arXiv subjects

Shlomo Shamai

Publications and source records attributed to Shlomo Shamai.

At least 73 records · Page 4Linked to original sources

arXiv2021

Computable Upper Bounds on the Capacity of Finite-State Channels

We consider the use of the well-known dual capacity bounding technique for deriving upper bounds on the capacity of indecomposable finite-state channels (FSCs) with finite input and output alphabets. In this technique, capacity upper bounds are obtained by choosing suitable test distributions on the sequence of channel outputs. We propose test distributions that arise from certain graphical structures called Q-graphs. As we show in this paper, the advantage of this choice of test distribution is that, for the important classes of unifilar and input-driven FSCs, the resulting upper bounds can be formulated as dynamic programming (DP) problem, which makes the bounds tractable. We illustrate this for several examples of FSCs, where we are able to solve the associated DP problems explicitly to obtain capacity upper bounds that either match or beat the best previously reported bounds. For instance, for the classical trapdoor channel, we improve the best known upper bound of 0.66$ (due to Lutz (2014)) to 0.584, shrinking the gap to the best known lower bound of 0.572, all bounds being in units of bits per channel use.

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arXiv2021

Cooperative Encoding and Decoding of Mixed Delay Traffic under Random-User Activity

This paper analyses the multiplexing gain (MG) achievable over Wyner's symmetric network with random user activity and random arrival of mixed-delay traffic. The mixed-delay traffic is composed of delay-tolerant traffic and delay-sensitive traffic where only the former can benefit from transmitter and receiver cooperation since the latter is subject to stringent decoding delays. The total number of cooperation rounds at transmitter and receiver sides is limited to $\D$ rounds. We derive inner and outer bounds on the MG region. In the limit as $\D\to \infty$, the bounds coincide and the results show that transmitting delay-sensitive messages does not cause any penalty on the sum MG. For finite $\D$ our bounds are still close and prove that the penalty caused by delay-sensitive transmissions is small.

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arXiv2021

Information Bottleneck for an Oblivious Relay with Channel State Information: the Vector Case

This paper considers the information bottleneck (IB) problem of a Rayleigh fading multiple-input multiple-out (MIMO) channel. Due to the bottleneck constraint, it is impossible for the oblivious relay to inform the destination node of the perfect channel state information (CSI) in each channel realization. To evaluate the bottleneck rate, we provide an upper bound by assuming that the destination node can get the perfect CSI at no cost and two 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.

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arXiv2021

Information Bottleneck for a Rayleigh Fading MIMO Channel with an Oblivious Relay

This paper considers the information bottleneck (IB) problem of a Rayleigh fading multiple-input multiple-out (MIMO) channel with an oblivious relay. The relay is constrained to operate without knowledge of the codebooks, i.e., it performs oblivious processing. Moreover, due to the bottleneck constraint, it is impossible for the relay to inform the destination node of the perfect channel state information (CSI) in each channel realization. To evaluate the bottleneck rate, we first provide an upper bound by assuming that the destination node can get the perfect CSI at no cost. Then, we provide four achievable schemes where each scheme satisfies the bottleneck constraint and gives a lower bound to the bottleneck rate. In the first and second schemes, the relay splits the capacity of the relay-destination link into two parts, and conveys both the CSI and its observation to the destination node. Due to CSI transmission, the performance of these two schemes is sensitive to the MIMO channel dimension, especially the channel input dimension. To ensure that it still performs well when the channel dimension grows large, in the third and fourth achievable schemes, the relay only transmits compressed observation to the destination node. Numerical results show that with simple symbol-by-symbol oblivious relay processing and compression, the proposed achievable schemes work well and can demonstrate lower bounds coming quite close to the upper bound on a wide range of relevant system parameters.

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arXiv2021

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

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.

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arXiv2021

A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications

Consider a channel ${\bf Y}={\bf X}+ {\bf N}$ where ${\bf X}$ is an $n$-dimensional random vector, and ${\bf N}$ is a Gaussian vector with a covariance matrix ${\bf \mathsf{K}}_{\bf N}$. The object under consideration in this paper is the conditional mean of ${\bf X}$ given ${\bf Y}={\bf y}$, that is ${\bf y} \to E[{\bf X}|{\bf Y}={\bf y}]$. Several identities in the literature connect $E[{\bf X}|{\bf Y}={\bf y}]$ to other quantities such as the conditional variance, score functions, and higher-order conditional moments. The objective of this paper is to provide a unifying view of these identities. In the first part of the paper, a general derivative identity for the conditional mean is derived. Specifically, for the Markov chain ${\bf U} \leftrightarrow {\bf X} \leftrightarrow {\bf Y}$, it is shown that the Jacobian of $E[{\bf U}|{\bf Y}={\bf y}]$ is given by ${\bf \mathsf{K}}_{\bf N}^{-1} {\bf Cov} ( {\bf X}, {\bf U} | {\bf Y}={\bf y})$. In the second part of the paper, via various choices of ${\bf U}$, the new identity is used to generalize many of the known identities and derive some new ones. First, a simple proof of the Hatsel and Nolte identity for the conditional variance is shown. Second, a simple proof of the recursive identity due to Jaffer is provided. Third, a new connection between the conditional cumulants and the conditional expectation is shown. In particular, it is shown that the $k$-th derivative of $E[X|Y=y]$ is the $(k+1)$-th conditional cumulant. The third part of the paper considers some applications. In a first application, the power series and the compositional inverse of $E[X|Y=y]$ are derived. In a second application, the distribution of the estimator error $(X-E[X|Y])$ is derived. In a third application, we construct consistent estimators (empirical Bayes estimators) of the conditional cumulants from an i.i.d. sequence $Y_1,...,Y_n$.

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arXiv2021

Collaborative Cloud and Edge Mobile Computing in C-RAN Systems with Minimal End-to-End Latency

Mobile cloud and edge computing protocols make it possible to offer computationally heavy applications to mobile devices via computational offloading from devices to nearby edge servers or more powerful, but remote, cloud servers. Previous work assumed that computational tasks can be fractionally offloaded at both cloud processor (CP) and at a local edge node (EN) within a conventional Distributed Radio Access Network (D-RAN) that relies on non-cooperative ENs equipped with one-way uplink fronthaul connection to the cloud. In this paper, we propose to integrate collaborative fractional computing across CP and ENs within a Cloud RAN (C-RAN) architecture with finite-capacity two-way fronthaul links. Accordingly, tasks offloaded by a mobile device can be partially carried out at an EN and the CP, with multiple ENs communicating with a common CP to exchange data and computational outcomes while allowing for centralized precoding and decoding. Unlike prior work, we investigate joint optimization of computing and communication resources, including wireless and fronthaul segments, to minimize the end-to-end latency by accounting for a two-way uplink and downlink transmission. The problem is tackled by using fractional programming (FP) and matrix FP. Extensive numerical results validate the performance gain of the proposed architecture as compared to the previously studied D-RAN solution.

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arXiv2021

Single-RF Multi-User Communication Through Reconfigurable Intelligent Surfaces: An Information-Theoretic Analysis

Reconfigurable intelligent surfaces (RISs) are typically used in multi-user systems to mitigate interference among active transmitters. In contrast, this paper studies a setting with a conventional active encoder as well as a passive encoder that modulates the reflection pattern of the RIS. The RIS hence serves the dual purpose of improving the rate of the active encoder and of enabling communication from the second encoder. The capacity region is characterized, and information-theoretic insights regarding the trade-offs between the rates of the two encoders are derived by focusing on the high- and low-power regimes.

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arXiv2021

The Broadcast Approach in Communication Networks

This paper reviews the theoretical and practical principles of the broadcast approach to communication over state-dependent channels and networks in which the transmitters have access to only the probabilistic description of the time-varying states while remaining oblivious to their instantaneous realizations. When the temporal variations are frequent enough, an effective long-term strategy is adapting the transmission strategies to the system's ergodic behavior. However, when the variations are infrequent, their temporal average can deviate significantly from the channel's ergodic mode, rendering a lack of instantaneous performance guarantees. To circumvent a lack of short-term guarantees, the {\em broadcast approach} provides principles for designing transmission schemes that benefit from both short- and long-term performance guarantees. This paper provides an overview of how to apply the broadcast approach to various channels and network models under various operational constraints.

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arXiv2020

The Secrecy Capacity of Cost-Constrained Wiretap Channels

In many information-theoretic channel coding problems, adding an input cost constraint to the operational setup amounts to restricting the optimization domain in the capacity formula. This paper shows that, in contrast to common belief, such a simple modification does not hold for the cost-constrained (CC) wiretap channel (WTC). The secrecy-capacity of the discrete memoryless (DM) WTC without cost constraints is described by a single auxiliary random variable. For the CC DM-WTC, however, we show that two auxiliaries are necessary to achieve capacity. Specifically, we first derive the secrecy-capacity formula, proving the direct part via superposition coding. Then, we provide an example of a CC DM-WTC whose secrecy-capacity cannot be achieved using a single auxiliary. This establishes the fundamental role of superposition coding over CC WTCs.

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arXiv2020

Coordinated Multi Point Transmission and Reception for Mixed-Delay Traffic

This paper analyzes the multiplexing gains (MG) for simultaneous transmission of delay-sensitive and delay-tolerant data over interference networks. In the considered model, only delay-tolerant data can profit from coordinated multipoint (CoMP) transmission or reception techniques, because delay-sensitive data has to be transmitted without further delay. Transmission of delay-tolerant data is also subject to a delay constraint, which is however less stringent than the one on delay-sensitive data. Different coding schemes are proposed, and the corresponding MG pairs for delay-sensitive and delay-tolerant data are characterized for Wyner's linear symmetric network and for Wyner's two-dimensional hexagonal network with and without sectorization. For Wyner's linear symmetric also an information-theoretic converse is established and shown to be exact whenever the cooperation rates are sufficiently large or the delay-sensitive MG is small or moderate. These results show that on Wyner's symmetric linear network and for sufficiently large cooperation rates, the largest MG for delay-sensitive data can be achieved without penalizing the maximum sum-MG of both delay-sensitive and delay-tolerant data. A similar conclusion holds for Wyner's hexagonal network only for the model with sectorization. In the model without sectorization, a penalty in sum-MG is incurred whenever one insists on a positive delay-sensitive MG.

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arXiv2020

Adaptive Coding and Channel Shaping Through Reconfigurable Intelligent Surfaces: An Information-Theoretic Analysis

A communication link aided by a reconfigurable intelligent surface (RIS) is studied in which the transmitter can control the state of the RIS via a finite-rate control link. Channel state information (CSI) is acquired at the receiver based on pilot-assisted channel estimation, and it may or may not be shared with the transmitter. Considering quasi-static fading channels with imperfect CSI, capacity-achieving signalling is shown to implement joint encoding of the transmitted signal and of the response of the RIS. This demonstrates the information-theoretic optimality of RIS-based modulation, or "single-RF MIMO" systems. In addition, a novel signalling strategy based on separate layered encoding that enables practical successive cancellation-type decoding at the receiver is proposed. Numerical experiments show that the conventional scheme that fixes the reflection pattern of the RIS, irrespective of the transmitted information, as to maximize the achievable rate is strictly suboptimal, and is outperformed by the proposed adaptive coding strategies at all practical signal-to-noise ratio (SNR) levels.

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arXiv2020

On Sampling Continuous-Time AWGN Channels

For a continuous-time additive white Gaussian noise (AWGN) channel with possible feedback, it has been shown that as sampling gets infinitesimally fine, the mutual information of the associative discrete-time channels converges to that of the original continuous-time channel. We give in this paper more quantitative strengthenings of this result, which, among other implications, characterize how over-sampling approaches the true mutual information of a continuous-time Gaussian channel with bandwidth limit. The assumptions in our results are relatively mild. In particular, for the non-feedback case, compared to the Shannon-Nyquist sampling theorem, a widely used tool to connect continuous-time Gaussian channels to their discrete-time counterparts that requires the band-limitedness of the channel input, our results only require some integrability conditions on the power spectral density function of the input.

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arXiv2020

Canonical Conditions for K/2 Degrees of Freedom

We present a necessary and sufficient condition for $1/2$ degree of freedom for each user in constant $K$-user single-antenna interference channels. This condition applies to all channel topologies, i.e., to fully-connected channels as well as channels that have individual links absent, reflected by corresponding zeros in the channel matrix. Moreover, it captures the essence of interference alignment by virtue of being expressed in terms of a generic injectivity condition that guarantees separability of signal and interference. Finally, we provide codebook constructions achieving $1/2$ degree of freedom for each user for all channel matrices satisfying our condition.

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arXiv2020

Broadcast Approach for the Information Bottleneck Channel

This work considers a layered coding approach for efficient transmission of data over a wireless block fading channel without transmitter channel state information (CSI), which is connected to a limited capacity reliable link, known as the bottleneck channel. Two main approaches are considered, the first is an oblivious approach, where the sampled noisy observations are compressed and transmitted over the bottleneck channel without having any knowledge of the original information codebook. The second approach is a non-oblivious decode-forward (DF) relay where the sampled noisy data is decoded, and whatever is successfully decoded is reliably transmitted over the bottleneck channel. The bottleneck channel from relay to destination has a fixed capacity C. We examine also the case where the channel capacity can dynamically change due to variable loads on the backhaul link. The broadcast approach is analyzed for cases that only the relay knows the available capacity for next block, and for the case that neither source nor relay know the capacity per block, only its capacity distribution. Fortunately, it is possible to analytically describe in closed form expressions, the optimal continuous layering power distribution which maximizes the average achievable rate. Numerical results demonstrate the achievable broadcasting rates.

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arXiv2020

Optimizing Over-the-Air Computation in IRS-Aided C-RAN Systems

Over-the-air computation (AirComp) is an efficient solution to enable federated learning on wireless channels. AirComp assumes that the wireless channels from different devices can be controlled, e.g., via transmitter-side phase compensation, in order to ensure coherent on-air combining. Intelligent reflecting surfaces (IRSs) can provide an alternative, or additional, means of controlling channel propagation conditions. This work studies the advantages of deploying IRSs for AirComp systems in a large-scale cloud radio access network (C-RAN). In this system, worker devices upload locally updated models to a parameter server (PS) through distributed access points (APs) that communicate with the PS on finite-capacity fronthaul links. The problem of jointly optimizing the IRSs' reflecting phases and a linear detector at the PS is tackled with the goal of minimizing the mean squared error (MSE) of a parameter estimated at the PS. Numerical results validate the advantages of deploying IRSs with optimized phases for AirComp in C-RAN systems.

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arXiv2020

Rate Splitting for Multi-Antenna Downlink: Precoder Design and Practical Implementation

Rate splitting (RS) is a potentially powerful and flexible technique for multi-antenna downlink transmission. In this paper, we address several technical challenges towards its practical implementation for beyond 5G systems. To this end, we focus on a single-cell system with a multi-antenna base station (BS) and K single-antenna receivers. We consider RS in its most general form, and joint decoding to fully exploit the potential of RS. First, we investigate the achievable rates under joint decoding and formulate the precoder design problems to maximize a general utility function, or to minimize the transmit power under pre-defined rate targets. Building upon the concave-convex procedure (CCCP), we propose precoder design algorithms for an arbitrary number of users. Our proposed algorithms approximate the intractable non-convex problems with a number of successively refined convex problems, and provably converge to stationary points of the original problems. Then, to reduce the decoding complexity, we consider the optimization of the precoder and the decoding order under successive decoding. Further, we propose a stream selection algorithm to reduce the number of precoded signals. With a reduced number of streams and successive decoding at the receivers, our proposed algorithm can even be implemented when the number of users is relatively large, whereas the complexity was previously considered as prohibitively high in the same setting. Finally, we propose a simple adaptation of our algorithms to account for the imperfection of the channel state information at the transmitter. Numerical results demonstrate that the general RS scheme provides a substantial performance gain as compared to state-of-the-art linear precoding schemes, especially with a moderately large number of users.

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arXiv2020

On the Information Bottleneck Problems: Models, Connections, Applications and Information Theoretic Views

This tutorial paper focuses on the variants of the bottleneck problem taking an information theoretic perspective and discusses practical methods to solve it, as well as its connection to coding and learning aspects. The intimate connections of this setting to remote source-coding under logarithmic loss distortion measure, information combining, common reconstruction, the Wyner-Ahlswede-Korner problem, the efficiency of investment information, as well as, generalization, variational inference, representation learning, autoencoders, and others are highlighted. We discuss its extension to the distributed information bottleneck problem with emphasis on the Gaussian model and highlight the basic connections to the uplink Cloud Radio Access Networks (CRAN) with oblivious processing. For this model, the optimal trade-offs between relevance (i.e., information) and complexity (i.e., rates) in the discrete and vector Gaussian frameworks is determined. In the concluding outlook, some interesting problems are mentioned such as the characterization of the optimal inputs ("features") distributions under power limitations maximizing the "relevance" for the Gaussian information bottleneck, under "complexity" constraints.

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