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Register a new userEdge removal in undirected networks
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Added by
Michael Langberg
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The edge-removal problem asks whether the removal of a $lambda$-capacity edge from a given network can decrease the communication rate between source-terminal pairs by more than $lambda$. In this short manuscript, we prove that for undirected networks, removing a $lambda$-capacity edge decreases the rate by $O(lambda)$. Through previously known reductive arguments, here newly applied to undirected networks, our result implies that the zero-error capacity region of an undirected network equals its vanishing-error capacity region. Whether it is possible to prove similar results for directed networks remains an open question.
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This paper explores the relationship between two ideas in network information theory: edge removal and strong converses. Edge removal properties state that if an edge of small capacity is removed from a network, the capacity region does not change too much. Strong converses state that, for rates outside the capacity region, the probability of error converges to 1 as the blocklength goes to infinity. Various notions of edge removal and strong converse are defined, depending on how edge capacity and error probability scale with blocklength, and relations between them are proved. Each class of strong converse implies a specific class of edge removal. The opposite directions are proved for deterministic networks. Furthermore, a technique based on a novel, causal version of the blowing-up lemma is used to prove that for discrete memoryless networks, the weak edge removal property--that the capacity region changes continuously as the capacity of an edge vanishes--is equivalent to the exponentially strong converse--that outside the capacity region, the probability of error goes to 1 exponentially fast. This result is used to prove exponentially strong converses for several examples, including the discrete 2-user interference channel with strong interference, with only a small variation from traditional weak converse proofs.
The edge removal problem studies the loss in network coding rates that results when a network communication edge is removed from a given network. It is known, for example, that in networks restricted to linear coding schemes and networks restricted to Abelian group codes, removing an edge e* with capacity Re* reduces the achievable rate on each source by no more than Re*. In this work, we seek to uncover larger families of encoding functions for which the edge removal statement holds. We take a local perspective: instead of requiring that all network encoding functions satisfy certain restrictions (e.g., linearity), we limit only the function carried on the removed edge e*. Our central results give sufficient conditions on the function carried by edge e* in the code used to achieve a particular rate vector under which we can demonstrate the achievability of a related rate vector once e* is removed.
A Fog-Radio Access Network (F-RAN) is studied in which cache-enabled Edge Nodes (ENs) with dedicated fronthaul connections to the cloud aim at delivering contents to mobile users. Using an information-theoretic approach, this work tackles the problem of quantifying the potential latency reduction that can be obtained by enabling Device-to-Device (D2D) communication over out-of-band broadcast links. Following prior work, the Normalized Delivery Time (NDT) --- a metric that captures the high signal-to-noise ratio worst-case latency --- is adopted as the performance criterion of interest. Joint edge caching, downlink transmission, and D2D communication policies based on compress-and-forward are proposed that are shown to be information-theoretically optimal to within a constant multiplicative factor of two for all values of the problem parameters, and to achieve the minimum NDT for a number of special cases. The analysis provides insights on the role of D2D cooperation in improving the delivery latency.
This work studies the advantages of coded multicasting for the downlink of a Fog Radio Access Network (F-RAN) system equipped with a multicast fronthaul link. In this system, a control unit (CU) in the baseband processing unit (BBU) pool is connected to distributed edge nodes (ENs) through a multicast fronthaul link of finite capacity, and the ENs have baseband processing and caching capabilities. Each user equipment (UE) requests a file in a content library which is available at the CU, and the requested files are served by the closest ENs based on the cached contents and on the information received on the multicast fronthaul link. The performance of coded multicast fronthauling is investigated in terms of the delivery latency of the requested contents under the assumption of pipelined transmission on the fronthaul and edge links and of single-user encoding and decoding strategies based on the hard transfer of files on the fronthaul links. Extensive numerical results are provided to validate the advantages of the coded multicasting scheme compared to uncoded unicast and multicast strategies.
Mobile edge computing (MEC) can enhance the computing capability of mobile devices, and non-orthogonal multiple access (NOMA) can provide high data rates. Combining these two technologies can effectively benefit the network with spectrum and energy efficiency. In this paper, we investigate the task completion time minimization in NOMA multiuser MEC networks, where multiple users can offload their tasks simultaneously via the same frequency band. We adopt the emph{partial} offloading, in which each user can partition its computation task into offloading computing and locally computing parts. We aim to minimize the maximum task latency among users by optimizing their tasks partition ratios and offloading transmit power. By considering the energy consumption and transmitted power limitation of each user, the formulated problem is quasi-convex. Thus, a bisection search (BSS) iterative algorithm is proposed to obtain the minimum task completion time. To reduce the complexity of the BSS algorithm and evaluate its optimality, we further derive the closed-form expressions of the optimal task partition ratio and offloading power for two-user NOMA MEC networks based on the analysed results. Simulation results demonstrate the convergence and optimality of the proposed a BSS algorithm and the effectiveness of the proposed optimal derivation.
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