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Acyclic Network
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Aditya Ramamoorthy – One of the best experts on this subject based on the ideXlab platform.

zero error function computation on a directed Acyclic Network
Information Theory Workshop, 2018CoAuthors: Ardhendu Tripathy, Aditya RamamoorthyAbstract:We study the rate region of variablelength sourceNetwork codes that are used to compute a function of messages observed over a Network. The particular Network considered here is the simplest instance of a directed Acyclic graph (DAG) that is not a tree. Existing work on zeroerror function computation in DAG Networks provides bounds on the computation capacity, which is a measure of the amount of communication required per edge in the worst case. This work focuses on the average case: an achievable rate tuple describes the expected amount of communication required on each edge, where the expectation is over the probability mass function of the source messages. We describe a systematic procedure to obtain outer bounds to the rate region for computing an arbitrary demand function at the terminal. Our bounding technique works by lower bounding the entropy of the descriptions observed by the terminal conditioned on the function value and by utilizing the Schurconcave property of the entropy function.

Zeroerror Function Computation on a Directed Acyclic Network
arXiv: Information Theory, 2018CoAuthors: Ardhendu Tripathy, Aditya RamamoorthyAbstract:We study the rate region of variablelength sourceNetwork codes that are used to compute a function of messages observed over a Network. The particular Network considered here is the simplest instance of a directed Acyclic graph (DAG) that is not a tree. Existing work on zeroerror function computation in DAG Networks provides bounds on the \textit{computation capacity}, which is a measure of the amount of communication required per edge in the worst case. This work focuses on the average case: an achievable rate tuple describes the expected amount of communication required on each edge, where the expectation is over the probability mass function of the source messages. We describe a systematic procedure to obtain outer bounds to the rate region for computing an arbitrary demand function at the terminal. Our bounding technique works by lower bounding the entropy of the descriptions observed by the terminal conditioned on the function value and by utilizing the Schurconcave property of the entropy function. We evaluate these bounds for certain example demand functions.

sum Networks from incidence structures construction and capacity analysis
IEEE Transactions on Information Theory, 2018CoAuthors: Ardhendu Tripathy, Aditya RamamoorthyAbstract:A sumNetwork is an instance of a function computation problem over a directed Acyclic Network, in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of the wellstudied multiple unicast Network communication problem also hold for sumNetworks, due to a known reduction between the two problems. In this paper, we describe an algorithm to construct families of sumNetwork instances using incidence structures. The computation capacity of several of these sumNetwork families is evaluated. Unlike the coding capacity of a multiple unicast problem, the computation capacity of sumNetworks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong; we show examples of sumNetworks that have a rate1 solution over one characteristic but a rate close to zero over a different characteristic. In addition, a sumNetwork can have arbitrarily different computation capacities for different alphabets.
B. Sundar Rajan – One of the best experts on this subject based on the ideXlab platform.

Scalar Solvability of Network Computation Problems and Representable Matroids.
arXiv: Information Theory, 2016CoAuthors: Anindya Gupta, B. Sundar RajanAbstract:We consider the following \textit{Network computation problem}. In an Acyclic Network, there are multiple source nodes, each generating multiple messages, and there are multiple sink nodes, each demanding a function of the source messages. The Network coding problem corresponds to the case in which every demand function is equal to some source message, i.e., each sink demands some source message. Connections between Network coding problems and matroids have been well studied. In this work, we establish a relation between Network computation problems and representable matroids. We show that a Network computation problem in which the sinks demand linear functions of source messages admits a scalar linear solution if and only if it is matroidal with respect to a representable matroid whose representation fulfills certain constraints dictated by the Network computation problem. Next, we obtain a connection between Network computation problems and functional dependency relations (FDrelations) and show that FDrelations can be used to characterize Network computation problem with arbitrary (not necessarily linear) function demands as well as nonlinear Network codes.

PrecodingBased Network Alignment Using Transform Approach for Acyclic Networks With Delay
IEEE Transactions on Information Theory, 2014CoAuthors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar RajanAbstract:The algebraic formulation for linear Network coding in Acyclic Networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary Acyclic Network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)mlinear combination of the input symbols across different generations, where F(p)m denotes the field over which the Network operates (p is prime and m is a positive integer). We use finitefield discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)mlinear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the Acyclic Network with delay into ninstantaneous Networks (n is sufficiently large). We show that under certain conditions, there exists a Network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. When the zerointerference conditions are not satisfied, we propose three precodingbased Network alignment (PBNA) schemes for threesource threedestination multiple unicast Network with delays (3S 3D MUND) termed as PBNA using transform approach and timeinvariant local encoding coefficients (LECs), PBNA using timevarying LECs, and PBNA using transform approach and block timevarying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n’ + 1/2n’ + 1, n’/2n’ + 1, and n’/2n’ + 1 are achieved for the three sourcedestination pairs in a 3S 3D MUND employing PBNA using transform approach and timeinvariant LECs, and PBNA using transform approach and block timevarying LECs, where n’ is a positive integer. For PBNA using timevarying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three sourcedestination pairs in a 3S 3D MUND, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

Precoding Based Network Alignment using Transform Approach for Acyclic Networks with Delay
arXiv: Information Theory, 2013CoAuthors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar RajanAbstract:The algebraic formulation for linear Network coding in Acyclic Networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary Acyclic Network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a $\mathbb{F}_{p^m}$linear combination of the input symbols across different generations where, $\mathbb{F}_{p^m}$ denotes the field over which the Network operates ($p$ is prime and $m$ is a positive integer). We use finitefield discrete fourier transform (DFT) to convert the output symbols at the sink nodes, at any given time instant, into a $\mathbb{F}_{p^m}$linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the Acyclic Network with delay into {\em $n$instantaneous Networks} ($n$ is sufficiently large). We show that under certain conditions, there exists a Network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. When the zerointerference conditions are not satisfied, we propose three Precoding Based Network Alignment (PBNA) schemes for threesource threedestination multiple unicast Network with delays (3S 3D MUND) termed as PBNA using transform approach and timeinvariant local encoding coefficients (LECs), PBNA using timevarying LECs, and PBNA using transform approach and block timevarying LECs. Their feasibility conditions are then analyzed.
Weichang Yeh – One of the best experts on this subject based on the ideXlab platform.

New Method in Searching for All Minimal Paths for the Directed Acyclic Network Reliability Problem
IEEE Transactions on Reliability, 2016CoAuthors: Weichang YehAbstract:The directed Acyclic Network (DAN) is a directed Network without directed cycles and is always modeled various information, processes, and events or potential events of systems. Network reliability has been a popular tool to evaluate and validate the performance of DAN. In this study, a new simple algorithm is proposed to find all minimal paths to evaluate the DAN reliability. The proposed algorithm outperforms the existing known algorithms in calculating the DAN reliability from both theoretical and experimental aspects. The correctness and time complexity of the proposed algorithm are demonstrated and analyzed. The proposed algorithm is demonstrated on a benchmark DAN and tested its efficiency by applying it to another 20 randomly generated Networks.

Multistatenode Acyclic Networks reliability evaluation based on MC
Reliability Engineering & System Safety, 2003CoAuthors: Weichang YehAbstract:Abstract A multistatenode Acyclic Network (MNAN) is a generalization of the treestructured multistatenode system that does not satisfy the flow conservation law. The current known existing methods used to evaluate MNAN reliability are based on the minimal tree (MT) set. Instead of using the MT, an intuitive algorithm was developed in this to find the minimal cut (MC) set. The MNAN reliability can then be computed in terms of MCs. The proposed algorithm is simpler and more efficient compared to the bestknown existing methods. The computational complexity of the proposed algorithm is analyzed and compared with the bestknown existing methods. One example is used to show how all MCs are generated using the proposed algorithm. The corresponding reliabilities in this example are computed.

Multistatenode Acyclic Network reliability evaluation
Reliability Engineering & System Safety, 2002CoAuthors: Weichang YehAbstract:Abstract Many realworld systems (such as cellular telephones, transportation, etc.) are multistatenode Acyclic Network (MNAN) composed of multistatenodes. Such Network has a source node (position) where the signal source is located, a number of sink nodes that only receive the signal, and a number of intermediate nodes that retransmit the received signal to some other nodes. The nonsink node has different states determined by a set of nodes receiving the signal directly from it. The reliability of MNAN can be computed in terms of minimal trees (MTs). Based on the BranchandBound algorithm, we developed an intuitive algorithm that is simpler than the bestknown existing method. The computational complexity of the proposed algorithm is also analyzed. One example is illustrated to show how all MTs are generated by the proposed algorithm. The reliability of this example is then computed.
Ardhendu Tripathy – One of the best experts on this subject based on the ideXlab platform.

zero error function computation on a directed Acyclic Network
Information Theory Workshop, 2018CoAuthors: Ardhendu Tripathy, Aditya RamamoorthyAbstract:We study the rate region of variablelength sourceNetwork codes that are used to compute a function of messages observed over a Network. The particular Network considered here is the simplest instance of a directed Acyclic graph (DAG) that is not a tree. Existing work on zeroerror function computation in DAG Networks provides bounds on the computation capacity, which is a measure of the amount of communication required per edge in the worst case. This work focuses on the average case: an achievable rate tuple describes the expected amount of communication required on each edge, where the expectation is over the probability mass function of the source messages. We describe a systematic procedure to obtain outer bounds to the rate region for computing an arbitrary demand function at the terminal. Our bounding technique works by lower bounding the entropy of the descriptions observed by the terminal conditioned on the function value and by utilizing the Schurconcave property of the entropy function.

Zeroerror Function Computation on a Directed Acyclic Network
arXiv: Information Theory, 2018CoAuthors: Ardhendu Tripathy, Aditya RamamoorthyAbstract:We study the rate region of variablelength sourceNetwork codes that are used to compute a function of messages observed over a Network. The particular Network considered here is the simplest instance of a directed Acyclic graph (DAG) that is not a tree. Existing work on zeroerror function computation in DAG Networks provides bounds on the \textit{computation capacity}, which is a measure of the amount of communication required per edge in the worst case. This work focuses on the average case: an achievable rate tuple describes the expected amount of communication required on each edge, where the expectation is over the probability mass function of the source messages. We describe a systematic procedure to obtain outer bounds to the rate region for computing an arbitrary demand function at the terminal. Our bounding technique works by lower bounding the entropy of the descriptions observed by the terminal conditioned on the function value and by utilizing the Schurconcave property of the entropy function. We evaluate these bounds for certain example demand functions.

sum Networks from incidence structures construction and capacity analysis
IEEE Transactions on Information Theory, 2018CoAuthors: Ardhendu Tripathy, Aditya RamamoorthyAbstract:A sumNetwork is an instance of a function computation problem over a directed Acyclic Network, in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of the wellstudied multiple unicast Network communication problem also hold for sumNetworks, due to a known reduction between the two problems. In this paper, we describe an algorithm to construct families of sumNetwork instances using incidence structures. The computation capacity of several of these sumNetwork families is evaluated. Unlike the coding capacity of a multiple unicast problem, the computation capacity of sumNetworks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong; we show examples of sumNetworks that have a rate1 solution over one characteristic but a rate close to zero over a different characteristic. In addition, a sumNetwork can have arbitrarily different computation capacities for different alphabets.
Teja Damodaram Bavirisetti – One of the best experts on this subject based on the ideXlab platform.

PrecodingBased Network Alignment Using Transform Approach for Acyclic Networks With Delay
IEEE Transactions on Information Theory, 2014CoAuthors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar RajanAbstract:The algebraic formulation for linear Network coding in Acyclic Networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary Acyclic Network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)mlinear combination of the input symbols across different generations, where F(p)m denotes the field over which the Network operates (p is prime and m is a positive integer). We use finitefield discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)mlinear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the Acyclic Network with delay into ninstantaneous Networks (n is sufficiently large). We show that under certain conditions, there exists a Network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. When the zerointerference conditions are not satisfied, we propose three precodingbased Network alignment (PBNA) schemes for threesource threedestination multiple unicast Network with delays (3S 3D MUND) termed as PBNA using transform approach and timeinvariant local encoding coefficients (LECs), PBNA using timevarying LECs, and PBNA using transform approach and block timevarying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n’ + 1/2n’ + 1, n’/2n’ + 1, and n’/2n’ + 1 are achieved for the three sourcedestination pairs in a 3S 3D MUND employing PBNA using transform approach and timeinvariant LECs, and PBNA using transform approach and block timevarying LECs, where n’ is a positive integer. For PBNA using timevarying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three sourcedestination pairs in a 3S 3D MUND, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

Precoding Based Network Alignment using Transform Approach for Acyclic Networks with Delay
arXiv: Information Theory, 2013CoAuthors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar RajanAbstract:The algebraic formulation for linear Network coding in Acyclic Networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary Acyclic Network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a $\mathbb{F}_{p^m}$linear combination of the input symbols across different generations where, $\mathbb{F}_{p^m}$ denotes the field over which the Network operates ($p$ is prime and $m$ is a positive integer). We use finitefield discrete fourier transform (DFT) to convert the output symbols at the sink nodes, at any given time instant, into a $\mathbb{F}_{p^m}$linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the Acyclic Network with delay into {\em $n$instantaneous Networks} ($n$ is sufficiently large). We show that under certain conditions, there exists a Network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. When the zerointerference conditions are not satisfied, we propose three Precoding Based Network Alignment (PBNA) schemes for threesource threedestination multiple unicast Network with delays (3S 3D MUND) termed as PBNA using transform approach and timeinvariant local encoding coefficients (LECs), PBNA using timevarying LECs, and PBNA using transform approach and block timevarying LECs. Their feasibility conditions are then analyzed.

a transform approach to linear Network coding for Acyclic Networks with delay
International Symposium on Information Theory, 2012CoAuthors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, Sundar B RajanAbstract:The algebraic formulation for linear Network coding in Acyclic Networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary Acyclic Network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a F q –linear combination of the input symbols across different generations, where F q denotes the field over which the Network operates. We use finitefield discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a F q –linear combination of the input symbols generated during the same generation. We call this as transforming the Acyclic Network with delay into ninstantaneous Networks (n is sufficiently large). We show that under certain conditions, there exists a Network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual sourcedestination mincut (which are assumed to be equal to 1) for some classes of threesource threedestination multiple unicast Network with delays using alignment strategies when the zerointerference condition is not satisfied.