arXiv subjects

Shlomo Shamai

Publications and source records attributed to Shlomo Shamai.

At least 55 records · Page 3Linked to original sources

arXiv2022

On Information Bottleneck for Gaussian Processes

The information bottleneck problem (IB) of jointly stationary Gaussian sources is considered. A water-filling solution for the IB rate is given in terms of its SNR spectrum and whose rate is attained via frequency domain test-channel realization. A time-domain realization of the IB rate, based on linear prediction, is also proposed, which lends itself to an efficient implementation of the corresponding remote source-coding problem. A compound version of the problem is addressed, in which the joint distribution of the source is not precisely specified but rather in terms of a lower bound on the guaranteed mutual information. It is proved that a white SNR spectrum is optimal for this setting.

cs.IT↗

arXiv2022

Distributed Computations with Layered Resolution

Modern computationally-heavy applications are often time-sensitive, demanding distributed strategies to accelerate them. On the other hand, distributed computing suffers from the bottleneck of slow workers in practice. Distributed coded computing is an attractive solution that adds redundancy such that a subset of distributed computations suffices to obtain the final result. However, the final result is still either obtained within a desired time or not, and for the latter, the resources that are spent are wasted. In this paper, we introduce the novel concept of layered-resolution distributed coded computations such that lower resolutions of the final result are obtained from collective results of the workers -- at an earlier stage than the final result. This innovation makes it possible to have more effective deadline-based systems, since even if a computational job is terminated because of timing, an approximated version of the final result can be released. Based on our theoretical and empirical results, the average execution delay for the first resolution is notably smaller than the one for the final resolution. Moreover, the probability of meeting a deadline is one for the first resolution in a setting where the final resolution exceeds the deadline almost all the time, reducing the success rate of the systems with no layering.

cs.DC↗

arXiv2022

Distributed Information Bottleneck for a Primitive Gaussian Diamond Channel with Rayleigh Fading

This paper considers the distributed information bottleneck (D-IB) problem for a primitive Gaussian diamond channel with two relays and Rayleigh fading. Due to the bottleneck constraint, it is impossible for the relays to inform the destination node of the perfect channel state information (CSI) in each realization. To evaluate the bottleneck rate, we provide an upper bound by assuming that the destination node knows the CSI and the relays can cooperate with each other, and also three achievable schemes with simple symbol-by-symbol relay processing and compression. Numerical results show that the lower bounds obtained by the proposed achievable schemes can come close to the upper bound on a wide range of relevant system parameters.

cs.IT↗

arXiv2022

Joint Coding of URLLC and eMBB in Wyner's Soft-Handoff Network in the Finite Blocklength Regime

Wyner's soft-handoff network is considered where transmitters simultaneously send messages of enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC) services. Due to the low-latency requirements, the URLLC messages are transmitted over fewer channel uses compared to the eMBB messages. To improve the reliability of the URLLC transmissions, we propose a coding scheme with finite blocklength codewords that exploits dirty-paper coding (DPC) to precancel the interference from eMBB transmissions. Rigorous bounds are derived for the error probabilities of eMBB and URLLC transmissions achieved by our scheme. Numerical results illustrate that they are lower than for standard time-sharing.

cs.IT↗

arXiv2022

An Optimization Framework for General Rate Splitting for General Multicast

Immersive video, such as virtual reality (VR) and multi-view videos, is growing in popularity. Its wireless streaming is an instance of general multicast, extending conventional unicast and multicast, whose effective design is still open. This paper investigates general rate splitting for general multicast. Specifically, we consider a multi-carrier single-cell wireless network where a multi-antenna base station (BS) communicates to multiple single-antenna users via general multicast. We consider linear beamforming at the BS and joint decoding at each user in the slow fading and fast fading scenarios. In the slow fading scenario, we consider the maximization of the weighted sum average rate, which is a challenging nonconvex stochastic problem with numerous variables. To reduce computational complexity, we decouple the original nonconvex stochastic problem into multiple nonconvex deterministic problems, one for each system channel state. Then, we propose an iterative algorithm for each deterministic problem to obtain a Karush-Kuhn-Tucker (KKT) point using the concave-convex procedure (CCCP). In the fast fading scenario, we consider the maximization of the weighted sum ergodic rate. This problem is more challenging than the one for the slow fading scenario, as it is not separable. First, we propose a stochastic iterative algorithm to obtain a KKT point using stochastic successive convex approximation (SSCA) and the exact penalty method. Then, we propose two low-complexity iterative algorithms to obtain feasible points with promising performance for two cases of channel distributions using approximation and CCCP. The proposed optimization framework generalizes the existing ones for rate splitting for various types of services. Finally, we numerically show substantial gains of the proposed solutions over existing schemes in both scenarios.

cs.IT↗

arXiv2022

The Compound Information Bottleneck Outlook

We formulate and analyze the compound information bottleneck programming. In this problem, a Markov chain $ \mathsf{X} \rightarrow \mathsf{Y} \rightarrow \mathsf{Z} $ is assumed with fixed marginal distributions $\mathsf{P}_{\mathsf{X}}$ and $\mathsf{P}_{\mathsf{Y}}$, and the mutual information between $ \mathsf{X} $ and $ \mathsf{Z} $ is sought to be maximized over the choice of conditional probability of $\mathsf{Z}$ given $\mathsf{Y}$ from a given class, under the \textit{worst choice} of the joint probability of the pair $(\mathsf{X},\mathsf{Y})$ from a different class. We consider several classes based on extremes of: mutual information; minimal correlation; total variation; and the relative entropy class. We provide values, bounds, and various characterizations for specific instances of this problem: the binary symmetric case, the scalar Gaussian case, the vector Gaussian case and the symmetric modulo-additive case. Finally, for the general case, we propose a Blahut-Arimoto type of alternating iterations algorithm to find a consistent solution to this problem.

cs.IT↗

arXiv2022

Bounds on the Capacity of the Multiple Access Diamond Channel with Cooperating Base-Stations

A diamond network is considered in which the central processor is connected, via backhaul noiseless links, to multiple conferencing base stations, which communicate with a single user over a multiple access channel. We propose coding techniques along with lower and upper bounds on the capacity. Our achievability scheme uses a common cloud coding strategy based on the technique proposed by Wand, Wigger, and Zaidi (2018) and extends it beyond two relays. Our upper bounds generalize the method proposed by Bidokhti and Kramer for the two relay diamond network without cooperation (2016) and lead to new bounds for the multiple relay setting. Specializing our upper bounds for the two relay scenario (with cooperation), we provide new bounds and improve state-of-the-art.

cs.IT↗

arXiv2022

An Information-Theoretic View of Mixed-Delay Traffic in 5G and 6G

Fifth generation mobile communication systems (5G) have to accommodate both Ultra-Reliable Low-Latency Communication (URLLC) and enhanced Mobile Broadband (eMBB) services. While, eMBB applications support high data rates, URLLC services aim at guaranteeing low-latencies and high-reliabilities. eMBB and URLLC services are scheduled on the same frequency band, where the different latency requirements of the communications render the coexistence challenging. In this survey, we review, from an information theoretic perspective, coding schemes that simultaneously accommodate URLLC and eMBB transmissions and show that they outperform traditional scheduling approaches. Various communication scenarios are considered, including point-to-point channels, broadcast channels, interference networks, cellular models, and cloud radio access networks (C-RANs). The main focus is on the set of rate pairs that can simultaneously be achieved for URLLC and eMBB messages, which well captures the tension between the two types of communications. We also discuss finite-blocklength results where the measure of interest is the set of error probability pairs that can simultaneously be achieved on the two communication regimes.

cs.IT↗

arXiv2022

Robust Design of Rate-Splitting Multiple Access With Imperfect CSI for Cell-Free MIMO Systems

Rate-Splitting Multiple Access (RSMA) for multi-user downlink operates by splitting the message for each user equipment (UE) into a private message and a set of common messages, which are simultaneously transmitted by means of superposition coding. The RSMA scheme can enhance throughput and connectivity as compared to conventional multiple access techniques by optimizing the rate-splitting ratios along with the corresponding downlink beamforming vectors. This work examines the impact of erroneous channel state information (CSI) on the performance of RSMA in cell-free multiple-input multiple-output (MIMO) systems. An efficient robust optimization algorithm is proposed by using closed-form lower bound expressions on the expected data rates. Extensive numerical results show the importance of robust design in the presence of CSI errors and how the performance gain of RSMA over conventional schemes is affected by CSI imperfection.

eess.SP↗

arXiv2022

A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits the use of popular algorithms such as projected gradient ascent to find least favorable priors. Throughout the paper, in order to make progress on the problem, we restrict ourselves to Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.

stat.ML↗

arXiv2022

Broadcast Approach Meets Network Coding for Data Streaming

For data streaming applications, existing solutions are not yet able to close the gap between high data rates and low delay. This work considers the problem of data streaming under mixed delay constraints over a single communication channel with delayed feedback. We propose a novel layered adaptive causal random linear network coding (LAC-RLNC) approach with forward error correction. LAC-RLNC is a variable-to-variable coding scheme, i.e., variable recovered information data at the receiver over variable short block length and rate is proposed. Specifically, for data streaming with base and enhancement layers of content, we characterize a high dimensional throughput-delay trade-off managed by the adaptive causal layering coding scheme. The base layer is designed to satisfy the strict delay constraints, as it contains the data needed to allow the streaming service. Then, the sender can manage the throughput-delay trade-off of the second layer by adjusting the retransmission rate a priori and posterior as the enhancement layer, that contains the remaining data to augment the streaming service's quality, is with the relax delay constraints. We numerically show that the layered network coding approach can dramatically increase performance. We demonstrate that LAC-RLNC compared with the non-layered approach gains a factor of three in mean and maximum delay for the base layer, close to the lower bound, and factor two for the enhancement layer.

cs.IT↗

arXiv2022

Rate Splitting for General Multicast

cs.IT↗

arXiv2021

Learning to Broadcast for Ultra-Reliable Communication with Differential Quality of Service via the Conditional Value at Risk

Broadcast/multicast communication systems are typically designed to optimize the outage rate criterion, which neglects the performance of the fraction of clients with the worst channel conditions. Targeting ultra-reliable communication scenarios, this paper takes a complementary approach by introducing the conditional value-at-risk (CVaR) rate as the expected rate of a worst-case fraction of clients. To support differential quality-of-service (QoS) levels in this class of clients, layered division multiplexing (LDM) is applied, which enables decoding at different rates. Focusing on a practical scenario in which the transmitter does not know the fading distribution, layer allocation is optimized based on a dataset sampled during deployment. The optimality gap caused by the availability of limited data is bounded via a generalization analysis, and the sample complexity is shown to increase as the designated fraction of worst-case clients decreases. Considering this theoretical result, meta-learning is introduced as a means to reduce sample complexity by leveraging data from previous deployments. Numerical experiments demonstrate that LDM improves spectral efficiency even for small datasets; that, for sufficiently large datasets, the proposed mirror-descent-based layer optimization scheme achieves a CVaR rate close to that achieved when the transmitter knows the fading distribution; and that meta-learning can significantly reduce data requirements.

cs.IT↗

arXiv2021

Self-Secure Capacity-Achieving Feedback Schemes of Gaussian Multiple-Access Wiretap Channels with Degraded Message Sets

The Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the point-to-point white Gaussian channel with feedback, is secure by itself and also achieves the secrecy capacity of the Gaussian wiretap channel with feedback, i.e., the SK scheme is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel. For the multi-user wiretap channels, recently, it has been shown that Ozarow's capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel (GMAC-WT). In this paper, first, we propose a capacity-achieving feedback scheme for the two-user GMAC with degraded message sets (GMAC-DMS), and show that this scheme is the SSCA feedback scheme for the two-user GMAC-WT with degraded message sets (GMAC-WT-DMS). Next, we extend the above scheme to the two-user GMAC-DMS with noncausal channel state information at the transmitters (NCSIT), and show that the extended scheme is capacity-achieving and also a SSCA feedback scheme for the two-user GMAC-WT-DMS with NCSIT. Finally, we derive outer bounds on the secrecy capacity regions of the two-user GMAC-WT-DMS with or without NCSIT, and numerical results show the rate gains by the feedback.

cs.IT↗

arXiv2021

On information rates over a binary input channel

We study communication systems over band-limited Additive White Gaussian Noise (AWGN) channels in which the transmitter output is constrained to be symmetric binary (bi-polar). In this work we improve the original Ozarov-Wyner-Ziv (OWZ) lower bound on capacity by introducing new achievability schemes with two advantages over the studied OWZ scheme which is based on peak-power constrained pulse-amplitude modulation. Our schemes achieve a moderately improved information rate and do so with much less sign transitions of the binary signal. The gap between the known upper-bound based on spectral constrains of bi-polar signals and our achievable lower bound is reduced to 0.93 bits per Nyquist interval at high SNR.

cs.IT↗

arXiv2021

A Class of Nonbinary Symmetric Information Bottleneck Problems

We study two dual settings of information processing. Let $ \mathsf{Y} \rightarrow \mathsf{X} \rightarrow \mathsf{W} $ be a Markov chain with fixed joint probability mass function $ \mathsf{P}_{\mathsf{X}\mathsf{Y}} $ and a mutual information constraint on the pair $ (\mathsf{W},\mathsf{X}) $. For the first problem, known as Information Bottleneck, we aim to maximize the mutual information between the random variables $ \mathsf{Y} $ and $ \mathsf{W} $, while for the second problem, termed as Privacy Funnel, our goal is to minimize it. In particular, we analyze the scenario for which $ \mathsf{X} $ is the input, and $ \mathsf{Y} $ is the output of modulo-additive noise channel. We provide analytical characterization of the optimal information rates and the achieving distributions.

cs.IT↗

arXiv2021

The Filtered Gaussian Primitive Diamond Channel

We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response from the user to the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. It is proved that optimal CF-DF time sharing is advantageous over superposition of CF and DF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.

cs.IT↗

arXiv2021

Properties of the Support of the Capacity-Achieving Distribution of the Amplitude-Constrained Poisson Noise Channel

This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bounds on the number of mass points. Concretely, an upper bound of order $\mathsf{A} \log^2(\mathsf{A})$ and a lower bound of order $\sqrt{\mathsf{A}}$ are established where $\mathsf{A}$ is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For example, it is shown that the capacity is equal to $ - \log P_{Y^\star}(0)$ where $P_{Y^\star}$ is the optimal output distribution. Moreover, an upper bound on the values of the probability masses of the capacity-achieving distribution and a lower bound on the probability of the largest mass point are established. Furthermore, on the per-symbol basis, a nonvanishing lower bound on the probability of error for detecting the capacity-achieving distribution is established under the maximum a posteriori rule.

cs.IT↗