring correlated sparse signals, improvements in terms of recovery quality or the requiremen ..."
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Abstract: Compressed sensing is a thriving research field covering a class of problems where a large sparse signal is reconstructed from a few random measurements. In the presence of several sensor nodes measuring correlated sparse signals, improvements in terms of recovery quality or the requirement for a fewer number of local measurements can be expected if the nodes cooperate. In this paper, we provide an overview of the current literature regarding distributed compressed sensing; in particular, we discuss aspects of network topologies, signal models and recovery algorithms.