A sender holds a word x consisting of n blocks x_i, each of t bits, and wishes to broadcast a codeword to m receivers, R_1,...,R_m. Each receiver R_i is interested in one block, and has prior side information consisting of some subset of the other blocks. Let β_t be the minimum number of bits that has to be transmitted when each block is of length t, and let βbe the limit β= \lim_{t \to \infty} β_t/t. In words, βis the average communication cost per bit in each block (for long blocks). Finding the coding rate β, for such an informed broadcast setting, generalizes several coding theoretic parameters related to Informed Source Coding on Demand, Index Coding and Network Coding.
In this work we show that usage of large data blocks may strictly improve upon the trivial encoding which treats each bit in the block independently. To this end, we provide general bounds on β_t, and prove that for any constant C there is an explicit broadcast setting in which β= 2 but β_1 > C. One of these examples answers a question of Lubetzky and Stav.
In addition, we provide examples with the following counterintuitive direct-sum phenomena. Consider a union of several mutually independent broadcast settings. The optimal code for the combined setting may yield a significant saving in communication over concatenating optimal encodings for the individual settings. This result also provides new non-linear coding schemes which improve upon the largest known gap between linear and non-linear Network Coding, thus improving the results of Dougherty, Freiling, and Zeger.
The proofs use ideas related to Witsenhausen's rate, OR graph products, colorings of Cayley graphs and the chromatic numbers of Kneser graphs.
We consider the secure communication problem for broadcasting of two encrypted sources. The sender wishes to broadcast two secret messages via two common key cryptosystems. We assume that the adversary can use the side-channel, where the side information on common keys can be obtained via the rate constraint noiseless channel. To solve this problem we formulate the post encryption coding system. On the information leakage on two secrete messages to the adversary, we provide an explicit sufficient condition to attain the exponential decay of this quantity for large block lengths of encrypted so…
In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process…
We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols it demands. We view the message symbols as elements from a finite field and assume that the number of symbol errors in the noisy side information is upper bounded by a known constant. This communication problem, which we refer to as 'broadcasting with noisy side information' (BNSI), has applications in the re-transmission phase of downlink networks. We derive…
In this paper, the fading broadcast channel with confidential messages is studied in the presence of statistical quality of service (QoS) constraints in the form of limitations on the buffer length. We employ the effective capacity formulation to measure the throughput of the confidential and common messages. We assume that the channel side information (CSI) is available at both the transmitter and the receivers. Assuming average power constraints at the transmitter side, we first define the effective secure throughput region, and prove that the throughput region is convex. Then, we obtain the…
We propose a base-station (BS) cooperation model for broadcasting a discrete memoryless source in a cellular or heterogeneous network. The model allows the receivers to use helper BSs to improve network performance, and it permits the receivers to have prior side information about the source. We establish the model's information-theoretic limits in two operational modes: In Mode 1, the helper BSs are given information about the channel codeword transmitted by the main BS, and in Mode 2 they are provided correlated side information about the source. Optimal codes for Mode 1 use \emph{hash-and-f…
Using a broadcast channel to transmit clients' data requests may impose privacy risks. In this paper, we address such privacy concerns in the index coding framework. We show how a malicious client can infer some information about the requests and side information of other clients by learning the encoding matrix used by the server. We propose an information-theoretic metric to measure the level of privacy and show how encoding matrices can be designed to achieve specific privacy guarantees. We then consider a special scenario for which we design a transmission scheme and derive the achieved lev…
We study the problem of coding over a general discrete memoryless broadcast channel controlled by random parameters. The parameters are available at the transmitter in a non-causal manner and are subject to a state masking constraint on the receivers. We derive inner and outer bounds on the achievable region and show that for the special case of Gaussian broadcast channel with private messages, these bounds are tight.
The problem of broadcasting a parallel Gaussian source over an additive white Gaussian noise broadcast channel under the mean-squared error distortion criterion is studied. A hybrid digital-analog coding strategy which combines source coding with side information, channel coding with side information, layered source coding, and superposition broadcast channel coding is presented. When specialized to the open problem of broadcasting a white Gaussian source over an additive white Gaussian noise broadcast channel with bandwidth mismatch which has been the subject of several previous investigation…
The downlink of a massive MIMO system is considered for the case in which the base station must concurrently serve two categories of terminals: one group to which imperfect instantaneous channel state information (CSI) is available, and one group to which no CSI is available. Motivating applications include broadcasting of public channels and control information in wireless networks. A new technique is developed and analyzed: joint beamforming and broadcasting (JBB), by which the base station beamforms to the group of terminals to which CSI is available, and broadcasts to the other group of te…
The problem of channel coding over the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) with additive independent Gaussian states is considered. The states are known in a noncausal manner to the encoder, and it wishes to minimize the amount of information that the receivers can learn from the channel outputs about the state sequence. The state leakage rate is measured as a normalized blockwise mutual information between the state sequence and the channel outputs' sequences. We employ a new version of a state-dependent extremal inequality and show that Gaussian input maximi…
We consider simultaneous wireless information and power transfer (SWIPT) in MIMO Broadcast networks where one energy harvesting (EH) user and one information decoding (ID) user share the same time and frequency resource. In contrast to previous SWIPT systems based on the information rate, this paper addresses the problem in terms of the weighted minimum mean squared error (WMMSE) criterion. First, we formulate the WMMSE-SWIPT problem which minimizes the weighted sum-MSE of the message signal arrived at the ID user, while satisfying the requirement on the energy that can be harvested from the s…
For the Internet-of-unmanned aerial vehicles (UAVs) some challenges in broadcasting and from new points of view are explored. In this paper, first, we investigate a single broadcast transceiver. From a control of noisy-channel viewpoint, we consider: (\textit{i}) Alice sends $\mathcal{X}$ to Bob as more \textcolor{black}{efficient} as possible while she wishes Bob not to get access to the private message $\mathcal{S}$ regarding the correlation between $\mathcal{S}$ and $\mathcal{X}$ $-$ i.e., Alice purposefully sends a \textit{turbulent-flow} of the information to Bob; and (\textit{ii}) where …
Broadcasting $K$ independent messages to multiple users where each user demands all the messages and has a subset of the messages as side information is studied. Recently, Natarajan, Hong, and Viterbo proposed a novel broadcasting strategy called lattice index coding which uses lattices constructed over some principal ideal domains (PIDs) for transmission and showed that this scheme provides uniform side information gains. In this paper, we generalize this strategy to general rings of algebraic integers of number fields which may not be PIDs. Upper and lower bounds on the side information gain…
Index coding employs coding across clients within the same broadcast domain. This typically assumes that all clients learn the coding matrix so that they can decode and retrieve their requested data. However, learning the coding matrix can pose privacy concerns: it may enable clients to infer information about the requests and side information of other clients [1]. In this paper, we formalize the intuition that the achieved privacy can increase by decreasing the number of rows of the coding matrix that a client learns. Based on this, we propose the use of $k$-limited-access schemes: given an i…
We revisit the problem of broadcasting on $d$-ary trees: starting from a Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards its value across binary symmetric channels $\mathrm{BSC}_δ$ to $d$ descendants. The goal is to reconstruct $X_0$ given the vector $X_{L_h}$ of values of all variables at depth $h$. It is well known that reconstruction (better than a random guess) is possible as $h\to \infty$ if and only if $δ< δ_c(d)$. In this paper, we study the behavior of the mutual information and the probability of error when $δ$ is slightly subcritical. The innovation of o…
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…
This paper considers a basic MIMO information-energy (I-E) broadcast system, where a multi-antenna transmitter transmits information and energy simultaneously to a multi-antenna information receiver and a dual-functional multi-antenna energy receiver which is also capable of decoding information. Due to the open nature of wireless medium and the dual purpose of information and energy transmission, secure information transmission while ensuring efficient energy harvesting is a critical issue for such a broadcast system. Assuming that physical layer security techniques are applied to the system …
The limit of the entropy in the stochastic block model (SBM) has been characterized in the sparse regime for the special case of disassortative communities [COKPZ17] and for the classical case of assortative communities but in the dense regime [DAM16]. The problem has not been closed in the classical sparse and assortative case. This paper establishes the result in this case for any SNR besides for the interval (1, 3.513). It further gives an approximation to the limit in this window. The result is obtained by expressing the global SBM entropy as an integral of local tree entropies in a broadc…
This paper investigates the problem of information transmission over the simultaneous relay channel with two users (or two possible channel outcomes) where for one of them the more suitable strategy is Decode-and-Forward (DF) while for the other one is Compress-and-Forward (CF). In this setting, it is assumed that the source wishes to send common and private informations to each of the users (or channel outcomes). This problem is relevant to: (i) the transmission of information over the broadcast relay channel (BRC) with different relaying strategies and (ii) the transmission of information ov…
In this work, we consider a scenario wherein an energy harvesting wireless radio equipment sends information to multiple receivers alongside powering them. In addition to harvesting the incoming radio frequency (RF) energy, the receivers also harvest energy from {its environment (e.g., solar energy)}. This communication framework is captured by a fading Gaussian Broadcast Channel (GBC) with energy harvesting transmitter and receivers. In order to ensure {some quality of service (QoS)} in data reception among the receivers, we impose a \textit{minimum-rate} requirement on data transmission. For…
In this paper, we consider the wireless broadcasting scenario with a source node sending some common information to a group of closely located users, where each link is subject to certain packet erasures. To ensure reliable information reception by all users, the conventional approach generally requires repeated transmission by the source until all the users are able to decode the information, which is inefficient in many practical scenarios. In this paper, by exploiting the close proximity among the users, we propose a novel two-phase wireless broadcasting protocol with user cooperations base…
Wireless power transfer (WPT) is a promising new solution to provide convenient and perpetual energy supplies to wireless networks. In practice, WPT is implementable by various technologies such as inductive coupling, magnetic resonate coupling, and electromagnetic (EM) radiation, for short-/mid-/long-range applications, respectively. In this paper, we consider the EM or radio signal enabled WPT in particular. Since radio signals can carry energy as well as information at the same time, a unified study on simultaneous wireless information and power transfer (SWIPT) is pursued. Specifically, th…
In this paper, we derive information-theoretic performance limits for three classes of two-user state-dependent discrete memoryless broadcast channels, with noncausal side-information at the encoder. The first class of channels comprises a sender broadcasting two independent messages to two non-cooperating receivers; for channels of the second class, each receiver is given the message it need not decode; and the third class comprises channels where the sender is constrained to keep each message confidential from the unintended receiver. We derive inner bounds for all the three classes of chann…
We study the problem of constructing good space-time codes for broadcasting $K$ independent messages over a MIMO network to $L$ users, where each user demands all the messages and already has a subset of messages as side information. As a first attempt, we consider the $2\times 2$ case and propose golden-coded index coding by partitioning the golden codes into $K$ subcodes, one for each message. The proposed scheme is shown to have the property that for any side information configuration, the minimum determinant of the code increases exponentially with the amount of information contained in th…
In this paper, we design space-time block codes (STBCs) to broadcast the common information omnidirectionally in a massive MIMO downlink. To reduce the burden of the downlink channel estimation and achieve partial spatial diversity from base station (BS) transmit antennas, we propose channel-independently precoded low-dimensional STBC. The precoding matrix and the signal constellation in the low-dimensional STBC are jointly designed to guarantee omnidirectional coverage at any instant time and sufficiently utilize the power amplifier capacities of BS transmit antennas, and at the same time, ac…
We study the delay minimization in a direct multicast communication scheme where a base station wishes to transmit a set of original packets to a group of clients. Each of the clients already has in its cache a subset of the original packets, and requests for all the remaining packets. The base station communicates directly with the clients by broadcasting information to them. Assume that bandwidths vary between the station and different clients. We propose a method to minimize the total delay required for the base station to satisfy requests from all clients.
The compound secure groupcast problem is considered, where the key variables at $K$ receivers are designed so that a transmitter can securely groupcast a message to any $N$ out of the $K$ receivers through a noiseless broadcast channel. The metric is the information theoretic tradeoff between key storage $α$, i.e., the number of bits of the key variable per message bit, and broadcast bandwidth $β$, i.e., the number of bits of the broadcast information per message bit. We have three main results. First, when broadcast bandwidth is minimized, i.e., when $β= 1$, we show that the minimum key stora…
We study the joint source channel coding problem of transmitting an analog source over a Gaussian channel in two cases - (i) the presence of interference known only to the transmitter and (ii) in the presence of side information known only to the receiver. We introduce hybrid digital analog forms of the Costa and Wyner-Ziv coding schemes. Our schemes are based on random coding arguments and are different from the nested lattice schemes by Kochman and Zamir that use dithered quantization. We also discuss superimposed digital and analog schemes for the above problems which show that there are in…
Wyner's wiretap channel is extended to parallel broadcast channels and fading channels with multiple receivers. In the first part of the paper, we consider the setup of parallel broadcast channels with one sender, multiple intended receivers, and one eavesdropper. We study the situations where the sender broadcasts either a common message or independent messages to the intended receivers. We derive upper and lower bounds on the common-message-secrecy capacity, which coincide when the users are reversely degraded. For the case of independent messages we establish the secrecy sum-capacity when t…
The index coding problem is a problem of efficient broadcasting with side-information. We look at the uniprior index coding problem, in which the receivers have disjoint side-information symbols and arbitrary demand sets. Previous work has addressed single uniprior index coding, in which each receiver has a single unique side-information symbol. Modeling the uniprior index coding problem as a \textit{supergraph}, we focus on a class of uniprior problems defined on \textit{generalized cycle} supergraphs. For such problems, we prove upper and lower bounds on the optimal broadcast rate. Using a c…
The index coding problem studies the fundamental limit on broadcasting multiple messages to their respective receivers with different sets of side information that are represented by a directed graph. The generalized lexicographic product structure in the side information graph is introduced as a natural condition under which the corresponding index coding problem can be decomposed into multiple interacting subproblems. The capacity region is characterized in terms of the subproblem capacity regions combined in the same product structure. The proof is based on dual uses of random coding---one …
Network coding is commonly used to improve the energy efficiency of network-wide broadcasting in wireless multi-hop networks. In this work, we focus on XOR-based broadcasting in mobile ad hoc networks with multiple sources. We make the observation that the common approach, which is to benefit from the synergy of XOR network coding with a CDS-based broadcast algorithm, suffers performance breakdowns. After delving into the details of this synergy, we attribute this behavior to an important mechanism of the underlying broadcast algorithm, known as the "termination criterion". To tackle the probl…
The interplay between timeliness and rate efficiency is investigated in packet erasure broadcast channels with feedback. A scheduling framework is proposed in which coding actions, as opposed to users, are scheduled to attain desired tradeoffs between rate and age of information (AoI). This tradeoff is formalized by an upper bound on AoI as a function of the target rate constraints and two lower bounds: one as a function of the communication rate and one as a function of the arrival rate. Simulation results show that (i) coding can be beneficial in reducing AoI in the regime of moderate arriva…
This paper studies the problem of secure communication over the broadcast channel with receiver side information under the lens of individual secrecy constraints. That is, the transmitter wants to send two independent messages to two receivers which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the ca…
In 2000, Evans et al. [Eva+00] proved the subadditivity of the mutual information in the broadcasting on tree model with binary vertex labels and symmetric channels. They raised the question of whether such subadditivity extends to loopy graphs in some appropriate way. We recently proposed such an extension that applies to general graphs and binary vertex labels [AB18], using synchronization models and relying on percolation bounds. This extension requires however the edge channels to be symmetric on the product of the adjacent spins. A more general version of such a percolation bound that app…
We study a generalization of the well-known model of broadcasting on trees. Consider a directed acyclic graph (DAG) with a unique source vertex $X$, and suppose all other vertices have indegree $d\geq 2$. Let the vertices at distance $k$ from $X$ be called layer $k$. At layer $0$, $X$ is given a random bit. At layer $k\geq 1$, each vertex receives $d$ bits from its parents in layer $k-1$, which are transmitted along independent binary symmetric channel edges, and combines them using a $d$-ary Boolean processing function. The goal is to reconstruct $X$ with probability of error bounded away fro…
We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of side information, and is a generalization of the well known (and unsolved) index coding problem of information theory. Rather than achieving the full capacity region, we develop a code-constrained capacity region, which restricts attention to a pre-specified set of coding actions. We develop a dynamic max-weight algorithm that allows for random packet arrivals…
We introduce the idea of distortion side information, which does not directly depend on the source but instead affects the distortion measure. We show that such distortion side information is not only useful at the encoder, but that under certain conditions, knowing it at only the encoder is as good as knowing it at both encoder and decoder, and knowing it at only the decoder is useless. Thus distortion side information is a natural complement to the signal side information studied by Wyner and Ziv, which depends on the source but does not involve the distortion measure. Furthermore, when both…
We consider lossy source coding when side information affecting the distortion measure may be available at the encoder, decoder, both, or neither. For example, such distortion side information can model reliabilities for noisy measurements, sensor calibration information, or perceptual effects like masking and sensitivity to context. When the distortion side information is statistically independent of the source, we show that in many cases (e.g, for additive or multiplicative distortion side information) there is no penalty for knowing the side information only at the encoder, and there is no …
A lossy source coding problem is studied in which a source encoder communicates with two decoders, one with and one without correlated side information with an additional constraint on the privacy of the side information at the uninformed decoder. Two cases of this problem arise depending on the availability of the side information at the encoder. The set of all feasible rate-distortion-equivocation tuples are characterized for both cases. The difference between the informed and uninformed cases and the advantages of encoder side information for enhancing privacy are highlighted for a binary s…
Packets originated from an information source in the network can be highly correlated. These packets are often routed through different paths, and compressing them requires to process them individually. Traditional universal compression solutions would not perform well over a single packet because of the limited data available for learning the unknown source parameters. In this paper, we define a notion of correlation between information sources and characterize the average redundancy in universal compression with side information from a correlated source. We define the side information gain a…
Secure data compression in the presence of side information at both a legitimate receiver and an eavesdropper is explored. A noise-free, limited rate link between the source and the receiver, whose output can be perfectly observed by the eavesdropper, is assumed. As opposed to the wiretap channel model, in which secure communication can be established by exploiting the noise in the channel, here the existence of side information at the receiver is used. Both coded and uncoded side information are considered. In the coded side information scenario, inner and outer bounds on the compression-equi…
This paper studies the problem of secure communcation over the two-receiver discrete memoryless broadcast channel with one-sided receiver side information and with a passive eavesdropper. We proposed a coding scheme which is based upon the superposition-Marton framework. Secrecy techniques such as the one-time pad, Carleial-Hellman secrecy coding and Wyner serecy coding are applied to ensure individual secrecy. This scheme is shown to be capacity achieving for some cases of the degraded broadcast channel. We also notice that one-sided receiver side information provides the advantage of rate re…
This study considers a wireless network where an access point (AP) broadcasts timely updates to numerous mobile users. The timeliness of information owned by a user is characterized by the age of information. Frequently broadcasting the timely updates at constant maximum power can minimize the age of information for all users, but wastes valuable communication resources (ie., time and energy). To address the age-energy trade-off, it is critical to develop an efficient scheduling algorithm that identifies broadcast times and allocates power. Moreover, unpredictable user movement would cause rap…
