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In this correspondence, we compare the achievable throughput for the optimal strategy of dirty paper coding (DPC) to that achieved with suboptimal and lower complexity linear precoding techniques (zero-forcing and block diagonalization). Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR. Furthermore, the difference is not affected by asymmetric channel behavior when each user has a different average SNR. Weighted sum rate maximization is also considered. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we consider a status updating system where updates are generated at a constant rate at $K$ sources and sent to the corresponding recipients through a noise-free broadcast channel. We assume that perfect channel state information (CSI) is available at the transmitter before each transmission, and the transmitter is able to utilize the CSI to precode the updates. Our object is to design optimal precoding schemes to minimize the summed average age of information (AoI) at the recipients. Under various assumptions on the size of each update $B$ , the number of transmit antennas $M$ , and the number of receive antennas $N$ at each user, this paper identifies the corresponding age-optimal precoding and transmission scheduling strategies. Specifically, for the case when $N=1$ , a round-robin based updating scheme is shown to be optimal. For the two-user systems with $N>B$ or $M\notin [N:2N]$ , framed updating schemes are proven to be optimal. For other cases in the two-user systems, a framed alternating updating scheme is proven to be 2-optimal. [ABSTRACT FROM AUTHOR]

We introduce a fundamental lemma called the Poisson matching lemma, and apply it to prove one-shot achievability results for various settings, namely channels with state information at the encoder, lossy source coding with side information at the decoder, joint source-channel coding, broadcast channels, distributed lossy source coding, multiple access channels and channel resolvability. Our one-shot bounds improve upon the best known one-shot bounds in most of the aforementioned settings (except multiple access channels and channel resolvability, where we recover bounds comparable to the best known bounds), with shorter proofs in some settings even when compared to the conventional asymptotic approach using typicality. The Poisson matching lemma replaces both the packing and covering lemmas, greatly simplifying the error analysis. This paper extends the work of Li and El Gamal on Poisson functional representation, which mainly considered variable-length source coding settings, whereas this paper studies fixed-length settings, and is not limited to source coding, showing that the Poisson functional representation is a viable alternative to typicality for most problems in network information theory. [ABSTRACT FROM AUTHOR]

Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general K-user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams – crucial to the overall complexity – while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme’s constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded. [ABSTRACT FROM AUTHOR]

This paper aims to characterize the capacity limits of a wireless cellular network with a full-duplex (FD) base-station (BS) and half-duplex user terminals, in which three independent messages are communicated: the uplink message m1 from the uplink user to the BS, the downlink message m2 from the BS to the downlink user, and the device-to-device (D2D) message m3 from the uplink user to the downlink user. From an information theoretical perspective, the overall network can be viewed as a generalization of the FD relay broadcast channel with a side message transmitted from the relay to the destination. We begin with a simpler case that involves the uplink and downlink transmissions of (m1, m2) only, and propose an achievable rate region based on a novel strategy that uses the BS as a FD relay to facilitate the interference cancellation at the downlink user. We also prove a new converse, which is strictly tighter than the cut-set bound, and characterize the capacity region of the scalar Gaussian FD network without a D2D message to within a constant gap. This paper further studies a general setup wherein (m1, m2, m3) are communicated simultaneously. To account for the D2D message, we incorporate Marton’s broadcast coding into the previous scheme to obtain a larger achievable rate region than the existing ones in the literature. We also improve the cut-set bound by means of genie and show that by using one of the two simple rate-splitting schemes, the capacity region of the scalar Gaussian FD network with a D2D message can already be reached to within a constant gap. Finally, a generalization to the vector Gaussian channel case is discussed. Simulation results demonstrate the advantage of using the BS as relay in enhancing the throughput of the FD cellular network. [ABSTRACT FROM AUTHOR]

When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit correlation matrices have mutually exclusive eigenspaces, allowing non-interfering training and transmission. This paper broadens the scope of transmit correlation diversity to the case of partially and fully overlapping eigenspaces and introduces techniques to harvest these generalized gains. For the two-user MIMO broadcast channel, we derive achievable degrees of freedom (DoF) and achievable rate regions with/without channel state information at the receiver (CSIR). When CSIR is available, the proposed achievable DoF region is tight in some configurations of the number of receive antennas and the channel correlation ranks. We then extend the DoF results to the $K$ -user case by analyzing the interference graph that characterizes the overlapping structure of the eigenspaces. Our achievability results employ a combination of product superposition in the common part of the eigenspaces, and pre-beamforming (rate splitting) to create multiple data streams in non-overlapping parts of the eigenspaces. Massive MIMO is a natural example in which spatially correlated link gains are likely to occur. We study the achievable downlink sum rate for a frequency-division duplex massive MIMO system under transmit correlation diversity. [ABSTRACT FROM AUTHOR]

This paper addresses lossy transmission of a common source over a broadcast channel when there is correlated side information at the receivers, with emphasis on the quadratic Gaussian and binary Hamming cases. A digital scheme that combines ideas from the lossless version of the problem, i.e., Slepian-Wolf coding over broadcast channels, and dirty paper coding, is presented and analyzed. This scheme uses layered coding where the common layer information is intended for both receivers and the refinement information is destined only for one receiver. For the quadratic Gaussian case, a quantity characterizing the combined quality of each receiver is identified in terms of channel and side information parameters. It is shown that it is more advantageous to send the refinement information to the receiver with "better" combined quality. In the case where all receivers have the same overall quality, the presented scheme becomes optimal. Unlike its lossless counterpart, however, the problem eludes a complete characterization. [ABSTRACT FROM AUTHOR]

This paper employs auxiliary receivers as a mathematical tool to identify Gallager-type auxiliary random variables and write outer bounds for some basic multiuser settings. This approach is then applied to the relay, interference, and broadcast channel settings, yielding new outer bounds that improve on existing outer bounds and strictly outperform classical outer bounds. For instance, we strictly improve on: the cutset outer bound for the scalar Gaussian relay channel, the outer bounds for the Gaussian Z-interference channel, and the outer bounds for the two receiver broadcast channel. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user’s local cache memory, even without knowledge of user’s later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users’ demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work. First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the “acyclic index coding converse bound.” This converse bound is proved to be achievable by the Maddah-Ali and Niesen’s scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used “composite (index) coding” achievable bound and its improvements, and is of independent interest. An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al has however shown that coded cache placement can at most half the network load compared to the results presented in this paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is well known that the capacity region of an average transmit power constrained Gaussian Broadcast Channel (GBC) with independent noise realizations at the receivers is enlarged by the presence of causal noiseless feedback. When the noise variances at the receivers are identical, even passive feedback via independent memoryless Gaussian links can lead to a capacity region enlargement. The last fact remains true even when the feedback noise variance is very high, and available only from one of the receivers. While such capacity enlargements are feasible for several other feedback models in the Gaussian BC setting, it is also known that feedback does not change the capacity region for physically degraded broadcast channels. In this paper, we consider a two user GBC with independent noise realizations at the receivers, where the feedback links from the receivers are corrupted by independent additive Gaussian noise processes. We investigate the set of four noise variances, two forward and two feedback, for which no capacity enlargement is possible. A sharp characterization of this region is derived, i.e., any quadruple outside the presented region will lead to a capacity enlargement, whereas quadruples inside will leave the capacity region unchanged. Our results lead to the conclusion that when the forward noise variances are different, too noisy a feedback from one of the receivers alone is not always beneficial for enlarging the capacity region, be it from the stronger user or the weaker one, in sharp contrast to the case of equal forward noise variances. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of secret key generation with one-way communication through both a rate-limited public channel and a rate-limited secure channels where the public channel is from Alice to Bob and Eve and the secure channel is from Alice to Bob. In this model, we do not pose any constraints on the sources, i.e. Bob is not degraded to or less noisy than Eve. We obtain the optimal secret key rate in this problem, both for the discrete memoryless sources and vector Gaussian sources. The vector Gaussian characterization is derived by suitably applying the enhancement argument, and proving a new extremal inequality. The extremal inequality can be seen as coupling of two extremal inequalities, which are related to the degraded compound MIMO Gaussian broadcast channel, and the vector generalization of Costa’s entropy power inequality, accordingly. [ABSTRACT FROM AUTHOR]

Communication for omniscience (CO) refers to the problem where the users in a finite set V observe a discrete multiple random source and want to exchange data over broadcast channels to reach omniscience, the state where everyone recovers the entire source. This paper studies how to improve the computational complexity for the problem of minimizing the sum-rate for attaining omniscience in V. While the existing algorithms rely on the submodular function minimization (SFM) techniques and complete in O(|V|2⋅SFM (|V|) time, we prove the strict strong map property of the nesting SFM problem. We propose a parametric (PAR) algorithm that utilizes the parametric SFM techniques and reduces the complexity to O(|V| ⋅SFM (|V|). We propose efficient solutions to the successive omniscience (SO): attaining omniscience successively in user subsets. We first focus on how to determine a complimentary subset X* ⊄ V in the existing two-stage SO such that if the local omniscience in X* is reached first, the global omniscience whereafter can still be attained with the minimum sum-rate. It is shown that such a subset can be extracted at one of the iterations of the PAR algorithm. We then propose a novel multi-stage SO strategy: a nesting sequence of complimentary user subsets X*(1) ⊄ . . . ⊆ X*(K) = V, the omniscience in which is attained progressively by the monotonic rate vectors rV(1) ≤ . . . rV(K). We propose algorithms to obtain this K-stage SO from the returned results by the PAR algorithm. The run time of these algorithms is the same as the PAR algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we develop the first method for finding strong converse bounds in quantum network information theory. The general scheme relies on a recently obtained result in the field of non-commutative functional inequalities, namely the tensorization property of quantum reverse hypercontractivity for the quantum depolarizing semigroup. We develop a novel technique to employ this result to find both finite blocklength and exponential strong converse bounds for the tasks of quantum source coding with compressed classical side information, and distributed quantum hypothesis testing with communication constraints for a classical-quantum state. In the classical setting, these two problems can be reformulated in a unified framework in terms of the so-called image-size characterization problem, which we extend to the classical-quantum setting. We also use this technique to establish analogous strong converse bounds in broadcast communication scenarios. In particular, we consider the transmission of classical information through a degraded broadcast channel, whose outputs are two quantum systems, with the state of one being a degraded version of the other. In establishing this last result, we prove a second-order Fano-type inequality, which is of independent interest. Our method to study strong converses has potential applications in other important tasks of quantum network information theory. [ABSTRACT FROM AUTHOR]

An index code for broadcast channel with receiver side information is locally decodable if each receiver can decode its demand by observing only a subset of the transmitted codeword symbols instead of the entire codeword. Local decodability in index coding is known to reduce receiver complexity, improve user privacy and decrease decoding error probability in wireless fading channels. Conventional index coding solutions assume that the receivers observe the entire codeword, and as a result, for these codes the number of codeword symbols queried by a user per decoded message symbol, which we refer to as locality, could be large. In this paper, we pose the index coding problem as that of minimizing the broadcast rate for a given value of locality (or vice versa) and designing codes that achieve the optimal trade-off between locality and rate. We identify the optimal broadcast rate corresponding to the minimum possible value of locality for all single unicast problems. We present new structural properties of index codes which allow us to characterize the optimal trade-off achieved by: vector linear codes when the side information graph is a directed cycle; and scalar linear codes when the minrank of the side information graph is one less than the order of the problem. We also identify the optimal trade-off among all codes, including non-linear codes, when the side information graph is a directed 3-cycle. Finally, we present techniques to design locally decodable index codes for arbitrary single unicast problems and arbitrary values of locality. [ABSTRACT FROM AUTHOR]

Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix \mathbf H and a Gaussian MIMO broadcast channel (BC) with channel matrix \mathbf H ^\mathsf T . For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter, so that each receiver can obtain its desired codeword by decoding an integer-linear combination. In both the cases, integer-forcing offers higher achievable rates than zero-forcing while maintaining a similar implementation complexity. This paper establishes an uplink-downlink duality relationship for integer-forcing, i.e., any sum rate that is achievable via integer-forcing on the MIMO MAC can be achieved via integer-forcing on the MIMO BC with the same sum power and vice versa. Using this duality relationship, it is shown that integer-forcing can operate within a constant gap of the MIMO BC sum capacity. Finally, the paper proposes a duality-based iterative algorithm for the non-convex problem of selecting optimal beamforming and equalization vectors, and establishes that it converges to a local optimum. [ABSTRACT FROM PUBLISHER]

In the index coding problem a sender holds a message $x \in \{0,1\}^{n}$ and wishes to broadcast information to $n$ receivers in a way that enables the $i$ th receiver to retrieve the $i$ th bit $x_{i}$. Every receiver has prior side information comprising a subset of the bits of $x$ , and the goal is to minimize the length of the information sent via the broadcast channel. Porter and Wootters have recently introduced the model of embedded index coding, where the receivers also play the role of the sender and the goal is to minimize the total length of their broadcast information. An embedded index code is said to be task-based if every receiver retrieves its bit based only on the information provided by one of the receivers. This paper studies the effect of the task-based restriction on linear embedded index coding. It is shown that for certain side information maps there exists a linear embedded index code of length quadratically smaller than that of any task-based embedded index code. The result attains, up to a multiplicative constant, the largest possible gap between the two quantities. The proof is by an explicit construction and the analysis involves spectral techniques. [ABSTRACT FROM AUTHOR]

The performance of existing coded caching schemes is sensitive to the worst channel quality, a problem which is exacerbated when communicating over fading channels. In this paper, we address this limitation in the following manner: in short-term, we allow transmissions to subsets of users with good channel quality, avoiding users with fades, while in long-term we ensure fairness among users. Our online scheme combines (i) the classical decentralized coded caching scheme with (ii) joint scheduling and power control for the fading broadcast channel, as well as (iii) congestion control for ensuring the optimal long-term average performance. We prove that our online delivery scheme maximizes the alpha-fair utility among all schemes restricted to decentralized placement. By tuning the value of alpha, the proposed scheme can achieve different operating points on the average delivery rate region and tune performance according to an operator’s choice. We demonstrate via simulations that our scheme outperforms two baseline schemes: (a) standard coded caching with multicast transmission, limited by the worst channel user yet exploiting the global caching gain; (b) opportunistic scheduling with unicast transmissions exploiting the fading diversity but limited to local caching gain. [ABSTRACT FROM AUTHOR]

In this paper, we study the arbitrarily varying broadcast channel (AVBC) when the state information is available at the transmitter in a causal manner. We establish the inner and outer bounds on both the random code capacity region and the deterministic code capacity region with degraded message sets. The capacity region is then determined for a class of channels satisfying a condition on the mutual information between the strategy variables and the channel outputs. As an example, we consider the arbitrarily varying binary symmetric broadcast channel. We show the cases where the condition holds and, hence, the capacity region is determined and other cases where there is a gap between the bounds. This gap shows that the minimax theorem does not hold for rate regions. [ABSTRACT FROM AUTHOR]

In this paper, we make use of channel symmetry properties to determine the capacity region of three types of two-way networks: 1) two-user memoryless two-way channels (TWCs); 2) two-user TWCs with memory; and 3) three-user multiaccess/degraded broadcast (MA/DB) TWCs. For each network, symmetry conditions under which a Shannon-type random coding inner bound (under independent non-adaptive inputs) is tight are given. For two-user memoryless TWCs, prior results are substantially generalized by viewing a TWC as two interacting state-dependent one-way channels. The capacity of symmetric TWCs with memory, whose outputs are functions of the inputs and independent stationary and ergodic noise processes, is also obtained. Moreover, various channel symmetry properties under which the Shannon-type inner bound is tight are identified for three-user MA/DB TWCs. The results not only enlarge the class of symmetric TWCs whose capacity region can be exactly determined but also imply that interactive adaptive coding, not improving capacity, is unnecessary for such channels. [ABSTRACT FROM AUTHOR]

To address the exponentially rising demand for wireless content, the use of caching is emerging as a potential solution. It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. Coded caching is well suited to emerging heterogeneous wireless architectures which consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). This enables design of coded caching-and-delivery schemes that equip APs with storage, and place content in them in a way that creates coded-multicast opportunities for combining with macro-cell broadcast to satisfy users even with different demands. Such coded-caching schemes have been shown to be order-optimal with respect to the BS transmission rate, for a system with single-level content, i.e., one where all content is uniformly popular. In this paper, we consider a system with non-uniform popularity content which is divided into multiple levels, based on varying degrees of popularity. The main contribution of this paper is the derivation of an order-optimal scheme which judiciously shares cache memory among files with different popularities. To show order-optimality we derive new information-theoretic lower bounds, which use a sliding-window entropy inequality, effectively creating a non-cut-set bound. We also extend the ideas to when users can access multiple caches along with the broadcast. Finally, we consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup), and demonstrate a dichotomy in the order-optimal strategies for these two extreme cases. [ABSTRACT FROM PUBLISHER]

Building on the recent coded-caching breakthrough by Maddah-Ali and Niesen, the work here considers the $K$ -user cache-aided wireless multi-antenna symmetric broadcast channel with random fading and imperfect feedback, and analyzes the throughput performance as a function of feedback statistics and cache size. In this setting, this paper identifies the optimal cache-aided degrees-of-freedom (DoF) within a factor of 4, by identifying near-optimal schemes that exploit a new synergy between coded caching and delayed CSIT, as well as by exploiting the unexplored interplay between caching and feedback-quality. The DoF expressions reveal an initial gain due to current CSIT, and an additional gain due to coded caching, which is exponential in the sense that any linear decrease in the required DoF performance, allows for an exponential reduction in the required cache size. In the end, this paper reveals three new aspects of caching: a synergy between memory and delayed feedback, a tradeoff between memory and current CSIT, and a powerful ability to provide cache-aided feedback savings. [ABSTRACT FROM PUBLISHER]

This paper considers a state dependent broadcast channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem is to effectively convey (“amplify”) the channel state sequence to Bob while “masking” it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage. This can be viewed as a secrecy problem, where we desire that the channel state itself be minimally leaked to Eve while being communicated to Bob. This paper is aimed at characterizing the tradeoff region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter transmits a partial state information over the channel to facilitate the amplification process. For the case when Bob observes a stronger signal than Eve, the achievable coding scheme is enhanced with secure refinement. Outer bounds on the tradeoff region are also derived, and used in characterizing some special case results. In particular, the optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the reversely degraded discrete memoryless channel, the degraded binary, and the degraded Gaussian channels. In addition, for the degraded Gaussian model, the extremal corner points of the tradeoff region are characterized, and the gap between the outer bound and achievable rate-regions is shown to be less than half a bit for a wide set of channel parameters. [ABSTRACT FROM PUBLISHER]

This paper contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two different methods of code expurgation will be used, that will provide two competing error exponents. The second is the derivation of expurgated exponents under the generalized stochastic likelihood decoder (GLD). We prove that the expurgated exponents achieved for the hierarchical ensemble under GLD decoding are at least as good as the maximum between the random coding error exponents derived in an earlier work by Averbuch and Merhav (2018) and one of our ML–based expurgated exponents. [ABSTRACT FROM AUTHOR]

In this paper, we design energy-efficient space constellations for multiuser multi-input single-output visible light communication broadcast systems with channel state information (CSI) at the receiver in the three scenarios: 1) with CSI at the transmitter (CSIT); 2) with statistical CSIT; and 3) without CSIT. By utilizing the cooperation of multiuser interference, optimal multidimensional additively uniquely decomposable constellation groups are designed to optimize the received worst case performance metrics of all users subject to two commonly used power constraints, i.e., average and peak optical power constraints. The resulting optimal designs are proved to be pulse amplitude modulated with an optimal beamformer, which can be efficiently attained by numerical search for Scenarios 1 and 2 and be given in a closed form for Scenario 3. One of the common significant advantages of these designs is the fast demodulation of the sum signal from a noisy received signal, since these optimal designs result in an equivalent ideal scalar AWGN channel. Comprehensive computer simulations demonstrate that our designs significantly outperform traditional zero-forcing, minimum mean square error, and time-division methods. [ABSTRACT FROM AUTHOR]

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley which showed that the Cover-van der Muelen region was exhausted by the randomized-time-division strategy. [ABSTRACT FROM AUTHOR]

We investigate the maximum coding rate for a given average blocklength and error probability over a $K$ -user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiyet al.(2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e.,zero dispersion. In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message $K$ -user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaardet al.(2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of plausible deniability in an information theoretic framework. We consider a scenario where an entity that eavesdrops through a broadcast channel summons one of the parties in a communication protocol to reveal their message (or signal vector). It is desirable that the summoned party has enough freedom to produce a fake output that is likely plausible given the eavesdropper’s observation. We examine three variants of this problem—message deniability, transmitter deniability, and receiver deniability. In the first setting, the message sender is summoned to produce the sent message. Similarly, in the second and third settings, the transmitter and the receiver are required to produce the transmitted codeword and the received vector, respectively. For each of these settings, we examine the maximum communication rate that allows a given minimum rate of plausible fake outputs. First, for the message deniability problem, we fully characterize the capacity region for general broadcast channels. Next, for the transmitter deniability problem, we give an achievable region for general broadcast channels by fully characterizing the set of rate pairs’ achievable using deterministic coding schemes. Finally, for the receiver deniability problem, we give an achievable rate region for physically degraded broadcast channels. [ABSTRACT FROM AUTHOR]

The polarization process of polar codes over a prime $q$ -ary alphabet is studied. Recently, it has been shown that the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap between code rate and channel capacity. However, except for the binary case, the degree of the polynomial in the bound is extremely large. In this paper, a different approach to computing the degree of this polynomial for any prime alphabet size is shown. This approach yields a lower degree polynomial for various values of the alphabet size that were examined. It is also shown that even lower degree polynomial can be computed with an additional numerical effort. [ABSTRACT FROM AUTHOR]

This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommendation systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth constraints, as is the case over wireless networks. We formulate this as a new problem in the context of index coding: we relax the index coding requirements to capture scenarios where each client has preferences associated with messages. The client is satisfied to receive any message she does not already have, with a satisfaction proportional to her preference for that message. We consistently find, over a number of scenarios we sample, that although the optimization problems are in general NP-hard, significant bandwidth savings are possible even when restricted to polynomial time algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the basic question of whether a given channel $V$ can be dominated (in the precise sense of being more noisy) by a $q$ -ary symmetric channel. The concept of less noisy relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback–Leibler divergence. We provide an equivalent characterization in terms of $\chi ^{2}$ -divergence. Furthermore, we develop a simple criterion for domination by a $q$ -ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel $V$. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel. [ABSTRACT FROM AUTHOR]

This paper presents an outage analysis for a two-user parallel Gaussian interference channel consisting of two sub-channels. Each sub-channel is modeled as a two-user Gaussian interference channel with quasi-static and flat fading. Both users employ single-layer Gaussian code-books and maintain a statistical correlation \rho between the signals transmitted over the underlying sub-channels. When joint decoding (JD) is performed at the receivers, setting \rho =0 minimizes the outage probability, regardless of the value of the signal-to-noise ratio (SNR). It is shown, however, that if the receivers treat interference as noise (TIN) or cancel interference (CI), the value of optimum \rho approaches 1 as SNR goes to infinity. Motivated by these observations, we let \rho =0 under JD and \rho =1 , it is shown that the outage probability scales like \mathrm snr^-(1-r) under both TIN and CI, while it vanishes at least as fast as \mathrm snr^-\min \2-r,4(1-r)\\log \mathrm snr under JD. This paper is concluded by extending some of the results to a two-user parallel Gaussian interference channel with an arbitrary number of sub-channels. [ABSTRACT FROM AUTHOR]

This paper investigates various subtleties of applying linear physical-layer network coding (PNC) with $q$ -level pulse amplitude modulation ( $q$ -PAM) in two-way relay channels. A critical issue is how the PNC system performs when the received powers from the two users at the relay are imbalanced. In particular, how would the PNC system perform under slight power imbalance that is inevitable in practice, even when power control is applied? To answer these questions, this paper presents a comprehensive analysis of $q$ -PAM PNC. Our contributions are as follows. First, we give a systematic way to obtain the analytical relationship between the minimum distance of the signal constellation induced by the superimposed signals of the two users (a key performance determining factor) and the channel-gain ratio of the two users, for all $q$ . In particular, we show how the minimum distance changes in a piecewise linear fashion as the channel-gain ratio varies. Second, we show that the performance of $q$ -PAM PNC is highly sensitive to imbalanced received powers from the two users at the relay, even when the power imbalance is slight (e.g., the residual power imbalance in a power-controlled system). This sensitivity problem is exacerbated as $q$ increases, calling into question the robustness of high-order modulated PNC. Third, we propose an asynchronized PNC system in which the symbol arrival times of the two users at the relay are deliberately made to be asynchronous. We show that such asynchronized PNC, when operated with a belief propagation decoder, can remove the sensitivity problem, allowing a robust high-order modulated PNC system to be built. [ABSTRACT FROM AUTHOR]

This paper introduces Manhattan sampling in two and higher dimensions, and proves sampling theorems for them. In 2-D, Manhattan sampling, which takes samples densely along a Manhattan grid of lines, can be viewed as sampling on the union of two rectangular lattices, one dense horizontally and the other vertically, with the coarse spacing of each being a multiple of the fine spacing of the other. The sampling theorem shows that the images bandlimited to the union of the Nyquist regions of the two rectangular lattices can be recovered from their Manhattan samples, and an efficient procedure for doing so is given. Such recovery is possible even though there is an overlap among the spectral replicas induced by Manhattan sampling. In three and higher dimensions, there are many possible configurations for Manhattan sampling, each consisting of the union of special rectangular lattices called bi-step lattices. This paper identifies them, proves a sampling theorem showing that the images bandlimited to the union of the Nyquist regions of the bi-step rectangular lattices are recoverable from Manhattan samples, presents an efficient onion-peeling procedure for doing so, and shows that the union of Nyquist regions is as large as any bandlimited region, such that all images supported by such can be stably reconstructed from samples taken at the rate of the Manhattan sampling. It also develops a special representation for the bi-step lattices with a number of useful properties. While most of this paper deals with continuous-space images, Manhattan sampling of discrete-space images is also considered, for infinite, as well as finite, support images. [ABSTRACT FROM AUTHOR]

In this paper, we study a security problem on a simple wiretap network, consisting of a source node S, a destination node D, and an intermediate node R. The intermediate node connects the source and the destination nodes via a set of noiseless parallel channels, with sizes n1 and n2 , respectively. A message $M$ is to be sent from S to D. The information in the network may be eavesdropped by a set of wiretappers. The wiretappers cannot communicate with one another. Each wiretapper can access a subset of channels, called a wiretap set. All the chosen wiretap sets form a wiretap pattern. A random key $K$ is generated at S, and a coding scheme on $(M, K)$ is employed to protect $M$ . We define two decoding classes at D. In Class-I, only $M$ is required to be recovered, and in Class-II, both $M$ and $K$ are required to be recovered. The objective is to minimize $H(K)/H(M)$ for a given wiretap pattern under the perfect secrecy constraint. The first question we address is whether routing is optimal on this simple network. By enumerating all the wiretap patterns on the Class-I/II (3, 3) networks and harnessing the power of Shannon-type inequalities, we find that gaps exist between the bounds implied by routing and the bounds implied by Shannon-type inequalities for a small fraction (<2%) of all the wiretap patterns. The second question we investigate is the following: What is $\min H(K)/H(M)$ for the remaining wiretap patterns where gaps exist? We study some simple wiretap patterns and find that their Shannon bounds (i.e., the lower bound induced by Shannon-type inequalities) can be achieved by linear codes, which means routing is not sufficient even for the (3, 3) network. For some complicated wiretap patterns, we study the structures of linear coding schemes under the assumption that they can achieve the corresponding Shannon bounds. This paper indicates that the determination of the entropic region of six linear vector spaces cannot be sidestepped. Some subtle issues on the network models are discussed, and interesting observations are stated. [ABSTRACT FROM AUTHOR]

The problem of sending two correlated vector Gaussian sources over a bandwidth-matched two-user scalar Gaussian broadcast channel is studied in this paper, where each receiver wishes to reconstruct its target source under a covariance distortion constraint. We derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair. Our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources. Furthermore, it is shown that this lower bound is achievable by a class of hybrid schemes for the special case, where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint. [ABSTRACT FROM AUTHOR]

This paper presents polar coding schemes for the two-user discrete memoryless broadcast channel (DM-BC) which achieve Marton’s region with both common and private messages. This is the best achievable rate region known to date, and it is tight for all classes of two-user DM-BCs whose capacity regions are known. To accomplish this task, we first construct polar codes for both the superposition as well as binning strategy. By combining these two schemes, we obtain Marton’s region with private messages only. Finally, we show how to handle the case of common information. The proposed coding schemes possess the usual advantages of polar codes, i.e., they have low encoding and decoding complexity and a superpolynomial decay rate of the error probability. We follow the lead of Goela, Abbe, and Gastpar, who recently introduced polar codes emulating the superposition and binning schemes. To align the polar indices, for both schemes, their solution involves some degradedness constraints that are assumed to hold between the auxiliary random variables and channel outputs. To remove these constraints, we consider the transmission of $k$ blocks and employ a chaining construction that guarantees the proper alignment of the polarized indices. The techniques described in this paper are quite general, and they can be adopted to many other multiterminal scenarios whenever there polar indices need to be aligned. [ABSTRACT FROM AUTHOR]

This paper studies the capacity of the two-receiver multiple-input broadcast packet erasure channels (PECs) with channel output feedback, which is in contrast with the single-input setting of the existing works. Motivated by the immense success of linear network coding (LNC) in theory and in practice, this paper first focuses on LNC schemes and characterizes the LNC feedback capacity region of two-receiver multiple-input broadcast PECs. A new linear-space-based approach is proposed, which unifies the problems of finding a capacity outer bound and devising the achievability scheme into a single linear programming problem. In particular, an LP solver is used to exhaustively search for the LNC scheme(s) with the best possible throughput, the result of which is thus guaranteed to attain the LNC feedback capacity. It is then proven by pure algebraic arguments that the LNC capacity region matches a simple capacity region outer bound, which proves that the derived LNC capacity region is indeed the true capacity. A byproduct of the above results is a complete LNC capacity region characterization for two-receiver partially Markovian and partially controllable broadcast PECs. [ABSTRACT FROM AUTHOR]

This paper contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both users. These universal decoders are certain variants of the maximum mutual information universal decoder, and they achieve the corresponding random coding exponents of optimal decoding. In addition, we introduce some lower bounds, which involve optimizations over very few parameters, unlike the original, exact exponents, which involve minimizations over auxiliary probability distributions. Numerical results for the binary symmetric broadcast channel show improvements over previously derived error exponents for the same model. [ABSTRACT FROM AUTHOR]

We consider a broadcast channel with three receivers and three-degraded message sets, i.e., the transmitter has a common message intended for all three receivers, a message intended for receivers 2 and 3, and a private message intended only for receiver 3. The messages are transmitted over a family of parallel degraded broadcast channels. In the most general case, the broadcast channel consists of the product of six parallel degraded broadcast channels, each with a different order of degradedness. We first consider an achievable rate region of Nair and El Gamal, by appropriately choosing independent input random variables and auxiliary random variables for each subchannel. We then show that the achievable rate region attains the capacity region for two different classes of such broadcast channels, one consisting of the product of five parallel degraded broadcast channels and another consisting of the product of three parallel degraded broadcast channels. To accomplish this, we make use of an information-theoretic inequality that may be proven using the Csiszár-sum identity. Next, we extend the result to the Gaussian case. We consider the aligned Gaussian MIMO broadcast channel consisting of the product of six parallel degraded Gaussian broadcast channels, where the Gaussian noise vectors for each of the users in each of the subchannels follow a degradedness order, i.e., the noise covariance matrices may be ordered in a positive semi-definite sense. We show that the Nair–El Gamal achievable rate region considered in this paper is maximized by Gaussian inputs. To prove that Gaussian inputs are optimal, we prove an extremal entropy inequality employing a new method recently introduced by Geng and Nair to prove the capacity region of the two-user Gaussian MIMO broadcast channel with common and private messages. [ABSTRACT FROM AUTHOR]

This paper considers the communication for omniscience problem: a set of users observe a discrete memoryless multiple source and want to recover the entire multiple source via noise-free broadcast communications. We study the problem of how to determine an optimal rate vector that attains omniscience with the minimum sum rate, the total number of communications. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. We propose a modified decomposition algorithm (MDA) and a sum-rate increment algorithm (SIA) for the asymptotic and non-asymptotic models, respectively, both of which determine the value of the minimum sum rate and a corresponding optimal rate vector in polynomial time. For the coordinate saturation capacity algorithm, a nesting algorithm in MDA and SIA, we propose to implement it by a fusion method and show by experimental results that this fusion method contributes to a reduction in computation complexity. Finally, we show that the separable convex minimization problem over the optimal rate vector set in the asymptotic model can be decomposed by the fundamental partition, the optimal partition of the user set that determines the minimum sum rate, so that the problem can be solved more efficiently. [ABSTRACT FROM PUBLISHER]

It is well known that cooperation between users in a communication network can lead to significant performance gains. A common assumption in past works is that all the users are aware of the resources available for cooperation, and know exactly to what extent these resources can be used. Unfortunately, in many modern communication networks, the availability of cooperation links cannot be guaranteed a priori, due to the dynamic nature of the network. In this paper, a family of models is suggested where the cooperation links may or may not be present. Coding schemes are devised that exploit the cooperation links if they are present, and can still operate (although at reduced rates) if cooperation is not possible. [ABSTRACT FROM AUTHOR]

We establish the degree of freedom (DoF) regions of the two-user multiple-input multiple-output (MIMO) broadcast channel with a general message set (BC-GM), that includes private and common messages, under fast fading. Nine different channel state knowledge assumptions—collectively known as hybrid channel state information at the transmitter (CSIT) models—are considered wherein the transmitter has either perfect/instantaneous, delayed, or no CSI from each of the two receivers. General antenna configurations are addressed wherein the three terminals have arbitrary numbers of antennas. The DoF regions are established for the five hybrid CSIT models in which either both channels are unknown at the transmitter or each of the two channels is known perfectly or with delay. In the four remaining cases in which exactly one of the two channels is unknown at the transmitter, the DoF regions under the restriction of linear encoding strategies—also known as the linear DoF (LDoF) regions—are established. As the key to the converse proofs of the LDoF region of the MIMO BC-GM under such hybrid CSIT assumptions, we show that, when only considering linear encoding strategies, the CSI from the receiver with more antennas does not help if there is no CSI available from the receiver with fewer antennas. This result is conjectured to be true even without the restriction on the encoding strategies to be linear. If true, the LDoF regions obtained for the four hybrid CSIT cases herein will also be the DoF regions for those cases. Many of the results of this paper when specialized to even the two-message problems are new. These include the LDoF regions, when one of the two channels is not known, of the MIMO BC-GM when specialized to the MIMO BC with private messages. They also include the DoF/LDoF regions for all the hybrid CSIT models obtained by specializing the corresponding regions for the MIMO BC-GM to the case with degraded messages. [ABSTRACT FROM AUTHOR]

This paper studies the problem of secure communications over broadcast channels under the individual secrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon Carleial–Hellman’s secrecy coding, Wyner’s secrecy coding, and the framework of Marton’s coding together with techniques, such as rate splitting and indirect decoding, an achievable individual secrecy rate region is established with the characterization of capacity regions for some special cases. In particular, the individual secrecy capacity region for the linear deterministic model is fully characterized, and for the Gaussian model, a constant gap (i.e., 0.5 b within the individual secrecy capacity region) result is obtained. To illustrate the impact of different secrecy constraints on the corresponding capacity regions, comparisons are made with those satisfying joint secrecy and without secrecy constraints. Overall, when compared with the joint secrecy constraint, the results allow for trading off secrecy level and throughput in the system. [ABSTRACT FROM AUTHOR]

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 rate 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 capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) is characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a rectangle with missing corners; a phenomenon occurring due to the coupling between user’s rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper’s channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper’s channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage rate from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate, making secrecy more affordable but still acceptable to the end user. [ABSTRACT FROM PUBLISHER]

The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii , i=1,2 where I_{1}, I_{2}\in \{\mathsf {P}, \mathsf {D}, \mathsf {N}\} , and the forms \mathsf {P} , \mathsf D , and \mathsf N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of I1I2 , with each state occurring for \lambda I1I2 fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where \lambda I1 I2=\lambda I2I1 . The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f. [ABSTRACT FROM AUTHOR]

Broadcasting $K$ independent messages to multiple users where each user demands all the messages and already has a subset of the messages as side information is studied. Recently, Natarajan et al. proposed a novel broadcasting strategy called lattice index coding, which adopts lattices constructed over some principal ideal domains (PID) for transmission. Using the structure of lattices over PID, they showed that this scheme provides uniform side information gain for any side information configuration, a desired property which essentially guarantees a fair signal-to-noise ratio gain when normalized by the amount of information contained in side information. In this paper, we generalize this strategy to a general ring of algebraic integers, which may not be a PID. Upper and lower bounds on the side information gains for the proposed scheme constructed over some interesting classes of number fields are provided and are shown to coincide asymptotically in message rate. This generalization substantially enlarges the design space and partially includes the scheme by Natarajan et al. as a special case. Perhaps more importantly, in addition to side information gains, the proposed lattice index codes benefit from diversity gains inherent in constellations carved from number fields when used over Rayleigh fading channel. Some interesting examples are provided for which the proposed scheme allows the messages to be from the same field. [ABSTRACT FROM PUBLISHER]

In this paper, we study the problem of obtaining 1-of-2 string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users’ inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice–Bob and Alice–Eve), we derive the 1-of-2 string OT capacity for both 2-privacy (when Eve can collude with either Alice or Bob) and 1-privacy (when no such collusion is allowed). We generalize these capacity results to 1-of- $N$ string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice–Bob and Alice–Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice–Bob and Bob–Eve) and 1-of-2 string OT is desired between Alice and Bob with 1-privacy. For this setup, we derive an upper and lower bound on the 1-of-2 string OT capacity which match in one of two possible parameter regimes. [ABSTRACT FROM PUBLISHER]