Related papers: Dualities Between Entropy Functions and Network Co…
We investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each source-destination pair is constrained to be 1, it is obvious that the triangular…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, $s_1-t_1$ and $s_2-t_2$. Current characterizations of the multiple unicast capacity region in this…
In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
Recently, it has been shown that the max flow capacity can be achieved in a multicast network using network coding. In this paper, we propose and analyze a more realistic model for wireless random networks. We prove that the capacity of…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
The classical random graph model $G(n,\lambda/n)$ satisfies a `duality principle', in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved…
In this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Matroidal entropy functions are entropy functions in the form $\mathbf{h} = \log v \cdot \mathbf{r}_M$ , where $v \ge 2$ is an integer and $\mathbf{r}_M$ is the rank function of a matroid $M$. They can be applied into capacity…