Unicast Sessions Research Articles

A Note on the Multiple-Unicast Network Coding Conjecture

Network coding encourages in-network information mixing for enhanced network capacity. An important open problem in network coding, the multiple-unicast network coding (MUNC) conjecture, claims that network coding is equivalent to routing for multiple unicast sessions in an undirected network. Simple and intuitive as it appears, the MUNC conjecture has remained open for a decade. This work studies a special case of MUNC, where intra-session connections are better than inter-session connections. In the cost domain, we prove that if each source is closer to its own receiver than to other receivers, then network coding is equivalent to routing. In the throughput domain, an intuitive dual statement is that if each source has a larger max-flow to its own receiver than to other receivers, then network coding is equivalent to routing. We prove that this statement is equivalent to the original MUNC conjecture. An interesting consequence is that an equivalence between the two seemingly dual statements studied in this work, if true, would imply the original MUNC conjecture.

A Geometric Perspective to Multiple-Unicast Network Coding

The multiple-unicast network coding conjecture states that for multiple unicast sessions in an undirected network, network coding is equivalent to routing. Simple and intuitive as it appears, the conjecture has remained open since its proposal in 2004, and is now a well-known unsolved problem in the field of network coding. Based on a recently proposed tool of space information flow, we present a geometric framework for analyzing the multiple-unicast conjecture. The framework consists of four major steps, in which the conjecture is transformed from its throughput version to cost version, from the graph domain to the space domain, and then from high dimension to 1-D, where it is to be eventually proved. We apply the geometric framework to derive unified proofs to known results of the conjecture, as well as new results previously unknown. A possible proof to the conjecture based on this framework is outlined.

Bounds on the Benefit of Network Coding for Wireless Multicast and Unicast

In this paper, we explore fundamental limitations of the benefit of network coding in multihop wireless networks. We study two well-accepted scenarios in the field: single multicast session and multiple unicast sessions. We assume arbitrary but fixed topology and traffic patterns for the wireless network. We prove that the gain of network coding in terms of throughput and energy saving of a single multicast session is at most a constant factor. Also, we present a lower bound on the average number of transmissions of multiple unicast sessions under any arbitrary network coding. We identify scenarios under which network coding provides no gain at all, in the sense that there exists a simple flow scheme that achieves the same performance. Moreover, we prove that the gain of network coding in terms of the maximum transport capacity is bounded by a constant factor of at most $(\pi)$ in any arbitrary wireless network under all traditional Gaussian channel models. As a corollary, we find that the gain of network coding on the throughput of large homogeneous wireless networks is asymptotically bounded by a constant. Furthermore, we establish theorems which relate a network coding scheme to a simple routing scheme for multiple unicast sessions. The theorems can be used as criteria for evaluating the potential gain of network coding in a given wired or wireless network. Based on these criteria, we find more scenarios where network coding has no gain on throughput or energy saving.

A Deterministic Polynomial-Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi <etal xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial-time versions of our algorithm and show that for a network with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$g$</tex></formula> destinations, our deterministic algorithm can achieve the capacity in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\left \lceil \log (g+1)\right \rceil $</tex></formula> uses of the network and has the fastest construction time among algorithms for this problem.

Low Complexity and Provably Efficient Algorithm for Joint Inter and Intrasession Network Coding in Wireless Networks

The performance of wireless networks can be enhanced by performing network coding on the intermediate relay nodes. To enhance the throughput of large wireless networks, we can decompose them into a superposition of simple relay networks called two-hop relay networks. Previously, the capacity region of two-hop relay networks with multiple unicast sessions and limited feedback was characterized where packet erasure channels are used. A near-optimal coding scheme that exploits the broadcast nature and the diversity of the wireless links was proposed. However, the complexity of the scheme is exponential in terms of the number of sessions, as it requires the knowledge of the packets that are received by any subset of the receivers. In this paper, we provide a polynomial time coding scheme and characterize its performance using linear equations. The coding scheme uses random network coding to carefully mix intra and intersession network coding and makes a linear, not exponential, number of decisions. For two-hop relay networks with two sessions, we provide an optimal coding scheme that does not require the knowledge of the channel conditions. We also provide a linear programming formulation that uses our two-hop relay network results as a building block in large lossy multihop networks.

Multiuser Broadcast Erasure Channel With Feedback—Capacity and Algorithms

We consider the $N$-user broadcast erasure channel with $N$ unicast sessions (one for each user) where receiver feedback is regularly sent to the transmitter in the form of ACK/NACK messages. We first provide a generic outer bound to the capacity of this system; we then propose a virtual-queue-based inter-session mixing coding algorithm, determine its rate region and show that it achieves capacity under certain conditions on channel statistics, assuming that instantaneous feedback is known to all users. Removing this assumption results in a rate region that asymptotically differs from the outer bound by 1 bit as $L\to \infty$, where $L$ is the number of bits per packet (packet length). For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose rate region is identical to the outer bound for N=3, when instant feedback is known to all users, and differs from the bound by 1 bit as $L\to \infty$, when the 3 users know only their own ACK. The proposed algorithms do not require any prior knowledge of channel statistics.

Network Coding for Overhead Reduction in Delay Tolerant Networks

Employing Network Coding (NC) in routing protocols for Delay Tolerant Networks (DTNs) is a challenging issue during the last years due to its potential beneficial effect on improving relevant critical metrics. This paper proposes an effective NC scheme intended for sparse DTNs comprising nodes of limited storage capacity. The scheme employs a memory management algorithm that makes optimal use of the limited storage capacity and focuses on unicast sessions where source and intermediate nodes combine only packets belonging to the same generation and destined for the same destination node. Upon having received a sufficient number of linearly independent packets resulting in a matrix of full rank, the destination nodes can apply network decoding to retrieve the information intended for them. The proposed scheme is fully distributed since the network nodes make decisions based on information collected solely from their own buffers. Combined either with Epidemic or probabilistic routing protocols, the scheme manages to drastically reduce the overhead created per source packet.

Star-Structure Network Coding for Multiple Unicast Sessions in Wireless Mesh Networks

In this paper, first, we propose Star-NC, a new network coding (NC) scheme for multiple unicast sessions in an n-input n-output star structure. Then, we evaluate the network throughput of this coding scheme in wireless mesh network over the traditional non-NC transmission. Our scheme benefits from the proximity of all the nodes around the relay node and employs a more general form of overhearing different from other schemes such as COPE. We found that the gain of our NC scheme depends on both the star size and the routing pattern of the unicast transmissions. Based on this, we identify both the situations which the maximum gain is achievable and a lower bound for the expected value of the gain in the case of random routing pattern. Next, we propose an analytical framework for studying throughput gain of our Star-NC scheme in general wireless network topologies. Our theoretical formulation via linear programming provides a method for finding source-destination routes and utilizing the best choices of our NC scheme to maximize the throughput. Finally, we evaluate our model for various networks, traffic models and routing strategies over coding-oblivious routing. We also compare the throughput gain of our scheme with COPE-type NC scheme. We show that Star-NC exploits new coding opportunities different from COPE-type NC and thus can be used with or without this scheme. The results show that Star-NC has often better performance than COPE for a directional traffic model which is a typical model in wireless mesh networks. Moreover, we found that, joint Star and COPE-type NC has better throughput performance than each of Star or COPE alone.

Coding‐aware routing and scheduling in WiMAX‐based mesh networks: a cross‐layer design approach

ABSTRACTIn this paper, we propose a cross‐layer design framework for the joint problem of coding‐aware routing and scheduling in WiMAX‐based mesh networks with unicast sessions. The model attempts to maximize the system throughput by exploiting opportunistic coding opportunities through appropriate routing and by achieving efficient spectrum reuse through appropriate link scheduling. We assume centralized scheduling at the base station and focus on minimizing the total schedule length to satisfy a certain traffic demand. Minimizing the schedule length is equivalent to maximizing the system throughput. We present a linear programming optimization model for the joint problem, which relies on the enumeration of all possible schedules. Given its complexity, we decompose the problem using a column generation approach. Our numerical results show that significant gains may be achieved when network coding is incorporated into the design. We compare the performance with that of a joint coding‐oblivious model with and without transmission power control. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Network coding for multiple unicast sessions in multi-channel/interface wireless networks

Throughput limitation of wireless networks imposes many practical problems as a result of wireless media broadcast nature. The solutions of the problem are mainly categorized in two groups; the use of multiple orthogonal channels and network coding (NC). The networks with multiple orthogonal channels and possibly multiple interfaces can mitigate co-channel interference among nodes. However, efficient assignment of channels to the available network interfaces is a major problem for network designers. Existing heuristic and theoretical work unanimously focused on joint design of channel assignment with the conventional transport/IP/MAC architecture. Furthermore, NC has been a prominent approach to improve the throughput of unicast traffic in wireless multi-hop networks through opportunistic NC. In this paper we seek a collaboration scheme for NC in multi-channel/interface wireless networks, i.e., the integration of NC, routing and channel assignment problem. First, we extend the NC for multiple unicast sessions to involve both COPE-type and a new proposed scheme named as Star-NC. Then, we propose an analytical framework that jointly optimizes the problem of routing, channel assignment and NC. Our theoretical formulation via a linear programming provides a method for finding source---destination routes and utilizing the best choices of different NC schemes to maximize the aggregate throughput. Through this LP, we propose a novel channel assignment algorithm that is aware of both coding opportunities and co-channel interference. Finally, we evaluate our model for various networks, traffic models, routing and coding strategies over coding-oblivious routing.

IP-based mobility management for heterogeneous wireless access

Abstract. Future high quality communication services will be offered in an integrated or converged network infrastructure maintaining both fixed wireless and mobile access via multi-mode user terminals. A support of various scenarios of user and/or terminal mobility within a common IP-based infrastructure requires intelligently designed control protocols. A major challenge is to provide seamless (i.e. lossless and low delay) handover between different radio cells and operator domains to enable continuation of unicast and multicast sessions while using network resources most efficiently. IETF (Internet Engineering Task Force) is specifying related IP mobility management protocols to be applicable also to a flat architecture as envisaged by Next Generation (Mobile) Networks (NGNs/NGMNs). The contribution will describe operator requirements towards such an approach. Both single-domain and multi-domain scenarios will be discussed based on federation ideas. Already existing solutions are taken into consideration and application of solution proposals towards a Distributed Mobility Management (DMM) currently under evaluation within IETF will be outlined.

On the Capacity of Wireless 1-Hop Intersession Network Coding—A Broadcast Packet Erasure Channel Approach

Motivated by practical wireless network protocols, this paper focuses on wireless intersession network coding (INC) over a 1-hop neighborhood, of which the exact capacity region remains an open problem. Towards better understanding of the capacity, this work first models the wireless overhearing events by broadcast packet erasure channels that are memoryless and stationary. Since most INC gain is resulted from destinations overhearing packets transmitted by other sources, this work then focuses exclusively on the 2-staged INC schemes, which fully capture the throughput benefits of overheard message side information (MSI) through the use of one-time feedback but refrain from exploiting the broadcast spatial diversity gain of channel output feedback. Under this setting, a capacity outer bound is provided for any number of M coexisting unicast sessions. For the special cases of M ≤ 3, it is shown that the outer bound can be achieved and is indeed the capacity. To quantify the tightness of the outer bound for M ≥ 4, a capacity inner bound for general M is provided. Both the outer and inner bounds can be evaluated by any linear programming solver. Numeric results show that for 4 ≤ M ≤ 5 with randomly chosen channel parameters, the difference between the outer and inner bounds is within 1% for 96.7% of the times. Focusing exclusively on the benefits of MSI, the results in this paper can also be viewed as the generalization of index-coding capacity from wireline broadcast with binary alphabets to wireless broadcast with high-order alphabets.

On multicast throughput scaling of hybrid wireless networks with general node density

In this paper, we consider hybrid wireless networks with a general node density λ ∈ [1, n], where n ad hoc nodes are uniformly distributed and m base stations (BSs) are regularly placed in a square region A ( n , A ) = 1 , A × 1 , A with A ∈ [1, n]. We focus on multicast sessions in which each ad hoc node as a user chooses randomly d ad hoc nodes as its destinations. Specifically, when d = 1 (or d = n − 1), a multicast session is essentially a unicast (or broadcast) session. We study the asymptotic multicast throughput for such a hybrid wireless network according to different cases in terms of m ∈ [1, n] and d ∈ [1, n], as n → ∞. To be specific, we design two types of multicast schemes, called hybrid scheme and BS- based scheme, respectively. For the hybrid scheme, there are two alternative routing backbones: sparse backbones and dense backbones. Particularly, according to different regimes of the node density λ = n A , we derive the thresholds in terms of m and d. Depending on these thresholds, we determine which scheme is preferred for the better performance of network throughput.

A Max-Flow/Min-Cut Algorithm for Linear Deterministic Relay Networks

The linear deterministic model of relay networks (LDRN) is a generalization of the traditional directed network model which has become popular in the study of the flow of information over wireless communication networks. The max-flow/min-cut theorem for a multicast session over a directed network has been extended to this wireless relay model. The result was first proved by a random coding scheme over large blocks of transmitted signals. In this paper, in the special case of a unicast session, a simple capacity-achieving transmission scheme for LDRN which codes over one symbol of information at each use of the network is obtained by a connection to the submodular flow problem and through the application of tools from matroid theory and submodular optimization theory. Polynomial-time algorithms for calculating the capacity of the network and the optimal coding scheme are implied by our analysis.

Impact of deployment size on the asymptotic capacity for wireless ad hoc networks under Gaussian channel model

We study the throughput capacity and transport capacity for both random and arbitrary wireless networks under Gaussian Channel model when all wireless nodes have the same constant transmission power P and the transmission rate is determined by Signal to Interference plus Noise Ratio (SINR). We consider networks with n wireless nodes $$\{v_1,v_2,\ldots,v_n\}$$ (randomly or arbitrarily) distributed in a square region B a with a side-length a. We randomly choose n s node as the source nodes of n s multicast sessions. For each source node v i , we randomly select k points and the closest k nodes to these points as destination nodes of this multicast session. We derive achievable lower bounds and some upper bounds on both throughput capacity and transport capacity for both unicast sessions and multicast sessions. We found that the asymptotic capacity depends on the size a of the deployment region, and it often has three regimes.

A unified framework for distributed video rate allocation over wireless networks

When multiple video streams share a wireless network, careful rate allocation is needed to prevent congestion, as well as to balance the video qualities among the competing streams. In this paper, we present a unified optimization framework for video rate allocation over wireless networks. Our framework applies to both unicast and multicast sessions, and accommodates both scalable and non-scalable streams. The optimization objective is to minimize the total distortion of all video streams without incurring excessive network utilization. Our system model explicitly accounts for heterogeneity in wireless link capacities, traffic contention among neighboring links, as well as different video rate-distortion (RD) characteristics. The proposed distributed media-aware rate allocation scheme leverages cross-layer information exchange between the MAC and application layers to achieve fast convergence at the optimal allocation. We evaluate performance of the proposed scheme for streaming of high-definition (HD) and standard-definition (SD) video sequences over 802.11-based wireless networks, both in unicast and multicast scenarios. The scheme consistently outperforms conventional TCP-Friendly Rate Control (TFRC) in terms of overall video quality, and achieves more balanced qualities among the streams.

Intelligent p-Cycle Protection for Dynamic Multicast Sessions in WDM Networks

In WDM networks, it is important to maintain the survivability of communication sessions when link failure occurs due to the high bandwidth provided by a fiber link. Link failures have more serious impact on multicast sessions than on unicast sessions since a link used by a multicast session may carry traffic to multiple destinations. Thus, it is more critical to protect multicast sessions against single link failures. Researchers have proposed various protection schemes for multicast sessions, including tree-based, path-based, and segment-based schemes. Tree-based schemes suffer excessive use of network capacity, whereas path-based and segment-based schemes require long restoration times. In this paper, we propose a new p-cycle-based dynamic multicast protection scheme named IpC, which achieves both fast restoration and high capacity efficiency. The main feature of IpC is that it computes high efficiency p-cycles on demand to protect dynamic multicast sessions as they arrive. Extensive simulations have been conducted to evaluate the proposed IpC scheme, and the results show that it outperforms an existing p-cycle-based scheme.

Rate Control With Pairwise Intersession Network Coding

In this paper, we develop a distributed rate-control algorithm for networks with multiple unicast sessions when network coding is allowed across different sessions. Building on recent flow-based characterization of pairwise intersession network coding, the corresponding optimal rate-control problem is formulated as a convex optimization problem. The formulation exploits pairwise coding possibilities between any pair of sessions, where any coded symbol is formed by coding over at most two original symbols. The objective function is the sum of the utilities based on the rates supported by each unicast session. Working on the Lagrangian of the formulated problem, a distributed algorithm is developed with little coordination among intermediate nodes. Each unicast session has the freedom to choose its own utility function. The only information exchange required by the source is the weighted sum of the queue length of each link, which can be piggybacked to the acknowledgment messages. In addition to the optimal rate-control algorithm, we propose a decentralized pairwise random coding scheme that decouples the decision of coding from that of rate control, which further enhances the distributiveness of the proposed scheme. The convergence of the rate-control algorithm is proven analytically and verified by extensive simulations. Simulation results also demonstrate the advantage of the proposed algorithm over the state-of-the-art in terms of both throughput and fairness.

On describing the routing capacity regions of networks

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.

Multicast throughput for large scale cognitive networks

In this paper, we focus on the achievable throughput of cognitive networks consisting of the primary ad hoc network (PaN) and the secondary ad hoc network (SaN). We construct PaN and SaN by placing nodes according to Poisson point processes of density n and m respectively over a unit square region. We directly study the multicast throughput of cognitive network to unify that of unicast and broadcast sessions. In order to ensure the priority of primary users in meanings of throughput, we design a metric called throughput decrement ratio (TDR) to measure the ratio of the throughput of PaN in presence of SaN to that of PaN in absence of SaN. Endowing PaN with the right to determine the threshold of the TDR, we propose multicast schemes based on TDMA and multihop routing for the two networks respectively and derive their achievable multicast throughput depending on the given threshold. Specially, we show when PaN has sparser density than SaN, to be specific, $$n=o\left({\frac{m} {(\log m)^2}}\right),$$ and if PaN only cares about the order of its throughput, SaN can simultaneously achieve the same order of the aggregated multicast throughput as it were a stand-alone network in absence of PaN.