Gaussian Broadcast Channel Research Articles

Gaussian Broadcast Channels With Heterogeneous Finite Blocklength Constraints: Inner and Outer Bounds

Gaussian Broadcast Channels With Heterogeneous Finite Blocklength Constraints: Inner and Outer Bounds

Maximizing Weighted Sum-Rate Over Gaussian Broadcast Channels

Maximizing Weighted Sum-Rate Over Gaussian Broadcast Channels

Second Order Rate Regions of Gaussian Broadcast Channels Under Heterogeneous Blocklength Constraints

Second Order Rate Regions of Gaussian Broadcast Channels Under Heterogeneous Blocklength Constraints

Low-Delay Digital and Hybrid Digital/Analog Schemes for Wyner-Ziv Problem Over Gaussian Broadcast Channel

Low-Delay Digital and Hybrid Digital/Analog Schemes for Wyner-Ziv Problem Over Gaussian Broadcast Channel

On Second Order Rate Regions for the Static Scalar Gaussian Broadcast Channel

This paper considers the single antenna, static, scalar Gaussian broadcast channel in the finite blocklength regime. Second order achievable and converse rate regions are presented. Both a global reliability and per-user reliability requirements are considered. The two-user case is analyzed in detail, and generalizations to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user case are also discussed. The largest second order achievable regions presented here require both superposition and rate splitting in the code construction, as opposed to the (infinite blocklength, first order) capacity region which does not require rate splitting. Indeed, the finite blocklength penalty causes superposition alone to underperform other coding techniques in some parts of the region. In addition, the proposed scheme uses joint simultaneous decoding as opposed to successive interference cancellation. Interestingly, in the two-user case with per-user reliability requirements, the capacity achieving superposition encoding order (with the codeword intended for the user with the smallest received SNR as cloud center) does not necessarily give the largest second order region. Instead, the message of the user with the smallest point-to-point second order capacity should be encoded in the cloud center in order to obtain the largest second order region for the proposed scheme.

Zero-Delay Joint Source Channel Coding for a Bivariate Gaussian Source over the Broadcast Channel with One-Bit ADC Front Ends.

In this work, we consider the zero-delay transmission of bivariate Gaussian sources over a Gaussian broadcast channel with one-bit analog-to-digital converter (ADC) front ends. An outer bound on the conditional distortion region is derived. Focusing on the minimization of the average distortion, two types of methods are proposed to design nonparametric mappings. The first one is based on the joint optimization between the encoder and decoder with the use of an iterative algorithm. In the second method, we derive the necessary conditions to develop the optimal encoder numerically. Using these necessary conditions, an algorithm based on gradient descent search is designed. Subsequently, the characteristics of the optimized encoding mapping structure are discussed, and inspired by which, several parametric mappings are proposed. Numerical results show that the proposed parametric mappings outperform the uncoded scheme and previous parametric mappings for broadcast channels with infinite resolution ADC front ends. The nonparametric mappings succeed in outperforming the parametric mappings. The causes for the differences between the performances of two nonparametric mappings are analyzed. The average distortions of the parametric and nonparametric mappings proposed here are close to the bound for the cases with one-bit ADC front ends in low channel signal-to-noise ratio regions.

Uplink-Downlink Duality Between Multiple-Access and Broadcast Channels With Compressing Relays

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.

On the Capacity Enlargement of Gaussian Broadcast Channels With Passive Noisy Feedback

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.

The Broadcast Channel With Degraded Message Sets and Unreliable Conference

It has long been observed that cooperation between users in a communication network can improve its performance. Unfortunately, in practical ad-hoc networks, cooperation links can be unreliable, and in many cases part of the users in the system cannot be updated about their availability. In such a case we need robust coding schemes that exploit the cooperation links if they are present, but can still operate if cooperation is not possible. In this work we study the general broadcast channel with degraded message sets and cooperation link that may be absent, and derive its capacity region under such uncertainty conditions. A generalization of this model is studied, where the cooperation link capacity is one of k possible values, and its capacity region is derived. We examine the situation where the cooperation link capacity is random and suggest the following performance criterion: maximize the average rate of one user, subject to a constraint on the rate of the other user and the requirement that the system will operate in any realization of the (random) cooperation link. As examples to illustrate our results, the Gaussian broadcast channel is extensively examined, and its capacity is derived for the various cooperation models and assumptions suggested throughout.

Secret Key Generation From Vector Gaussian Sources With Public and Private Communications

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.

Fundamental Limits of Wireless Caching Under Mixed Cacheable and Uncacheable Traffic

We consider cache-aided wireless communication scenarios where each user requests both a file from an a-priori generated cacheable library (referred to as ‘content’), and an uncacheable ‘non-content’ message generated at the start of the wireless transmission session. This scenario is easily found in real-world wireless networks, where the two types of traffic coexist and share limited radio resources. We focus on single-transmitter, single-antenna wireless networks with cache-aided receivers, where the wireless channel is modelled by a degraded Gaussian broadcast channel (GBC). For this setting, we study the delay-rate trade-off, which characterizes the content delivery time and non-content communication rates that can be achieved simultaneously. We propose a scheme based on the separation principle, which isolates the coded caching and multicasting problem from the physical layer transmission problem. We show that this separation-based scheme is sufficient for achieving an information-theoretically order-optimal performance, up to a multiplicative factor of 2.01 for the content delivery time, when working in the generalized degrees of freedom (GDoF) limit. We further show that the achievable performance is near-optimal after relaxing the GDoF limit, up to an additional additive factor of 2 bits per dimension for the non-content rates. A key insight emerging from our scheme is that in some scenarios considerable amounts of non-content traffic can be communicated while maintaining the minimum content delivery time, achieved in the absence of non-content messages; compliments of ‘topological holes’ arising from asymmetries in wireless channel gains.

Fundamental Limits of Non-Orthogonal Multiple Access (NOMA) for the Massive Gaussian Broadcast Channel in Finite Block-Length.

Superposition coding (SC) has been known to be capacity-achieving for the Gaussian memoryless broadcast channel for more than 30 years. However, SC regained interest in the context of non-orthogonal multiple access (NOMA) in 5G. From an information theory point of view, SC is capacity-achieving in the broadcast Gaussian channel, even when the number of users tends to infinity. However, using SC has two drawbacks: the decoder complexity increases drastically with the number of simultaneous receivers, and the latency is unbounded since SC is optimal only in the asymptotic regime. To evaluate these effects quantitatively in terms of fundamental limits, we introduce a finite time transmission constraint imposed at the base station, and we evaluate fundamental trade-offs between the maximal number of superposed users, the coding block-length and the block error probability. The energy efficiency loss due to these constraints is evaluated analytically and by simulation. Orthogonal sharing appears to outperform SC for hard delay constraints (equivalent to short block-length) and in low spectral efficiency regime (below one bit per channel use). These results are obtained by the association of stochastic geometry and finite block-length information theory.

Sparse Non-Orthogonal Frequency Division Multiplexing for Secure Transmission Over Broadcast Channels

We propose a novel transmission scheme for the parallel Gaussian broadcast channel with confidential messages (BCCM). In this model, The source node wishes to transmit a confidential message to each user over N independent sub-channels, where each sub-channel is degraded for one user than others. Our objective is to design a secure transmission technique that maximizes the sum secrecy rate under an average power constraint. The most common technique to tackle this problem in practice is orthogonal frequency division multiplexing (OFDM). Nevertheless, the OFDM-based BCCM suffers from excessive bandwidth utilization due to the sub-carrier orthogonality requirement. We propose a sparse non-orthogonal frequency-division Multiplexing (SNOFDM) transmission scheme. In SNOFDM, sub-carriers are generated by first selecting a subset of orthogonal sub-channels to reduce spectral resources. Then, the selected sub-channels are multiplexed in time to generate non-orthogonal sub-carriers. This, in effect increases, the spectral efficiency compared to OFDM. To overcome the interference introduced due to the non-orthogonality of sub-carriers, the transmitter sends the sparsest representation of the transmitted codeword. Furthermore, we provide a sub-carrier selection and power control procedures to maximize the sum rate of SNOFDM according to CSI fed back from receivers to source node. Our numerical results show that SNOFDM offers better spectral efficiency and a higher secrecy rate compared to OFDM. We provide extensive simulation results to study the effects of transmission parameters of SNOFDM on the achievable secrecy rate.

Beyond Dirty Paper Coding for Multi-Antenna Broadcast Channel With Partial CSIT: A Rate-Splitting Approach

Imperfect Channel State Information at the Transmitter (CSIT) is inevitable in modern wireless communication networks, and results in severe multi-user interference in multi-antenna Broadcast Channel (BC). While the capacity of multi-antenna (Gaussian) BC with perfect CSIT is known and achieved by Dirty Paper Coding (DPC), the capacity and the capacity-achieving strategy of multi-antenna BC with imperfect CSIT remain unknown. Conventional approaches therefore rely on applying communication strategies designed for perfect CSIT to the imperfect CSIT setting. In this work, we break this conventional routine and make two major contributions. First, we show that linearly precoded Rate-Splitting (RS), relying on the split of messages into common and private parts and linear precoding at the transmitter, and successive interference cancellation at the receivers, can achieve larger rate region than DPC in multi-antenna BC with partial CSIT. Second, we propose a novel scheme, denoted as Dirty Paper Coded Rate-Splitting (DPCRS), that relies on RS to split the user messages into common and private parts, and DPC to encode the private parts. We show that the rate region of DPCRS in Multiple-Input Single-Output (MISO) BC with partial CSIT is enlarged beyond that of conventional DPC and that of linearly precoded RS. Gaining benefits from the capability of RS to partially decode the interference and partially treat interference as noise, DPCRS is less sensitive to CSIT inaccuracies, networks loads and user deployments compared with DPC and other existing transmission strategies.

New Capacity Results for Fading Gaussian Multiuser Channels With Statistical CSIT

In this paper, fast fading Gaussian multiuser channels are considered. If the channel state information (CSI) is perfectly known to the transmitter, capacities have been derived for many cases in which the channels satisfy certain information-theoretic orders such as degradedness, or strong/very strong interference. We study the case when only the statistics of the CSI are known at the transmitter, which is an open problem in general. The main contributions of this paper are the following: First, we derive a sufficient condition to construct equivalent (having the same capacity region as the original channel) degraded Gaussian broadcast channels, which is based on the marginal distributions of the channel gains. To achieve this goal, we leverage three schemes: coupling, maximal coupling, and copulas, in addition to the same marginal property. The underlying idea of all schemes is to obtain an equivalent channel by changing the joint distribution in such a way that it satisfies a certain information-theoretic order while ensuring that the marginal distributions of the channels to different users are not changed. The construction of this equivalent multiuser channel allows us to directly apply existing capacity results. We then further derive the capacity regions of Gaussian interference channels with strong and very strong interferences, and also the secrecy capacity of Gaussian wiretap channels, while in all cases, the transmitters know only the statistics of the channels. Several practical examples such as Rayleigh fading and Nakagami- ${m}$ fading illustrate the applicability of the derived results.

On the Optimality of Treating Inter-Cell Interference as Noise: Downlink Cellular Networks and Uplink-Downlink Duality

We consider the information-theoretic optimality of treating inter-cell interference as noise (multi-cell TIN) in downlink cellular networks. We focus on scenarios modeled by the Gaussian interfering broadcast channel (IBC), comprising $K$ mutually interfering Gaussian broadcast channels (BCs), each formed by a base station communicating independent messages to an arbitrary number of users. We establish a new power allocation duality between the IBC and its dual interfering multiple access channel (IMAC), which entails that the corresponding generalized degrees-of-freedom regions achieved through multi-cell TIN and power control (TINA regions) for both networks are identical. As by-products of this duality, we obtain an explicit characterization of the IBC TINA region from a previously established characterization of the IMAC TINA region; and identify a multi-cell convex-TIN regime in which the IBC TINA region is a polyhedron (hence convex) without the need for time-sharing. We then identify a smaller multi-cell TIN regime in which the IBC TINA region is optimal and multi-cell TIN achieves the entire capacity region of the IBC, up to a constant gap. This is accomplished by deriving a new genie-aided outer bound for the IBC, that reveals a novel BC-type order that holds amongst users in each constituent BC (or cell) under inter-cell interference, which in turn is not implied by previously known BC-type orders (i.e. degraded, less noisy and more capable orders). The multi-cell TIN regime that we identify for the IBC coincides with a corresponding multi-cell TIN regime previously identified for the IMAC, hence establishing a comprehensive uplink-downlink duality of multi-cell TIN in the GDoF (and approximate capacity) sense.

The Distortions Region of Broadcasting Correlated Gaussians and Asymmetric Data Transmission Over a Gaussian BC

A memoryless bivariate Gaussian source is transmitted to a pair of receivers over an average-power limited bandwidth-matched Gaussian broadcast channel. Based on their observations, Receiver 1 reconstructs the first source component while Receiver 2 reconstructs the second source component both seeking to minimize the expected squared-error distortions. In addition to the source transmission digital information at a specified rate should be conveyed reliably to Receiver 1–the “stronger” receiver. Given the message rate we characterize the achievable distortions region. Specifically, there is an ${\sf SNR}$ -threshold below which Dirty Paper coding of the digital information against a linear combination of the source components is optimal. The threshold is a function of the digital information rate, the source correlation and the distortion at the “stronger” receiver. Above this threshold a Dirty Paper coding extension of the Tian-Diggavi-Shamai hybrid scheme is shown to be optimal.

Centralized Caching and Delivery of Correlated Contents Over Gaussian Broadcast Channels

Content delivery in a multi-user cache-aided broadcast network is studied, where a server holding a database of correlated contents communicates with the users over a Gaussian broadcast channel (BC). The minimum transmission power required to satisfy all possible demand combinations is studied, when the users are equipped with caches of equal size. Assuming uncoded cache placement, a lower bound on the required transmit power as a function of the cache capacity is derived. An achievable centralized caching scheme is proposed, which not only utilizes the user's local caches, but also exploits the correlation among the contents in the database. The performance of the scheme, which provides an upper bound on the required transmit power for a given cache capacity, is characterized. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussain BC can provide significant energy savings.

A Rotation-Based Precoding for MIMO Broadcast Channels With Integrated Services

The problem of merging multiple services over multiple-input multiple-output Gaussian broadcast channels with two receivers is studied. The transmitter provides two independent services: a public (multicast) service with a common message for both users, and a private service with a confidential message intended only for one of the users which is to be kept secret from the other. Under this scenario, a new linear precoding scheme is developed to maximize secrecy-multicast rate region. This scheme decomposes input covariance matrix using rotation matrices and results in a reformulation of the secrecy-multicast capacity region which is easier to be optimized. Next, by finding the distributions to which eigenvalues and rotation angles fit in, a search algorithm is proposed to solve the new capacity expression to find precoding and power allocation matrices. Numerical results illustrate that the proposed precoding method significantly increases the rate region compared to the existing methods.

Source Broadcasting and Asymmetric Data Transmission With Bandwidth Expansion

We consider the broadcasting of a scalar memoryless Gaussian source over a two-user Gaussian broadcast channel with bandwidth expansion. In concurrent with the source description, a message that should be decoded reliably just by the “higher quality” user is sent. Conditioned on the message rate, we derive a necessary condition for the achievability of a mean-squared-error distortion pair at the two receivers, which extends the Reznic–Feder–Zamir bound. This necessary condition and a sufficient condition that we derive establish the set of achievable energy-distortion exponents for this setting.