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 formal result is in the context of channel models for which "good" local schemes, that achieve the cut-set bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks).
Layered architectures, common in the engineering-design of wireless networks, can have near-optimal performance if the {\em locality} over which physical-layer schemes should operate is carefully designed. Feedback is shown to play a critical role in enabling the separation between the physical and the network layers. The key technical idea is the modeling of a wireless network by an undirected "polymatroidal" network, for which we establish a max-flow min-cut approximation theorem.
We show that the maximum possible energy benefit of network coding for multiple unicast on wireless networks is at least 3. This improves the previously known lower bound of 2.4 from [1].
We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form $mD_1 + D_2 \leq m$. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless …
Recently, network coding technique has emerged as a promising approach that supports reliable transmission over wireless loss channels. In existing protocols where users have no interest in considering the encoded packets they had in coding or decoding operations, this rule is expensive and inefficient. This paper studies the impact of encoded packets in the reliable unicast network coding via some theoretical analysis. Using our approach, receivers do not only store the encoded packets they overheard, but also report these information to their neighbors, such that users enable to take account…
We characterize the degrees-of-freedom (DoF) region of a class of two-unicast wireless networks under the assumption of delayed channel state information at the transmitters. We consider a layered topology with arbitrary connectivity, and we introduce new outer-bounds on the DoF region through the graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed channel state information. Combining our outer-bounds with new achievability schemes, we characterize the DoF region of two-unicast wireless networks with informational bottlen…
We consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $Θ(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus can be …
We propose a simple yet effective wireless network coding and decoding technique. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block codes. For this purpose, we make use of greedy codes over the binary field and show that desired diversity orders can be flexibly assigned to nodes in a multiple unicast network, contrary to the previous findings in the literature. Furthermore, we present the optimal detection rule for the given model that accounts for intermediate node errors and suggest a…
We consider two-source two-destination (i.e., two-unicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous distributions, then, with probability 1, two-unicast layered Gaussian networks can only have 1, 3/2 or 2 sum degrees-of-freedom (unless both source-destination pairs are disconnected, in which case no degrees-of-freedom can be achieved). We provide sufficient and necessary conditions for each case based on network connectivity and a new notion of source-destination pa…
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…
Unicast IPTV services that can support live TV, video-on-demand (VoD), video conferencing, and online gaming applications over broadband wireless cellular networks have been becoming popular in recent years. However, video streaming services significantly impact the performance of wireless cellular networks because they are bandwidth hogs. To maintain the system performance, effective admission control and resource allocation mechanisms based on an accurate mathematical analysis are required. On the other hand, the quality of a wireless link usually changes with time due to the user mobility o…
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 routin…
The deterministic channel model for wireless relay networks proposed by Avestimehr, Diggavi and Tse `07 has captured the broadcast and inference nature of wireless communications and has been widely used in approximating the capacity of wireless relay networks. The authors generalized the max-flow min-cut theorem to the linear deterministic wireless relay networks and characterized the unicast capacity of such deterministic network as the minimum rank of all the binary adjacency matrices describing source-destination cuts whose number grows exponentially with the size of the network. In this p…
We propose a simple yet effective wireless network coding and decoding technique for a multiple unicast network. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block codes. In order to exemplify the technique, we make use of greedy codes over the binary field and show that the arbitrary diversity orders can be flexibly assigned to nodes. Furthermore, we present the optimal detection rule for the given model that accounts for intermediate node errors and suggest a low-complexity network dec…
We consider multicommodity flow and cut problems in {\em polymatroidal} networks where there are submodular capacity constraints on the edges incident to a node. Polymatroidal networks were introduced by Lawler and Martel and Hassin in the single-commodity setting and are closely related to the submodular flow model of Edmonds and Giles; the well-known maxflow-mincut theorem holds in this more general setting. Polymatroidal networks for the multicommodity case have not, as far as the authors are aware, been previously explored. Our work is primarily motivated by applications to information flo…
Intelligent reflecting surfaces (IRSs) have received much attention recently and are envisioned to promote 6G communication networks. In this paper, for wireless communications aided by IRS units, we formulate optimization problems for power control under quality of service (QoS) and max-min fair QoS under three kinds of traffic patterns from a base station (BS) to mobile users (MUs): unicast, broadcast, and multicast. The optimizations are achieved by jointly designing the transmit beamforming of the BS and the phase shift matrix of the IRS. For power control under QoS, existing IRS studies i…
The problem of communicating a single message to a destination in presence of multiple relay nodes, referred to as cooperative unicast network, is considered. First, we introduce "Mixed Noisy Network Coding" (MNNC) scheme which generalizes "Noisy Network Coding" (NNC) where relays are allowed to decode-and-forward (DF) messages while all of them (without exception) transmit noisy descriptions of their observations. These descriptions are exploited at the destination and the DF relays aim to decode the transmitted messages while creating full cooperation among the nodes. Moreover, the destinati…
A framework is developed for analyzing capacity gains from user cooperation in slow fading wireless networks when the number of nodes (network size) is large. The framework is illustrated for the case of a simple multipath-rich Rayleigh fading channel model. Both unicasting (one source and one destination) and multicasting (one source and several destinations) scenarios are considered. We introduce a meaningful notion of Shannon capacity for such systems, evaluate this capacity as a function of signal-to-noise ratio (SNR), and develop a simple two-phase cooperative network protocol that achiev…
We consider the problem of network coding across three unicast sessions over a directed acyclic graph, when each session has min-cut one. Previous work by Das et al. adapted a precoding-based interference alignment technique, originally developed for the wireless interference channel, specifically to this problem. We refer to this approach as precoding-based network alignment (PBNA). Similar to the wireless setting, PBNA asymptotically achieves half the minimum cut; different from the wireless setting, its feasibility depends on the graph structure. Das et al. provided a set of feasibility con…
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…
Recently, network coding technique has emerged as a promising approach that supports reliable transmission over wireless loss channels. In existing protocols where users have no interest in considering the encoded packets they had in coding or decoding operations, this rule is expensive and inef-ficient. This paper studies the impact of encoded packets in the reliable unicast network coding via some theoretical analysis. Using our approach, receivers do not only store the encoded packets they overheard, but also report these information to their neighbors, such that users enable to take accoun…
A new precoding-based intersession network coding (NC) scheme has recently been proposed, which applies the interference alignment technique, originally devised for wireless interference channels, to the 3-unicast problem of directed acyclic networks. The main result of this work is a graph-theoretic characterization of the feasibility of the 3-unicast interference alignment scheme. To that end, we first investigate several key relationships between the point-to-point network channel gains and the underlying graph structure. Such relationships turn out to be critical when characterizing graph-…
In this paper, we investigate a hybrid multicast/ unicast scheme for a multiple-input single-output cache-aided non-orthogonal multiple access (NOMA) vehicular scenario in the face of rapidly fluctuating vehicular wireless channels. Considering a more practical situation, imperfect channel state information is taking into account. In this paper, we formulate an optimization problem to maximize the unicast sum rate under the constraints of the peak power, the peak backhaul, the minimum unicast rate, and the maximum multicast outage probability. To solve the formulated non-convex problem, a lowe…
The work of Avestimehr et al. '07 has recently proposed a deterministic model for wireless networks and characterized the unicast capacity C of such networks as the minimum rank of the adjacency matrices describing all possible source-destination cuts. Amaudruz & Fragouli first proposed a polynomial-time algorithm for finding the unicast capacity of a linear deterministic wireless network in their 2009 paper. In this work, we improve upon Amaudruz & Fragouli's work and further reduce the computational complexity of the algorithm by fully exploring the useful combinatorial features intrinsic in…
A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr, Diggavi and Tse proposed a linear deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of dete…
Not only is network coding essential to achieve the capacity of a single-session multicast network, it can also help to improve the throughput of wireless networks with multiple unicast sessions when overheard information is available. Most previous research aimed at realizing such improvement by using perfectly overheard information, while in practice, especially for wireless networks, overheard information is often imperfect. To date, it is unclear whether network coding should still be used in such situations with imperfect overhearing. In this paper, a simple but ubiquitous wireless networ…
We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where each sender and the receiver is connected to the network via a single edge of unit capacity. We consider a network model in which the middle of the network only performs random linear network coding, and restrict our approaches to precoding-based linear schemes, where the senders use precoding matrices to encode source symbols. We adapt a precoding-based interference alignment technique, originally developed for the wireless interference channel, to construct a precoding-based linear sc…
An intuitive overview of the scalability of a variety of types of wireless networks is presented. Simple heuris- tic arguments are demonstrated here for scaling laws presented in other works, as well as for conditions not previously considered in the literature. Unicast and multicast messages, topology, hierarchy, and effects of reliability protocols are discussed. We show how two key factors, bottlenecks and erasures, can often domi- nate the network scaling behavior. Scaling of through- put or delay with the number of transmitting nodes, the number of receiving nodes, and the file size is de…
This paper considers a wireless communication network consisting of multiple interfering multicast sessions. Different from a unicast system where each transmitter has only one receiver, in a multicast system, each transmitter has multiple receivers. It is a well known result for wireless unicast systems that the feasibility of an signal-to-interference-plus-noise power ratio (SINR) without power constraint is decided by the Perron-Frobenius eigenvalue of a nonnegative matrix. We generalize this result and propose necessary and sufficient conditions for the feasibility of an SINR in a wireless…
We define a class of multi--hop erasure networks that approximates a wireless multi--hop network. The network carries unicast flows for multiple users, and each information packet within a flow is required to be decoded at the flow destination within a specified delay deadline. The allocation of coding rates amongst flows/users is constrained by network capacity. We propose a proportional fair transmission scheme that maximises the sum utility of flow throughputs. This is achieved by {\em jointly optimising the packet coding rates and the allocation of bits of coded packets across transmission…
We study optimal delivery strategies of one common and $K$ independent messages from a source to multiple users in wireless environments. In particular, two-layered superposition of broadcast/multicast and unicast signals is considered in a downlink multiuser OFDMA system. In the literature and industry, the two-layer superposition is often considered as a pragmatic approach to make a compromise between the simple but suboptimal orthogonal multiplexing (OM) and the optimal but complex fully-layered non-orthogonal multiplexing. In this work, we show that only two-layers are necessary to achieve…
In this paper, we introduce novel coding schemes for wireless networks with random transmission delays. These coding schemes obviate the need for synchronicity, reduce the number of transmissions and achieve the optimal rate region in the corresponding wired model for both multiple unicast and multicast cases with up to three users under the equal rate constraint. The coding schemes are presented in two phases; first, coding schemes for line, star and line-star topologies with random transmission delays are provided. Second, any general topology with multiple bidirectional unicast and multicas…
We consider a hybrid delivery scheme for streaming content, combining cache-enabled Orthogonal Multipoint Multicast (OMPMC) and on-demand Single-Point Unicast (SPUC) transmissions for heterogeneous networks. The OMPMC service transmits cached files through the whole network to interested users, and users not being satisfied by this service are assigned to the SPUC service to be individually served. The SPUC fetches the requested files from the core network and unicasts them to UEs using cellular beamforming transmissions. We optimize the delivery scheme to minimize the average resource consump…
We consider arbitrary dense wireless networks, in which $n$ nodes are placed in an arbitrary (deterministic) manner on a square region of unit area and communicate with each other over Gaussian fading channels. We provide inner and outer bounds for the $n\times n$-dimensional unicast and the $n\times 2^n$-dimensional multicast capacity regions of such a wireless network. These inner and outer bounds differ only by a factor $O(\log(n))$, yielding a fairly tight scaling characterization of the entire regions. The communication schemes achieving the inner bounds use interference alignment as a ce…
Consider a lossy packet network of queues, communicating over a wireless medium. This paper presents a throughput-optimal transmission strategy for a unicast network when feedback is available, which has the following advantages: It requires a very limited form of acknowledgment feedback. It is completely distributed, and independent of the network topology. Finally, communication at the information theoretic cut-set rate requires no network coding and no rateless coding on the packets. This simple strategy consists of each node randomly choosing a packet from its buffer to transmit at each op…
This work investigates the maximum broadcast throughput and its achievability in multi-hop wireless networks with half-duplex node constraint. We allow the use of physical-layer network coding (PNC). Although the use of PNC for unicast has been extensively studied, there has been little prior work on PNC for broadcast. Our specific results are as follows: 1) For single-source broadcast, the theoretical throughput upper bound is n/(n+1), where n is the "min vertex-cut" size of the network. 2) In general, the throughput upper bound is not always achievable. 3) For grid and many other networks, t…
We consider multi--hop networks comprising Binary Symmetric Channels ($\mathsf{BSC}$s). The network carries unicast flows for multiple users. The utility of the network is the sum of the utilities of the flows, where the utility of each flow is a concave function of its throughput. Given that the network capacity is shared by the flows, there is a contention for network resources like coding rate (at the physical layer), scheduling time (at the MAC layer), etc., among the flows. We propose a proportional fair transmission scheme that maximises the sum utility of flow throughputs subject to the…
In this paper, a compress-and-forward scheme with backward decoding is presented for the unicast wireless relay network. The encoding at the source and relay is a generalization of the noisy network coding scheme (NNC). While it achieves the same reliable data rate as noisy network coding scheme, the backward decoding allows for a better decoding complexity as compared to the joint decoding of the NNC scheme. Characterizing the layered decoding scheme is shown to be equivalent to characterizing an information flow for the wireless network. A node-flow for a graph with bisubmodular capacity con…
The rate optimization for wireless networks with low SNR is investigated. While the capacity in the limit of disappearing SNR is known to be linear for fading and non-fading channels, we study the problem of operating in low SNR wireless network with given node locations that use network coding over flows. The model we develop for low SNR Gaussian broadcast channel and multiple access channel respectively operates in a non-trivial feasible rate region. We show that the problem reduces to the optimization of total network power which can be casted as standard linear multi-commodity min-cost flo…
The flux of social media and the convenience of mobile connectivity has created a mobile data phenomenon that is expected to overwhelm the mobile cellular networks in the foreseeable future. Despite the advent of 4G/LTE, the growth rate of wireless data has far exceeded the capacity increase of the mobile networks. A fundamentally new design paradigm is required to tackle the ever-growing wireless data challenge. In this article, we investigate the problem of massive content delivery over wireless networks and present a systematic view on content-centric network design and its underlying chall…
We consider multi--hop wireless networks carrying unicast flows for multiple users. Each flow has a specified delay deadline, and the lossy wireless links are modelled as binary symmetric channels (BSCs). Since transmission time, also called airtime, on the links is shared amongst flows, increasing the airtime for one flow comes at the cost of reducing the airtime available to other flows sharing the same link. We derive the joint allocation of flow airtimes and coding rates that achieves the proportionally fair throughput allocation. This utility optimisation problem is non--convex, and one o…
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…
We consider the problem of energy-efficient transmission in delay constrained cooperative multihop wireless networks. The combinatorial nature of cooperative multihop schemes makes it difficult to design efficient polynomial-time algorithms for deciding which nodes should take part in cooperation, and when and with what power they should transmit. In this work, we tackle this problem in memoryless networks with or without delay constraints, i.e., quality of service guarantee. We analyze a wide class of setups, including unicast, multicast, and broadcast, and two main cooperative approaches, na…
The deterministic wireless relay network model, introduced by Avestimehr et al., has been proposed for approximating Gaussian relay networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. Avestimehr et al. showed that the Min-cut Max-flow theorem holds in the ADT network. In this paper, we show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Medard. We prove that the ADT network problem can be captured by a single matrix, called the "system matrix". We …
Multicast transmission has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include (i) identical packets must be delivered successfully to several nodes, (ii) outage could simultaneously happen at different receivers, and (iii) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. To capture these key traits, we utilize a Poisson cluster process consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capaci…
We consider the problem of simultaneous on-demand streaming of stored video to multiple users in a multi-cell wireless network where multiple unicast streaming sessions are run in parallel and share the same frequency band. Each streaming session is formed by the sequential transmission of video "chunks," such that each chunk arrives into the corresponding user playback buffer within its playback deadline. We formulate the problem as a Network Utility Maximization (NUM) where the objective is to fairly maximize users' video streaming Quality of Experience (QoE) and then derive an iterative con…
We consider wireless device-to-device (D2D) caching networks with single-hop transmissions. Previous work has demonstrated that caching and coded multicasting can significantly increase per user throughput. However, the state-of-the-art coded caching schemes for D2D networks are generally impractical because content files are partitioned into an exponential number of packets with respect to the number of users if both library and memory sizes are fixed. In this paper, we present two combinatorial approaches of D2D coded caching network design with reduced packetizations and desired throughput …
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 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…
The problem of characterizing the optimal rate achievable with analog network coding (ANC) for a unicast communication over general wireless relay networks is computationally hard. A relay node performing ANC scales and forwards its input signals. The source-destination channel in such communication scenarios is, in general, an intersymbol interference (ISI) channel which leads to the single-letter characterization of the optimal rate in terms of an optimization problem with nonconvex, non closed-form objective function and non-convex constraints. For a special class of such networks, called l…
Consider a transmission scheme with a single transmitter and multiple receivers over a faulty broadcast channel. For each receiver, the transmitter has a unique infinite stream of packets, and its goal is to deliver them at the highest throughput possible. While such multiple-unicast models are unsolved in general, several network coding based schemes were suggested. In such schemes, the transmitter can either send an uncoded packet, or a coded packet which is a function of a few packets. The packets sent can be received by the designated receiver (with some probability) or heard and stored by…
In this paper, we study capacity scaling laws of the deterministic dissemination (DD) in random wireless networks under the generalized physical model (GphyM). This is truly not a new topic. Our motivation to readdress this issue is two-fold: Firstly, we aim to propose a more general result to unify the network capacity for general homogeneous random models by investigating the impacts of different parameters of the system on the network capacity. Secondly, we target to close the open gaps between the upper and the lower bounds on the network capacity in the literature. The generality of this …
Next generation of cellular networks deploying wireless distributed femtocaching infrastructure proposed by Golrezaei et. al. are studied. By taking advantage of multihop communications in each cell, the number of required femtocaching helpers is significantly reduced. This reduction of femtocaches is achieved by using the underutilized storage and communication capabilities in the User Terminals (UTs), which results in reducing the deployment costs of distributed femtocaches. A multihop index coding technique is proposed to code the cached contents in helpers to achieve order optimal capacity…
As wireless video transmission is the fastest-growing form of data traffic, methods for spectrally efficient video on-demand wireless streaming are essential to service providers and users alike. A key property of video on-demand is the asynchronous content reuse, such that a few dominant videos account for a large part of the traffic, but are viewed by users at different times. Caching of content on devices in conjunction with D2D communications allows to exploit this property, and provide a network throughput that is significantly in excess of both the conventional approach of unicasting fro…
Multicast transmission, wherein the same packet must be delivered to multiple receivers, is an important aspect of sensor and tactical networks and has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include (i) identical packets must be delivered successfully to several nodes, (ii) outage at any receiver requires the packet to be retransmitted at least to that receiver, and (iii) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. A first contribution of this paper is the develo…
We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finite-field networks, where we obtain a general outer-bound expression in terms of ranks of the transfer matrices. We then show that, even though our outer bound is for deterministic networks, a recent result relating the capacity of AWGN KxKxK networks and the capacity of a d…
We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average r…
