Achievable data rates in wireless systems rely heavily on the available channel state information (CSI) throughout the network. However, feedback links, which provide this information, are scarce, unreliable, and subject to security threats. In this work, we study the impact of having intermittent feedback links on the capacity region of the canonical two-user erasure broadcast channels. In our model, at any time instant, each receiver broadcasts its CSI, and at any other node, this information either becomes available with unit delay or gets erased. For this setting, we develop a new set of outer bounds to capture the intermittent nature of the feedback links. These outer bounds depend on the probability that the CSI from both receivers are erased at the transmitter. In particular, if at any time, the CSI from at least one of the two receivers is available at the other two nodes, then the outer-bounds match the capacity with global delayed CSI. We also provide capacity-achieving transmission strategies under certain scenarios, and we establish a connection between this problem and Blind Index Coding with feedback.
We derive a new outer bound on the capacity region of broadcast traffic in multiple input broadcast packet erasure channels with feedback, and extend this outer bound to packet erasure relay networks with feedback. We show the tightness of the outer bound for various classes of networks. An important engineering implication of this work is that for network coding schemes for parallel broadcast channels, the `xor' packets should be sent over correlated broadcast subchannels.
We study the effects of introducing a feedback channel in the two-receiver erasure source-broadcast problem in which a binary equiprobable source is to be sent over an erasure broadcast channel to two receivers subject to erasure distortion constraints. The receivers each require a certain fraction of a source sequence, and we are interested in the minimum latency, or transmission time, required to serve them all. We first show that for a two-user broadcast channel, a point-to-point outer bound can always be achieved. We further show that the point-to-point outer bound can also be achieved if …
We study a content delivery problem in a K-user erasure broadcast channel such that a content providing server wishes to deliver requested files to users, each equipped with a cache of a finite memory. Assuming that the transmitter has state feedback and user caches can be filled during off-peak hours reliably by the decentralized content placement, we characterize the achievable rate region as a function of the memory sizes and the erasure probabilities. The proposed delivery scheme, based on the broadcasting scheme by Wang and Gatzianas et al., exploits the receiver side information establis…
We consider a cache-aided communications system in which a transmitter communicates with many receivers over an erasure broadcast channel. The system serves as a basic model for communicating on-demand content during periods of high network congestion, where some content can be pre-placed in local caches near the receivers. We formulate the cache-aided communications problem as a joint cache-channel coding problem, and characterise some information-theoretic tradeoffs between reliable communications rates and cache sizes. We show that if the receivers experience different channel qualities, th…
Jolfaei et al. used feedback to create transmit signals that are simultaneously useful for multiple users in a broadcast channel. Later, Georgiadis and Tassiulas studied erasure broadcast channels with feedback, and presented the capacity region under certain assumptions. These results provided the fundamental ideas used in communication protocols for networks with delayed channel state information. However, to the best of our knowledge, the capacity region of erasure broadcast channels with feedback and with a common message for both receivers has never been presented. This latter problem sho…
Error and erasure exponents for the broadcast channel with degraded message sets are analyzed. The focus of our error probability analysis is on the main receiver where, nominally, both messages are to be decoded. A two-step decoding algorithm is proposed and analyzed. This receiver first attempts to decode both messages, failing which, it attempts to decode only the message representing the coarser information, i.e., the cloud center. This algorithm reflects the intuition that we should decode both messages only if we have confidence in the estimates; otherwise one should only decode the coar…
We consider a cache-enabled K-user broadcast erasure packet channel in which a server with a library of N files wishes to deliver a requested file to each user who is equipped with a cache of a finite memory M. Assuming that the transmitter has state feedback and user caches can be filled during off-peak hours reliably by decentralized cache placement, we characterize the optimal rate region as a function of the memory size, the erasure probability. The proposed delivery scheme, based on the scheme proposed by Gatzianas et al., exploits the receiver side information established during the plac…
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)). The main results of this paper are: (i) The capacity region for …
Consider the asymmetric broadcast channel with a random superposition codebook, which may be comprised of constant composition or \iid codewords. By applying Forney's optimal decoder for individual messages and the message pair for the receiver that decodes both messages, exact (ensemble-tight) error and erasure exponents are derived. It is shown that the optimal decoder designed to decode the pair of messages achieves the optimal trade-off between the total and undetected exponents associated with the optimal decoder for the private message. Convex optimization-based procedures to evaluate th…
We formulate and study a cryptographic problem relevant to wireless: a sender, Alice, wants to transmit private messages to two receivers, Bob and Calvin, using unreliable wireless broadcast transmissions and short public feedback from Bob and Calvin. We ask, at what rates can we broadcast the private messages if we also provide (information-theoretic) unconditional security guarantees that Bob and Calvin do not learn each-other's message? We characterize the largest transmission rates to the two receivers, for any protocol that provides unconditional security guarantees. We design a protocol …
Based on the erasure channel FEC model as defined in multimedia wireless broadcast standards, we illustrate how doping mechanisms included in the design of erasure coding and decoding may improve the scalability of the packet throughput, decrease overall latency and potentially differentiate among classes of multimedia subscribers regardless of their signal quality. We describe decoding mechanisms that allow for linear complexity and give complexity bounds when feedback is available. We show that elaborate coding schemes which include pre-coding stages are inferior to simple Ideal Soliton base…
One to Many communications are expected to be among the killer applications for the currently discussed 5G standard. The usage of coding mechanisms is impacting broadcasting standard quality, as coding is involved at several levels of the stack, and more specifically at the application layer where Rateless, LDPC, Reed Solomon codes and network coding schemes have been extensively studied, optimized and standardized in the past. Beyond reusing, extending or adapting existing application layer packet coding mechanisms based on previous schemes and designed for the foregoing LTE or other broadcas…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Outer and inner bounds on the capacity region are derived when the channel state is strictly causally known at the transmitter. The bounds are both formulated in terms of feasibility problems and they are matching in all but one of the constraints. The results are extended to feedback with larger delay. Numerical results show that the bounds are close in many examples and the gains offered through feedback can be quite large. T…
A cache-aided broadcast network is studied, in which a server delivers contents to a group of receivers over a packet erasure broadcast channel (BC). The receivers are divided into two sets with regards to their channel qualities: the weak and strong receivers, where all the weak receivers have statistically worse channel qualities than all the strong receivers. The weak receivers, in order to compensate for the high erasure probability they encounter over the channel, are equipped with cache memories of equal size, while the receivers in the strong set have no caches. Data can be pre-delivere…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of this hidden Markov chain are available at the transmitter through feedback. Matching outer and inner bounds are derived and the capacity region is determined. The capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. …
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. The capacity region of the 1-to-K PEC with COF was previously known only for the case K=2. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automa…
In this paper we describe a network coding scheme for the Broadcast Erasure Channel with multiple unicast stochastic flows, in the case of a single source transmitting packets to $N$ users, where per-slot feedback is fed back to the transmitter in the form of ACK/NACK messages. This scheme performs only binary (XOR) operations and involves a network of queues, along with special rules for coding and moving packets among the queues, that ensure instantaneous decodability. The system under consideration belongs to a class of networks whose stability properties have been analyzed in earlier work,…
In this paper, we investigate the impact of coding on the Age of Information (AoI) in a two-user broadcast symbol erasure channel with feedback. We assume each update consists of $K$ symbols and the source is able to broadcast one symbol in each time slot. Due to random channel noise, the intended symbol at each user will be erased according to an independent and identically distributed (i.i.d.) Bernoulli process. A user is able to successfully decode an update if it accumulates sufficient information and successfully decodes the $K$ symbols of the update. Assuming prefect feedback information…
We consider the N-user broadcast erasure channel with public feedback and side information. Before the beginning of transmission, each receiver knows a function of the messages of some of the other receivers. This situation arises naturally in wireless and in particular cognitive networks where a node may overhear transmitted messages destined to other nodes before transmission over a given broadcast channel begins. We provide an upper bound to the capacity region of this system. Furthermore, when the side information is linear, we show that the bound is tight for the case of two-user broadcas…
In this paper, the capacity region of the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter is investigated. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper derives capacity inner and outer bounds for the LPE-BC with COF for the case of two users and any number of layers. The inner bounds generalize past results for the two-user erasure BC, which is a special c…
Consider n nodes communicating over an unreliable broadcast channel. Each node has a single packet that needs to be communicated to all other nodes. Time is slotted, and a time slot is long enough for each node to broadcast one packet. Each broadcast reaches a random subset of nodes. The objective is to minimise the time until all nodes have received all packets. We study two schemes, (i) random relaying, and (ii) random linear network coding, and analyse their performance in an asymptotic regime in which n tends to infinity. Simulation results for a wide range of n are also presented.
We study the effects of introducing a feedback channel in the erasure source-broadcast problem for the case of three receivers. In our problem formulation, we wish to transmit a binary source to three users over the erasure broadcast channel when causal feedback is universally available to the transmitter and all three receivers. Each receiver requires a certain fraction of the source sequence, and we are interested in the minimum latency, or transmission time, required to serve them all. We propose a queue-based hybrid digital-analog coding scheme that achieves optimal performance for the dur…
We study noisy broadcast networks with local cache memories at the receivers, where the transmitter can pre-store information even before learning the receivers' requests. We mostly focus on packet-erasure broadcast networks with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. We present lower and upper bounds on the capacity-memory tradeoff of this network. The lower bound is achieved by a new joint cache-channel coding idea and significa…
In this paper, we characterize the throughput of a broadcast network with n receivers using rateless codes with block size K. We assume that the underlying channel is a Markov modulated erasure channel that is i.i.d. across users, but can be correlated in time. We characterize the system throughput asymptotically in n. Specifically, we explicitly show how the throughput behaves for different values of the coding block size K as a function of n, as n approaches infinity. For finite values of K and n, under the more restrictive assumption of Gilbert-Elliott channels, we are able to provide a low…
We consider broadcasting a block of packets to multiple wireless receivers under random packet erasures using instantly decodable network coding (IDNC). The sender first broadcasts each packet uncoded once, then generates coded packets according to receivers' feedback about their missing packets. We focus on strict IDNC (S-IDNC), where each coded packet includes at most one missing packet of every receiver. But we will also compare it with general IDNC (G-IDNC), where this condition is relaxed. We characterize two fundamental performance limits of S-IDNC: 1) the number of transmissions to comp…
We consider a transmitter broadcasting random linear combinations (over a field of size $d$) formed from a block of $c$ packets to a collection of $n$ receivers, where the channels between the transmitter and each receiver are independent erasure channels with reception probabilities $\mathbf{q} = (q_1,\ldots,q_n)$. We establish several properties of the random delay until all $n$ receivers have recovered all $c$ packets, denoted $Y_{n:n}^{(c)}$. First, we provide lower and upper bounds, exact expressions, and a recurrence for the moments of $Y_{n:n}^{(c)}$. Second, we study the delay per pack…
We consider a 1-to-$K$ communication scenario, where a source transmits private messages to $K$ receivers through a broadcast erasure channel, and the receivers feed back strictly causally and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret - in the information theoretical sense - from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-$K$ communication scenario without the requirement of security is known. As a…
We study the content delivery problem between a transmitter and two receivers through erasure links, when each receiver has access to some random side-information about the files requested by the other user. The random side-information is cached at the receiver via the decentralized content placement. The distributed nature of receiving terminals may also make the erasure state of two links and indexes of the cached bits not perfectly known at the transmitter. We thus investigate the capacity gain due to various levels of availability of channel state and cache index information at the transmi…
This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with Kw weak receivers and Ks strong receivers, where weak receivers, respectively strong receivers, have same erasure probabilities and cache sizes. The lower bounds are achieved by schemes that meticulously combine joint cache-channel coding with wiretap coding and key-aided one-time pads. The presented upper bound holds more generally for arbitrary degraded BCs and arbitrary cache sizes. When only weak receivers have cache memories, upper and lower bounds coincide fo…
This paper focuses on the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper provides a comparative overview of this channel model along the following lines: First, inner and outer bounds to the capacity region (set of achievable rates with backlogged arrivals) are presented: a) a new outer bound based on the idea…
We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the set $\mathcal{A}$ of the same cardinality. Instead of attempting to characterize the capacity region of general broadcast channels, we only consider the structure of the capacity region that any broadcast channel should bear. The concept of latent capacity region is useful in capturing these underlying constraints, and we provide a complete characterization …
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 oute…
This work considers the smart repeater network where a single source $s$ wants to send two independent packet streams to destinations $\{d_1,d_2\}$ with the help of relay $r$. The transmission from $s$ or $r$ is modeled by packet erasure channels: For each time slot, a packet transmitted by $s$ may be received, with some probabilities, by a random subset of $\{d_1,d_2,r\}$; and those transmitted by $r$ will be received by a random subset of $\{d_1,d_2\}$. Interference is avoided by allowing at most one of $\{s,r\}$ to transmit in each time slot. One example of this model is any cellular networ…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Two scenarios are considered: (i) when the transmitter has causal knowledge of the channel state (i.e., the state is visible), and (ii) when the channel state is unknown at the transmitter, but observations of it are available at the transmitter through feedback (i.e., the state is hidden). In both scenarios, matching outer and inner bounds on the rates of communication are derived and the capacity region is determined. It is s…
In the present paper, we propose a broadcast ARQ protocol based on the concept of index coding. In the proposed scenario, a server wishes to transmit a finite sequence of packets to multiple receivers via a broadcast channel with packet erasures until all of the receivers successfully receive all of the packets. In the retransmission phase, the server produces a coded packet as a retransmitted packet based on the side-information sent from the receivers via feedback channels. A notable feature of the proposed protocol is that the decoding process at the receiver side has low decoding complexit…
We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).
A status updating system is considered in which multiple data sources generate packets to be delivered to a destination through a shared energy harvesting sensor. Only one source's data, when available, can be transmitted by the sensor at a time, subject to energy availability. Transmissions are prune to erasures, and each successful transmission constitutes a status update for its corresponding source at the destination. The goal is to schedule source transmissions such that the collective long-term average age-of-information (AoI) is minimized. AoI is defined as the time elapsed since the la…
This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform the source node whether a packet is received correctly via feedback channels. In order to minimize the number of packet transmissions until all users have received all packets successfully, it is necessary that a data packet, if successfully received by a user, can increase the dimension of the vector space spanned by the encoding vectors he or she has receive…
The degrees-of-freedom (DoF) of the multi-antenna three-way channel (3WC) with an intermittent node is studied. Special attention is given to the impact of adaptation. A nonadaptive transmission scheme based on interference alignment, zero-forcing, and erasure-channel treatment is proposed, and its corresponding DoF region is derived. Then, it is shown that this scheme achieves the sum-DoF of the intermittent channel, in addition to the DoF region of the nonintermittent one. Thus, adaptation is not necessary from those perspectives. To the contrary, it is shown that adaptation is necessary for…
Two enablers of the 5th Generation (5G) of mobile communication systems are the high data rates achievable with millimeter-wave radio signals and the cloudification of the network's mobile edge, made possible also by Multi-access Edge Computing (MEC). In 5G networks, user devices may exploit the high capacity of their mobile connection and the computing capabilities of the edge cloud to offload computational tasks to MEC servers, which run applications on devices' behalf. This paper investigates new methods to perform power- and latency-constrained offloading. First, aiming to minimize user de…
In this paper, a lower bound on the capacity of wireless ad hoc erasure networks is derived in closed form in the canonical case where $n$ nodes are uniformly and independently distributed in the unit area square. The bound holds almost surely and is asymptotically tight. We assume all nodes have fixed transmit power and hence two nodes should be within a specified distance $r_n$ of each other to overcome noise. In this context, interference determines outages, so we model each transmitter-receiver pair as an erasure channel with a broadcast constraint, i.e. each node can transmit only one sig…
In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a $b$-bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eav…
Recent research indicates that packet transmission employing random linear network coding can be regarded as transmitting subspaces over a linear operator channel (LOC). In this paper we propose the framework of linear operator broadcast channels (LOBCs) to model packet broadcasting over LOCs, and we do initial work on the capacity region of constant-dimension multiplicative LOBCs(CMLOBCs), a generalization of broadcast erasure channels. Two fundamental problems regarding CMLOBCs are addressed-finding necessary and sufficient conditions for degradation and deciding whether time sharing suffice…
Streaming erasure codes encode a source stream to guarantee that each source packet is recovered within a fixed delay at the receiver over a burst-erasure channel. This paper introduces diversity embedded streaming erasure codes (DE-SCo), that provide a flexible tradeoff between the channel quality and receiver delay. When the channel conditions are good, the source stream is recovered with a low delay, whereas when the channel conditions are poor the source stream is still recovered, albeit with a larger delay. Information theoretic analysis of the underlying burst-erasure broadcast channel r…
Despite considerable progress on the information-theoretic broadcast channel, the capacity region of fading broadcast channels with channel state known at the receivers but unknown at the transmitter remains unresolved. We address this subject by introducing a layered erasure broadcast channel model in which each component channel has a state that specifies the received signal levels in an instance of a deterministic binary expansion channel. We find the capacity region of this class of broadcast channels. The capacity achieving strategy assigns each signal level to the user that derives the m…
The state-dependent $K$-user memoryless Broadcast Channel~(BC) with state feedback is investigated. We propose a novel transmission scheme and derive its corresponding achievable rate region, which, compared to some general schemes that deal with feedback, has the advantage of being relatively simple and thus is easy to evaluate. In particular, it is shown that the capacity region of the symmetric erasure BC with an arbitrary input alphabet size is achievable with the proposed scheme. For the fading Gaussian BC, we derive a symmetric achievable rate as a function of the signal-to-noise ratio~(…
The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and i…
Streaming erasure codes guarantee that each source packet is recovered within a fixed delay at the receiver over a burst-erasure channel. This paper introduces a new class of streaming codes: Diversity Embedded Streaming Erasure Codes (DE-SCo), that provide a flexible tradeoff between the channel quality and receiver delay. When the channel conditions are good, the source stream is recovered with a low delay, whereas when the channel conditions are poor the source stream is still recovered, albeit with a larger delay. Information theoretic analysis of the underlying burst-erasure broadcast cha…
We study the following private data transfer problem: Alice has a database of files. Bob and Cathy want to access a file each from this database (which may or may not be the same file), but each of them wants to ensure that their choices of file do not get revealed even if Alice colludes with the other user. Alice, on the other hand, wants to make sure that each of Bob and Cathy does not learn any more information from the database than the files they demand (the identities of which will be unknown to her). Moreover, they should not learn any information about the other files even if they coll…
We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the nofeedback capacity region for a large class of channels, including the class of \emph{strictly essentially less-noisy BCs} that we introduce in this article. Examples of strictly essentially less-noisy BCs are the binary symmetric BC (BSBC) or the binary erasure BC (BEBC) with unequal cross-over or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously k…
This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a Multi-Guess Algorithm extended from the Guess Algorithm and a new algorithm -- the In-place Algorithm. The Multi-Guess Algorithm can push the limit to break the stopping sets. However, the performance of the Guess and the Multi-Guess Algorithm depend on the parity-check matrix of the code. Simulations show that we can decrease the frame error rate by several …
We study random linear network coding for broadcasting in time division duplexing channels. We assume a packet erasure channel with nodes that cannot transmit and receive information simultaneously. The sender transmits coded data packets back-to-back before stopping to wait for the receivers to acknowledge the number of degrees of freedom, if any, that are required to decode correctly the information. We study the mean time to complete the transmission of a block of packets to all receivers. We also present a bound on the number of stops to wait for acknowledgement in order to complete transm…
Network Oblivious Transfer via Noisy Broadcast Channels
Institute for Communications Technology, Technische Universität Braunschweig（不伦瑞克工业大学通信技术研究所）；Technische Universität München（慕尼黑工业大学）；Munich Quantum Valley (MQV)（慕尼黑量子谷）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
We study the capacity limits of real-time streaming over burst-erasure channels. A stream of source packets must be sequentially encoded and the resulting channel packets must be transmitted over a two-receiver burst-erasure broadcast channel. The source packets must be sequentially reconstructed at each receiver with a possibly different reconstruction deadline. We study the associated capacity as a function of burst-lengths and delays at the two receivers. We establish that the operation of the system can be divided into two main regimes: a low-delay regime and a large-delay regime. We fully…
