The first result is on the separability of the unicast capacity of stationary multi-channel multi-radio wireless networks, i.e., whether the capacity of such a network is equal to the sum of the capacities of the corresponding single-channel single-radio wireless networks. For both the Arbitrary Network model and the Random Network model, given a channel assignment, the separability property does not always hold. However, if the number of radio interfaces at each node is equal to the number of channels, the separability property holds. The second result is on the impact of multi-channel routing (i.e., routing a bit through multiple channels as opposed to through a single channel) on the network capacity. For both network models, the network capacities conditioned on a channel assignment under the two routing schemes are not always equal, but if again the number of radio interfaces at each node is equal to the number of channels, the two routing schemes yield equal network capacities.
In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the whole rate region, and we refer to them as routing-optimal networks. We identify a class of routing-optimal networks, which we refer to as information-distributive networks, defined by three topological features. Due to these features, for each rate vector achieved by network coding, there is always a routing scheme such that it achieves the same rate vector…
We consider the energy savings that can be obtained by employing network coding instead of plain routing in wireless multiple unicast problems. We establish lower bounds on the benefit of network coding, defined as the maximum of the ratio of the minimum energy required by routing and network coding solutions, where the maximum is over all configurations. It is shown that if coding and routing solutions are using the same transmission range, the benefit in $d$-dimensional networks is at least $2d/\lfloor\sqrt{d}\rfloor$. Moreover, it is shown that if the transmission range can be optimized for…
One of the important unsolved problems in information theory is the conjecture that network coding has no rate benefit over routing in undirected unicast networks. Three known bounds on the symmetric rate in undirected unicast information networks are the sparsest cut, the LP bound and the partition bound. In this paper, we present three results on the partition bound. We show that the decision version problem of computing the partition bound is NP-complete. We give complete proofs of optimal routing schemes for two classes of networks that attain the partition bound. Recently, the conjecture …
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible. The network coding gap specifies how much coding packets together in a network can help compared to the more natural approach of routing. While makespan minimization using routing has been intensely studied for the multiple unicasts problem, no bounds on network coding gaps for this problem are known. We develop new techniques which allow us to upper bound …
In this paper, we present a new technique to obtain upper bounds on undirected unicast network information capacity. Using this technique, we characterize an upper bound, called partition bound, on the symmetric rate of information flow in undirected unicast networks and give an algorithm to compute it. Two classes of networks are presented for which the bound is tight and the capacity is achievable by routing thus confirming the undirected unicast conjecture for these classes of networks. We also show that the bound can be loose in general and present an approach to tighten it.
We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i-t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the $s_i - t_i$ pairs is quantified by means of a connectivity level vector, $[k_1 k_2 k_3]$ such that there exist $k_i$ edge-disjoint paths between $s_i$ and $t_i$. In this work we attempt to classify networks based on the connectivity level. It can be observed that unit-rate transmission can be supported by routing if $k_i \geq 3$, for all $i = 1, \dots, 3$. In…
A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we "extend" the wireline result to the wireless context. Our main result is the approximate optimality of a simple layering principle: {\em local physical-layer schemes combined with global routing}. We use the {\em reciprocity} of the wireless channel critically in this result. Our form…
We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). For wired networks with arbitrary connectivity, the sum capacity is achieved simply by routing. For wireless networks, we explore the degrees of freedom (DoF) of multihop X networks with a layered structure, allowing arbitrary number of hops, and arbitrary connectivity within each hop. For the case when there are no more th…
A Session Interaction Framework for The Multiple-Unicast Conjecture
Quan Cheng Laboratory（全成实验室）；University of Science and Technology Beijing（北京科技大学）；China Unicom（中国联通）；Institute for Network Sciences and Cyberspace, Tsinghua University（清华大学网络科学与网络空间研究院）
A new coding scheme for general N-node relay networks is presented for unicast, multicast, and broadcast. The proposed distributed decode-forward scheme combines and generalizes Marton coding for single-hop broadcast channels and the Cover-El Gamal partial decode-forward coding scheme for 3-node relay channels. The key idea of the scheme is to precode all the codewords of the entire network at the source by multicoding over multiple blocks. This encoding step allows these codewords to carry partial information of the messages implicitly without complicated rate splitting and routing. This part…
The routing capacity region of networks with multiple unicast sessions can be characterized using Farkas' lemma as an infinite set of linear inequalities. In this paper this result is sharpened by exploiting properties of the solution satisfied by each rate-tuple on the boundary of the capacity region, and a finite description of the routing capacity region which depends on network parameters is offered. For the special case of undirected ring networks additional results on the complexity of the description are provided.
There are two fundamentally different fronthaul techniques in the downlink communication of cloud radio access network (C-RAN): the data-sharing strategy and the compression-based strategy. Under the former strategy, each user's message is multicast from the central processor (CP) to all the serving remote radio heads (RRHs) over the fronthaul network, which then cooperatively serve the users through joint beamforming; while under the latter strategy, the user messages are first beamformed then quantized at the CP, and the compressed signal is unicast to the corresponding RRH, which then decom…
We consider the resource allocation problem in cooperative wireless networks wherein nodes perform mutual information accumulation. We consider a unicast setting and arbitrary arrival processes at the source node. Source arrivals can be broken down into numerous packets to better exploit the spatial and temporal diversity of the routes available in the network. We devise a linear-program-based algorithm which allocates network resource to meet a certain transmission objective. Given a network, a source with multiple arriving packets and a destination, our algorithm generates a policy that regu…
Online video games are getting more popular, attracting a continuously growing number of players. The main performance metrics of this application on the network level are packet ordering, communication throughput and transmission latency. Nowadays there is an interest in cyclic logical network topologies for online gaming, due to the easiness to preserve the packet order over cycles.Unfortunately, this approach increases the end-to-end transmission delays. In our paper, two main contributions are therefore presented. Firstly, it is shown that one can improve the latency of a gaming protocol o…
We consider the delay of network coding compared to routing with retransmissions in packet erasure networks with probabilistic erasures. We investigate the sub-linear term in the block delay required for unicasting $n$ packets and show that there is an unbounded gap between network coding and routing. In particular, we show that delay benefit of network coding scales at least as $\sqrt{n}$. Our analysis of the delay function for the routing strategy involves a major technical challenge of computing the expectation of the maximum of two negative binomial random variables. This problem has been …
We consider the problem of secure unicast transmission between two nodes in a directed graph, where an adversary eavesdrops/jams a subset of nodes. This adversarial setting is in contrast to traditional ones where the adversary controls a subset of links. In particular, we study, in the main, the class of routing-only schemes (as opposed to those allowing coding inside the network). Routing-only schemes usually have low implementation complexity, yet a characterization of the rates achievable by such schemes was open prior to this work. We first propose an LP based solution for secure communic…
Degree of freedom (DoF) region provides an approximation of capacity region in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling factor. In this correspondence, we analyse the DoF region and sum DoF for unicast layered multi-hop relay wireless networks with arbitrary number of source/destination/relay nodes, arbitrary number of hops and arbitrary number of antennas at each node. The result is valid for quite a few message topologies. We reveal the limitation on capacity of multi-hop network due to the concatenation structure and show the similarity with capacitor network…
In this paper we design throughput-optimal dynamic broad- cast algorithms for multi-hop networks with arbitrary topolo- gies. Most of the previous broadcast algorithms route pack- ets along spanning trees, rooted at the source node. For large dynamic networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper we design a class of dynamic algorithms which makes packet-by-packet schedul- ing and routing decisions and thus obviates the need for maintaining any global topological structures, such as span- ning trees. Ou…
We consider the problem of throughput-optimal broadcast- ing in time-varying wireless networks, whose underlying topology is restricted to Directed Acyclic Graphs (DAG). Previous broadcast algorithms route packets along spanning trees. In large networks with time-varying connectivities, these trees are difficult to compute and maintain. In this paper we propose a new online throughput-optimal broadcast algorithm which makes packet-by-packet scheduling and routing decisions, obviating the need for maintaining any global topological structures, such as spanning-trees. Our algorithm relies on sys…
