# Acyclic Network - Explore the Science & Experts | ideXlab

## Acyclic Network

The Experts below are selected from a list of 8427 Experts worldwide ranked by ideXlab platform

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

• ##### zero error function computation on a directed AcyclicNetwork
Information Theory Workshop, 2018
Abstract:

We study the rate region of variable-length source-Network 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 zero-error 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 Schur-concave property of the entropy function.

• ##### Zero-error Function Computation on a Directed AcyclicNetwork
arXiv: Information Theory, 2018
Abstract:

We study the rate region of variable-length source-Network 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 zero-error 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 Schur-concave 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, 2018
Abstract:

A sum-Network 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 well-studied multiple unicast Network communication problem also hold for sum-Networks, due to a known reduction between the two problems. In this paper, we describe an algorithm to construct families of sum-Network instances using incidence structures. The computation capacity of several of these sum-Network families is evaluated. Unlike the coding capacity of a multiple unicast problem, the computation capacity of sum-Networks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong; we show examples of sum-Networks that have a rate-1 solution over one characteristic but a rate close to zero over a different characteristic. In addition, a sum-Network 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, 2016
Co-Authors: Anindya Gupta, B. Sundar Rajan
Abstract:

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 (FD-relations) and show that FD-relations can be used to characterize Network computation problem with arbitrary (not necessarily linear) function demands as well as nonlinear Network codes.

• ##### Precoding-Based Network Alignment Using Transform Approach for AcyclicNetworks With Delay
IEEE Transactions on Information Theory, 2014
Co-Authors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar Rajan
Abstract:

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)m-linear 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 finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a 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 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 zero-interference conditions are not satisfied, we propose three precoding-based Network alignment (PBNA) schemes for three-source three-destination multiple unicast Network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying 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 source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n’ is a positive integer. For PBNA using time-varying 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 source-destination pairs in a 3-S 3-D MUN-D, 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 AcyclicNetworks with Delay
arXiv: Information Theory, 2013
Co-Authors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar Rajan
Abstract:

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 finite-field 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 (non-transform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three Precoding Based Network Alignment (PBNA) schemes for three-source three-destination multiple unicast Network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. Their feasibility conditions are then analyzed.

### Wei-chang 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 AcyclicNetwork Reliability Problem
IEEE Transactions on Reliability, 2016
Co-Authors: Wei-chang Yeh
Abstract:

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.

• ##### Multistate-node AcyclicNetworks reliability evaluation based on MC
Reliability Engineering & System Safety, 2003
Co-Authors: Wei-chang Yeh
Abstract:

Abstract A multistate-node Acyclic Network (MNAN) is a generalization of the tree-structured multistate-node 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 best-known existing methods. The computational complexity of the proposed algorithm is analyzed and compared with the best-known 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.

• ##### Multistate-node AcyclicNetwork reliability evaluation
Reliability Engineering & System Safety, 2002
Co-Authors: Wei-chang Yeh
Abstract:

Abstract Many real-world systems (such as cellular telephones, transportation, etc.) are multistate-node Acyclic Network (MNAN) composed of multistate-nodes. 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 non-sink 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 Branch-and-Bound algorithm, we developed an intuitive algorithm that is simpler than the best-known 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 AcyclicNetwork
Information Theory Workshop, 2018
Abstract:

We study the rate region of variable-length source-Network 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 zero-error 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 Schur-concave property of the entropy function.

• ##### Zero-error Function Computation on a Directed AcyclicNetwork
arXiv: Information Theory, 2018
Abstract:

We study the rate region of variable-length source-Network 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 zero-error 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 Schur-concave 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, 2018
Abstract:

A sum-Network 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 well-studied multiple unicast Network communication problem also hold for sum-Networks, due to a known reduction between the two problems. In this paper, we describe an algorithm to construct families of sum-Network instances using incidence structures. The computation capacity of several of these sum-Network families is evaluated. Unlike the coding capacity of a multiple unicast problem, the computation capacity of sum-Networks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong; we show examples of sum-Networks that have a rate-1 solution over one characteristic but a rate close to zero over a different characteristic. In addition, a sum-Network 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.

• ##### Precoding-Based Network Alignment Using Transform Approach for AcyclicNetworks With Delay
IEEE Transactions on Information Theory, 2014
Co-Authors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar Rajan
Abstract:

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)m-linear 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 finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a 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 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 zero-interference conditions are not satisfied, we propose three precoding-based Network alignment (PBNA) schemes for three-source three-destination multiple unicast Network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying 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 source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n’ is a positive integer. For PBNA using time-varying 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 source-destination pairs in a 3-S 3-D MUN-D, 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 AcyclicNetworks with Delay
arXiv: Information Theory, 2013
Co-Authors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, B. Sundar Rajan
Abstract:

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 finite-field 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 (non-transform) approach if and only if there exists a Network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three Precoding Based Network Alignment (PBNA) schemes for three-source three-destination multiple unicast Network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. Their feasibility conditions are then analyzed.

• ##### a transform approach to linear Network coding for AcyclicNetworks with delay
International Symposium on Information Theory, 2012
Co-Authors: Teja Damodaram Bavirisetti, Abhinav Ganesan, K. Prasad, Sundar B Rajan
Abstract:

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 finite-field 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 n-instantaneous Networks (n is sufficiently large). We show that under certain conditions, there exists a Network code satisfying sink demands in the usual (non-transform) 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 source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast Network with delays using alignment strategies when the zero-interference condition is not satisfied.