Erasure Broadcast Channel Research Articles

Identification over quantum broadcast channels

Identification over quantum broadcast channels is considered. As opposed to the information transmission task, the decoder only identifies whether a message of his choosing was sent or not. This relaxation allows for a double-exponential code size. An achievable identification region is derived for a quantum broadcast channel, and a full characterization for the class of classical-quantum broadcast channels. The identification capacity region of the single-mode pure-loss bosonic broadcast channel is obtained as a consequence. Furthermore, the results are demonstrated for the quantum erasure broadcast channel, where our region is suboptimal, but improves on the best previously known bounds.

Low Latency Allcast Over Broadcast Erasure Channels

Consider <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> tends to infinity. Simulation results for a wide range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> are also presented.

Content Delivery Over Broadcast Erasure Channels With Distributed Random Cache

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 transmitter. More precisely, we cover a wide range of settings from global delayed channel state knowledge and a non-blind transmitter (i.e. one that knows the exact cache index information at each receiver) all the way to no channel state information and a blind transmitter (i.e. one that only statistically knows cache index information at the receivers). We derive new inner and outer bounds for the problem under various settings and provide the conditions under which the two match and the capacity region is characterized. Surprisingly, for some interesting cases the capacity regions are the same even with single-user channel state or single-user cache index information at the transmitter.

Erasure Broadcast Channels With Intermittent Feedback

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.

Energy-Aware Scheduling for Broadcast Erasure Channels With Two Energy Harvesting Receivers

A feedback-based coding algorithm is studied for broadcast packet erasure channels (BPECs) with energy harvesting receivers. A probabilistic algorithm is outlined, which is able to achieve the capacity region of two-user BPECs. The probabilistic algorithm is carefully studied from the optimization perspective. In this paper, we take into account the energy levels of receivers. Two new feedback schemes are proposed to reduce the energy consumption of receivers and we explain the advantage of each feedback scheme. We formulate the problem of maximizing the minimum weighted throughput of receivers for each feedback scheme. After several convexifications, we make the formulated optimizations tractable and propose an algorithm to solve the problems globally without compromising optimality. Once optimization problems are solved, we propose an energy-aware scheduling for packet broadcasting. Finally, a packet header design is proposed to enable utilization of the energy-aware scheduling. Simulation results verify that to achieve the optimal throughput, network-coding is necessary.

Benefits of Cache Assignment on Degraded Broadcast Channels

Degraded K-user broadcast channels (BCs) are studied when the receivers are facilitated with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate of reliable communication over the BC as a function of the receivers’ cache sizes, and the bounds are shown to match for interesting special cases. The lower bounds are achieved by two new coding schemes that benefit from nonuniform cache assignments . Lower and upper bounds are also established on the global capacity-memory tradeoff, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers’ cache sizes subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, where the thresholds depend on the BC statistics. For small cache memories, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows by the total cache memory budget divided by the number of files in the system. In other words, a perfect global caching gain is achievable in this regime and the performance corresponds to a system where all the cache contents in the network are available to all receivers. For large cache memories, it is optimal to assign a positive cache memory to every receiver, such that the weaker receivers are assigned larger cache memories compared to the stronger receivers. In this regime, the growth rate of the global capacity-memory tradeoff is further divided by the number of users, which corresponds to a local caching gain. It is observed numerically that a uniform assignment of the total cache memory is suboptimal in all regimes, unless the BC is completely symmetric. For erasure BCs, this claim is proved analytically in the regime of small cache sizes.

Secrecy Capacity-Memory Tradeoff of Erasure Broadcast Channels

This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with ${\mathsf{K}}_{w} $ weak receivers and ${\mathsf {K}}_{s} $ strong receivers, where weak receivers and strong receivers have the same erasure probabilities and cache sizes, respectively. The lower bounds are achieved by the 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 for small and large cache memories, thus providing the exact secrecy capacity-memory tradeoff for this setup. The derived bounds further allow us to conclude that the secrecy capacity is positive even when the eavesdropper is stronger than all the legitimate receivers with cache memories. Moreover, they show that the secrecy capacity-memory tradeoff can be significantly smaller than its non-secure counterpart, but it grows much faster when cache memories are small. This paper also presents a lower bound on the global secrecy capacity-memory tradeoff where one is allowed to optimize the cache assignment subject to a total cache budget. It is close to the best known lower bound without secrecy constraint. For small total cache budget, the global secrecy capacity-memory tradeoff is achieved by assigning all the available cache memory uniformly over all the receivers if the eavesdropper is stronger than all the legitimate receivers, and it is achieved by assigning the cache memory uniformly only over the weak receivers if the eavesdropper is weaker than the strong receivers.

Gaussian Broadcast Channels With Intermittent Connectivity and Hybrid State Information at the Transmitter

In wireless networks, the link connectivity may be intermittent due to shadowing, burstiness of data arrival, or uncoordinated resource allocation. In this paper, we model the intermittence of links as Bernoulli distributed random channel states, termed intermittence channel states , and study the impact of the corresponding channel state information at the transmitter (CSIT) in a two-user Gaussian broadcast channel (BC). Moreover, due to the heterogeneous timeliness of intermittence channel states, the CSIT considered in this paper is hybrid . More specifically, the CSIT of each link can be perfectly (causally or non-causally) available, delayed, or not available. When the links are connected, we adopt a general setting that the received signal-to-noise ratios can be different. Our contribution is the characterization of the capacity regions of intermittent Gaussian BC to within bounded gaps for all combinations of hybrid CSIT, except for scenario DN (delayed CSIT of receiver 1, no CSIT of receiver 2). For scenario DN, we propose an opportunistic physical layer network coding scheme that achieves a strictly larger degree-of-freedom (DoF) region than the no-CSIT DoF region. As a corollary, single-user CSIT is able to increase the sum DoF for intermittent Gaussian BC (also the capacity region for the erasure BC, as a by-product). This result is in sharp contrast to the recent negative result by Davoodi and Jafar, where it is shown that for fast-fading multiple-input single-output BC with continuous channel states, single-user CSIT does not help at all in terms of sum DoF.

Capacity Regions of Two-Receiver Broadcast Erasure Channels With Feedback and Memory

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: 1) when the transmitter has causal knowledge of the channel state (i.e., the state is visible) and 2) 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 shown that similar results carry over to channels with memory and delayed feedback and memoryless compound channels with feedback. When the state is visible, the capacity region has a single-letter characterization and is in terms of a linear program. Two optimal coding schemes are devised that use feedback to keep track of the sent/received packets via a network of queues: a probabilistic scheme and a deterministic backpressure-like algorithm. The former bases its decisions solely on the past channel state information and the latter follows a max-weight queue-based policy. The performance of the algorithms is analyzed using the frameworks of rate stability in networks of queues, max-flow min-cut duality in networks, and finite-horizon Lyapunov drift analysis. When the state is hidden, 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. The first algorithm is a probabilistic coding scheme that bases its decisions on the past $L$ acknowledgments and its achievable rate region approaches the capacity region exponentially fast in $L$ . The second algorithm is a backpressure-like algorithm that performs optimally in the long run.

Reliable and enhanced cooperative cross‐layer medium access control scheme for vehicular communication

In an unreliable cluster-based, broadcast vehicular network setting, the authors investigate the transmission reliability and throughput performance of random network coding (RNC) as a function of the percentage of packet generation rate and transmit power-to-noise ratio. In this study, a novel scheme called reliable and efficient cooperative cross-layer medium access control (RECMAC) is proposed. The proposed scheme consists of a source vehicle broadcasting packets to a set of receivers (i.e. one-to-many) over independent broadcast erasure channels. The source vehicle performs RNC on N packets and broadcasts the encoded message to a set of receivers. In each hop, several vehicles form a cluster and cooperatively transmit the encoded or re-encoded packet. The combination of the RNC, cluster based, and cooperative communications enables RECMAC to optimally minimise data redundancy, which means less overhead, and improve reliability as opposed to coding-based solutions. Theoretical analyses and simulation results show that under the same conditions RECMAC scheme can achieve improved performance in terms of transmission reliability and throughput.

Cache-Aided Content Delivery Over Erasure Broadcast Channels

A cache-aided broadcast network is studied, in which a server delivers contents to a group of receivers over a packet erasure broadcast channel. The receivers are divided into two sets with regards to their channel qualities: the weak and the 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-delivered to the weak receivers’ caches over the off-peak traffic period before the receivers reveal their demands. Allowing arbitrary erasure probabilities for the weak and strong receivers, a joint caching and channel coding scheme, which divides each file into several subfiles, and applies a different caching and delivery scheme for each subfile, is proposed. It is shown that all the receivers, even those without any cache memories, benefit from the presence of caches across the network. An information theoretic tradeoff between the cache size and the achievable rate is formulated. It is shown that the proposed scheme improves upon the state-of-the-art in terms of the achievable tradeoff.

A Novel Transmission Scheme for the $K$ -User Broadcast Channel With Delayed CSIT

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 with some general schemes that deal with feedback, has the advantage of being relatively simple and thus is easy to evaluate. In particular, we show that the proposed scheme achieves the capacity region of the symmetric erasure BC with an arbitrary input alphabet size. For the fading Gaussian BC, numerical results show that the proposed scheme outperforms existing schemes in terms of symmetric rate. Our analysis also proves its optimality at high signal-to-noise ratio, in terms of degrees of freedom.

Decoding Delay Performance of Random Linear Network Coding for Broadcast

Characterization of the delay profile of systems employing random linear network coding is important for the reliable provision of broadcast services. Previous studies focused on network coding over large finite fields or developed Markov chains to model the delay distribution but did not look at the effect of transmission deadlines on the delay. In this work, we consider generations of source packets that are encoded and transmitted over the erasure broadcast channel. The transmission of packets associated to a generation is taken to be deadline-constrained, that is, the transmitter drops a generation and proceeds to the next one when a predetermined deadline expires. Closed-form expressions for the average number of required packet transmissions per generation are obtained in terms of the generation size, the field size, the erasure probability and the deadline choice. An upper bound on the average decoding delay, which is tighter than previous bounds found in the literature, is also derived. Analysis shows that the proposed framework can be used to fine-tune the system parameters and ascertain that neither insufficient nor excessive amounts of packets are sent over the broadcast channel.

Blind Index Coding

We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classical index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in each user’s side information but not its content. This problem can arise naturally in caching and wireless networks. In order to blindly exploit side information in the BIC problem, we develop a hybrid coding scheme that XORs uncoded bits of a subset of messages with random combinations of bits from other messages. This scheme allows us to strike the right balance between maximizing the transmission rate to each user and minimizing the interference leakage to others. We also develop a general outer bound, which relies on a strong data processing inequality to effectively capture the senders uncertainty about the users’ side information. Additionally, we consider the case where communication takes place over a shared wireless medium, modeled by an erasure broadcast channel, and show that surprisingly, combining repetition coding with hybrid coding improves the achievable rate region and outperforms alternative strategies of coping with channel erasure and while blindly exploiting side information.

Delay on Broadcast Erasure Channels Under Random Linear Combinations

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 packet $Y_{n:n}^{(c)}/c$ as a function of $c$, including the asymptotic delay (as $c \to \infty$), and monotonicity (in $c$) properties of the delay per packet. Third, we employ extreme value theory to investigate $Y_{n:n}^{(c)}$ as a function of $n$ (as $n \to \infty$). Several results are new, some results are extensions of existing results, and some results are proofs of known results using new (probabilistic) proof techniques.

Broadcast Erasure Channel with Feedback and Message Side Information, and Related Index Coding Results

We consider the $N$ -receiver broadcast erasure channel with feedback and message side information at the receivers prior to beginning of transmission. Specifically, the transmitter must deliver different, independent messages to each of the receivers, and each receiver knows a function of these messages before transmission begins. This situation can arise in multi-hop wireless networks, where a receiver may overhear transmissions consisting of possibly encoded combinations of messages (e.g., encoded using a network coding technique) prior to beginning of transmission over a given broadcast channel. We provide an outer bound to the capacity region of this system. For the case, where each message consists of a number of symbols taking values in a finite field and each receiver knows linear combinations of these symbols, the outer bound is given in terms of ranks of matrices expressing the linear combinations. For the latter case and when $N=2$ , the outer bound is tight under mild conditions on the limiting behavior of the ranks of matrices expressing the side information. We provide a capacity achieving code for this case. The special case, where each receiver either knows the entire message of another receiver or has no information about it, constitutes a generalization of the index coding problem that incorporates channel erasures. For this instance, and when there are no channel errors, we show that the outer bound reduces to the known maximum weighted acyclic induced subgraph bound.

Content Delivery in Erasure Broadcast Channels With Cache and Feedback

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 size. 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 for some special cases. The proposed delivery scheme, based on the broadcasting scheme by Wang and Gatzianas et al., exploits the receiver side information established during the placement phase. Our results can be extended to the centralized content placement as well as multi-antenna broadcast channels with state feedback.

Linear Network Coding for Erasure Broadcast Channel With Feedback: Complexity and Algorithms

This paper investigates the linear network coding problem for erasure broadcast channel with user feedback. An innovative linear network code is shown to be uniformly optimal for the system. In general, determining the existence of innovative packets is proved to be NP-complete. When the finite field size is larger than the number of users, innovative packets always exist and the problem of finding an innovative encoding vector with smallest Hamming weight is considered. The corresponding decision problem is shown to be NP-complete. Optimal and approximate network coding algorithms for maximizing the sparsity of encoding vectors are designed.

Coding Schemes With Rate-Limited Feedback That Improve Over the No Feedback Capacity for a Large Class of Broadcast Channels

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 no feedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this paper. Examples of strictly essentially less-noisy BCs are the binary symmetric BC or the binary erasure BC with unequal crossover or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feedback quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme, the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme also applies to memoryless BCs without feedback but with strictly causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.

Stable XOR-Based Policies for the Broadcast Erasure Channel With Feedback

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, which is used to provide a stabilizing policy employing the currently proposed coding scheme. Finally, we show the optimality of the proposed policy for $N=4$ and i.i.d. erasure events, in the sense that the policy's stability region matches a derived outer bound (which coincides with the system's information-theoretic capacity region), even when a restricted set of coding rules is used.