networkcoding (NC) is a new paradigm in data transport and promises to change many aspects of networking. Starting with an introduction to basic NC concepts and results, this paper reviews the state of the art on a n...
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ISBN:
(纸本)9781424442157
networkcoding (NC) is a new paradigm in data transport and promises to change many aspects of networking. Starting with an introduction to basic NC concepts and results, this paper reviews the state of the art on a number of topics and points out promising research directions.
Using tools from algebraic geometry and Grobner basis theory we solve two problems in networkcoding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second ...
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ISBN:
(纸本)9783540694984
Using tools from algebraic geometry and Grobner basis theory we solve two problems in networkcoding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.
In an acyclic multicast network, it is well known that a linear network coding solution over GF(q) exists when q is sufficiently large. In particular, for each prime power q no smaller than the number of receivers, a ...
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ISBN:
(纸本)9781479951864
In an acyclic multicast network, it is well known that a linear network coding solution over GF(q) exists when q is sufficiently large. In particular, for each prime power q no smaller than the number of receivers, a linear solution over GF(q) can be efficiently constructed. In this work, we reveal that a linear solution over a given finite field does not necessarily imply the existence of a linear solution over all larger finite fields. Specifically, we prove by construction that: (i) For every source dimension no smaller than 3, there is a multicast networklinearly solvable over GF(7) but not over GF(8), and there is another multicast networklinearly solvable over GF(16) but not over GF(17);(ii) There is a multicast networklinearly solvable over GF(5) but not over such GF(q) that q > 5 is a Mersenne prime plus 1, which can be extremely large.
This paper considers the problem of networkcoding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference network...
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ISBN:
(纸本)9781424469604
This paper considers the problem of networkcoding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference networks, is extended to analyze the performance of linear network coding in this setup and to provide a systematic code design approach. It is shown that, for a broad class of three-source three-destination unicast networks, a rate corresponding to half the individual source-destination min-cut is achievable via alignment strategies.
In this paper we introduce a novel linear network coding scheme, namely "rotate-and-add coding", that possesses low encoding complexity and operates fundamentally different from the traditional network codes...
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ISBN:
(纸本)9781424482641
In this paper we introduce a novel linear network coding scheme, namely "rotate-and-add coding", that possesses low encoding complexity and operates fundamentally different from the traditional network codes. This scheme can operate on a small field (e.g. F-2), thereby, it alleviates the computational complexities due to multiplication and addition operations in large finite fields. The key idea is to function on a vector of symbols instead of working with a single symbol of a large field. Each node encodes its received vectors by simply rotationally shifting the vectors and then adding them, i.e., here the addition is done in vector form and the multiplication is replaced by rotation. We verify that the new scheme requires lower computation and overhead than the existing schemes. However, as the cost of reducing the complexity, it provides slightly smaller throughput.
In this paper, we study joint networkcoding and distributed source coding of inter-node dependent messages, with the perspective of compressed sensing. Specifically, the theoretical guarantees for robust l(1)-min rec...
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ISBN:
(纸本)9781467309219;9781467309202
In this paper, we study joint networkcoding and distributed source coding of inter-node dependent messages, with the perspective of compressed sensing. Specifically, the theoretical guarantees for robust l(1)-min recovery of an under-determined set of linearnetwork coded sparse messages are investigated. We discuss the guarantees for l(1)-min 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 l(2)-norms 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 networkcoding coefficients results in a measurement matrix with an RIP behavior, similar to that of i.i.d. Gaussian matrix.
We present algorithms for initializing networks that use a convolutional networkcoding scheme and that may contain cycles. During the initialization process every source node transmits basis vectors and every sink no...
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ISBN:
(纸本)9781479962174
We present algorithms for initializing networks that use a convolutional networkcoding scheme and that may contain cycles. During the initialization process every source node transmits basis vectors and every sink node measures the impulse response of the network. The impulse response is then used to find a relation between the transmitted and the received symbols, which is needed for a decoding algorithm and to find the set of all achievable rates. An initialization process is needed if the network is unknown or if local encoding kernels are chosen randomly. Unlike acyclic networks, for which it is enough to transmit basis vectors one after another, the initialization of cyclic networks is more complicated, as pilot symbols interfere with each other and the impulse response is of infinite duration.
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 inter-node redundancy. Specifically, we propose a new transmission method, cal...
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ISBN:
(纸本)9781467301831
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 inter-node redundancy. Specifically, we propose a new transmission method, called quantized networkcoding, 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 l(1)-minimization 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 networkcoding coefficients, based on restricted isometry property, which results in robust l(1)-min decoding. Our numerical analysis show that the proposed quantized networkcoding scheme with l(1)-min decoding can achieve significant improvements, in terms of compression ratio and delivery delay, compared to conventional packet forwarding.
In this paper, a new scheme of combining cooperative diversity with networkcoding is proposed for wireless uplink multi-source multi-relay networks. The existing network-coded cooperative scheme always conducts netwo...
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In this paper, a new scheme of combining cooperative diversity with networkcoding is proposed for wireless uplink multi-source multi-relay networks. The existing network-coded cooperative scheme always conducts networkcoding operation at relays in moderate-to-high signal-to-noise ratio region. Distinct from it, the proposed scheme determines either a direct cooperative mode or a network-coded cooperative mode at relays according to the channel qualities of the broadcast phase. Compared with the existing network-coded cooperative scheme, the proposed scheme achieves a performance gain in terms of both diversity order and system ergodic capacity without extra bandwidth resource consumption. Both theoretical analysis and simulations verify the validity and superiority of the proposed cooperative scheme.
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