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Shlomo Shamai

Publications and source records attributed to Shlomo Shamai.

At least 181 records · Page 10Linked to original sources
arXiv2013

Worst-Case Expected-Capacity Loss of Slow-Fading Channels

For delay-limited communication over block-fading channels, the difference between the ergodic capacity and the maximum achievable expected rate for coding over a finite number of coherent blocks represents a fundamental measure of the penalty incurred by the delay constraint. This paper introduces a notion of worst-case expected-capacity loss. Focusing on the slow-fading scenario (one-block delay), the worst-case additive and multiplicative expected-capacity losses are precisely characterized for the point-to-point fading channel. Extension to the problem of writing on fading paper is also considered, where both the ergodic capacity and the additive expected-capacity loss over one-block delay are characterized to within one bit per channel use.

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arXiv2012

MAC with Action-Dependent State Information at One Encoder

Problems dealing with the ability to take an action that affects the states of state-dependent communication channels are of timely interest and importance. Therefore, we extend the study of action-dependent channels, which until now focused on point-to-point models, to multiple-access channels (MAC). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: a common message known to both encoders and a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a non-causal manner. Our framework generalizes previously evaluated settings of state dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The unique methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel; a problem was left open until this work. Finally, we establish some dualities between action-dependent channel coding and source coding problems. Specifically, we obtain a duality between the considered MAC setting and the rate distortion model known as "Successive Refinement with Actions". This is done by developing a set of simple duality principles that enable us to successfully evaluate the outcome of one problem given the other.

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arXiv2012

Minimum CSIT to achieve Maximum Degrees of Freedom for the MISO BC

Channel state information at the transmitter (CSIT) is a key ingredient in realizing the multiplexing gain provided by distributed MIMO systems. For a downlink multiple-input single output (MISO) broadcast channel, with M antennas at the transmitters and K single antenna receivers, the maximum multiplexing gain or the maximum degrees of freedom (DoF) is min(M,K). The optimal DoF of min(M,K) is achievable if the transmitter has access to perfect, instantaneous CSIT from all receivers. In this paper, we pose the question that what is minimum amount of CSIT required per user in order to achieve the maximum DoF of min(M,K). By minimum amount of CSIT per user, we refer to the minimum fraction of time that the transmitter has access to perfect and instantaneous CSIT from a user. Through a novel converse proof and an achievable scheme, it is shown that the minimum fraction of time, perfect CSIT is required per user in order to achieve the DoF of min(M,K) is given by min(M,K)/K.

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arXiv2012

Degrees of Freedom Region of the MIMO Interference Channel with Output Feedback and Delayed CSIT

The two-user multiple-input multiple-output (MIMO) interference channel (IC) with arbitrary number of antennas at each terminal is considered and the degrees of freedom (DoF) region is characterized in the presence of noiseless channel output feedback from each receiver to its respective transmitter and availability of delayed channel state information at the transmitters (CSIT). It is shown that having output feedback and delayed CSIT can strictly enlarge the DoF region of the MIMO IC when compared to the case in which only delayed CSIT is present. The proposed coding schemes that achieve the corresponding DoF region with feedback and delayed CSIT utilize both resources, i.e., feedback and delayed CSIT in a non-trivial manner. It is also shown that the DoF region with local feedback and delayed CSIT is equal to the DoF region with global feedback and delayed CSIT, i.e., local feedback and delayed CSIT is equivalent to global feedback and delayed CSIT from the perspective of the degrees of freedom region. The converse is proved for a stronger setting in which the channels to the two receivers need not be statistically equivalent.

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arXiv2012

Support Recovery with Sparsely Sampled Free Random Matrices

Consider a Bernoulli-Gaussian complex $n$-vector whose components are $V_i = X_i B_i$, with $X_i \sim \Cc\Nc(0,\Pc_x)$ and binary $B_i$ mutually independent and iid across $i$. This random $q$-sparse vector is multiplied by a square random matrix $\Um$, and a randomly chosen subset, of average size $n p$, $p \in [0,1]$, of the resulting vector components is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where $\Um$ is typically %A16 the identity or a matrix with iid components, to allow $\Um$ satisfying a certain freeness condition. This class of matrices encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verdú, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate in the limit of $n \to \infty$. We also extend the scope of the large deviation approach of Rangan, Fletcher and Goyal and characterize the performance of a class of estimators encompassing thresholded linear MMSE and $\ell_1$ relaxation.

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arXiv2012

On the Synergistic Benefits of Alternating CSIT for the MISO BC

The degrees of freedom (DoF) of the two-user multiple-input single-output (MISO) broadcast channel (BC) are studied under the assumption that the form, I_i, i=1,2, of the channel state information at the transmitter (CSIT) for each user's channel can be either perfect (P), delayed (D) or not available (N), i.e., I_1 and I_2 can take values of either P, D or N, and therefore the overall CSIT can alternate between the 9 resulting states, each state denoted as I_1I_2. The fraction of time associated with CSIT state I_1I_2 is denoted by the parameter λ_{I_1I_2} and it is assumed throughout that λ_{I_1I_2}=λ_{I_2I_1}, i.e., λ_{PN}=λ_{NP}, λ_{PD}=λ_{DP}, λ_{DN}=λ_{ND}. Under this assumption of symmetry, the main contribution of this paper is a complete characterization of the DoF region of the two user MISO BC with alternating CSIT. Surprisingly, the DoF region is found to depend only on the marginal probabilities (λ_P, λ_D,λ_N)=(\sum_{I_2}λ_{PI_2},\sum_{I_2}λ_{DI_2}, \sum_{I_2}λ_{NI_2}), I_2\in {P,D,N}, which represent the fraction of time that any given user (e.g., user 1) is associated with perfect, delayed, or no CSIT, respectively. As a consequence, the DoF region with all 9 CSIT states, \mathcal{D}(λ_{I_1I_2}:I_1,I_2\in{P,D,N}), is the same as the DoF region with only 3 CSIT states \mathcal{D}(λ_{PP}, λ_{DD}, λ_{NN}), under the same marginal distribution of CSIT states, i.e., (λ_{PP}, λ_{DD},λ_{NN})=(λ_P,λ_D,λ_N). The results highlight the synergistic benefits of alternating CSIT and the tradeoffs between various forms of CSIT for any given DoF value.

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arXiv2012

MMSE of "Bad" Codes

We examine codes, over the additive Gaussian noise channel, designed for reliable communication at some specific signal-to-noise ratio (SNR) and constrained by the permitted minimum mean-square error (MMSE) at lower SNRs. The maximum possible rate is below point-to-point capacity, and hence these are non-optimal codes (alternatively referred to as "bad" codes). We show that the maximum possible rate is the one attained by superposition codebooks. Moreover, the MMSE and mutual information behavior as a function of SNR, for any code attaining the maximum rate under the MMSE constraint, is known for all SNR. We also provide a lower bound on the MMSE for finite length codes, as a function of the error probability of the code.

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arXiv2012

Robust and Efficient Distributed Compression for Cloud Radio Access Networks

This work studies distributed compression for the uplink of a cloud radio access network where multiple multi-antenna base stations (BSs) are connected to a central unit, also referred to as cloud decoder, via capacity-constrained backhaul links. Since the signals received at different BSs are correlated, distributed source coding strategies are potentially beneficial, and can be implemented via sequential source coding with side information. For the problem of compression with side information, available compression strategies based on the criteria of maximizing the achievable rate or minimizing the mean square error are reviewed first. It is observed that, in either case, each BS requires information about a specific covariance matrix in order to realize the advantage of distributed source coding. Since this covariance matrix depends on the channel realizations corresponding to other BSs, a robust compression method is proposed for a practical scenario in which the information about the covariance available at each BS is imperfect. The problem is formulated using a deterministic worst-case approach, and an algorithm is proposed that achieves a stationary point for the problem. Then, BS selection is addressed with the aim of reducing the number of active BSs, thus enhancing the energy efficiency of the network. An optimization problem is formulated in which compression and BS selection are performed jointly by introducing a sparsity-inducing term into the objective function. An iterative algorithm is proposed that is shown to converge to a locally optimal point. From numerical results, it is observed that the proposed robust compression scheme compensates for a large fraction of the performance loss induced by the imperfect statistical information. Moreover, the proposed BS selection algorithm is seen to perform close to the more complex exhaustive search solution.

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arXiv2012

Minimum Expected Distortion in Gaussian Source Coding with Fading Side Information

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

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arXiv2012

On MMSE Properties and I-MMSE Implications in Parallel MIMO Gaussian Channels

The scalar additive Gaussian noise channel has the "single crossing point" property between the minimum-mean square error (MMSE) in the estimation of the input given the channel output, assuming a Gaussian input to the channel, and the MMSE assuming an arbitrary input. This paper extends the result to the parallel MIMO additive Gaussian channel in three phases: i) The channel matrix is the identity matrix, and we limit the Gaussian input to a vector of Gaussian i.i.d. elements. The "single crossing point" property is with respect to the snr (as in the scalar case). ii) The channel matrix is arbitrary, the Gaussian input is limited to an independent Gaussian input. A "single crossing point" property is derived for each diagonal element of the MMSE matrix. iii) The Gaussian input is allowed to be an arbitrary Gaussian random vector. A "single crossing point" property is derived for each eigenvalue of the MMSE matrix. These three extensions are then translated to new information theoretic properties on the mutual information, using the fundamental relationship between estimation theory and information theory. The results of the last phase are also translated to a new property of Fisher's information. Finally, the applicability of all three extensions on information theoretic problems is demonstrated through: a proof of a special case of Shannon's vector EPI, a converse proof of the capacity region of the parallel degraded MIMO broadcast channel (BC) under per-antenna power constrains and under covariance constraints, and a converse proof of the capacity region of the compound parallel degraded MIMO BC under covariance constraint.

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arXiv2012

Capacity Bounds and Exact Results for the Cognitive Z-interference Channel

We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide an upper bound on the capacity of this channel. We then show that, when the channel of the transmitter-receiver pair that does not experience interference is deterministic, our proposed upper bound matches the known lower bound provided by Cao and Chen in 2008. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gel'fand-Pinsker encoding at the cognitive transmitter are needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity under the generalized Gel'fand-Pinsker conditions where a transmitter-receiver pair communicates in the presence of interference noncausally known at the encoder.

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arXiv2012

Wyner-Ziv Type Versus Noisy Network Coding For a State-Dependent MAC

We consider a two-user state-dependent multiaccess channel in which the states of the channel are known non-causally to one of the encoders and only strictly causally to the other encoder. Both encoders transmit a common message and, in addition, the encoder that knows the states non-causally transmits an individual message. We find explicit characterizations of the capacity region of this communication model in both discrete memoryless and memoryless Gaussian cases. The analysis also reveals optimal ways of exploiting the knowledge of the state only strictly causally at the encoder that sends only the common message when such a knowledge is beneficial. The encoders collaborate to convey to the decoder a lossy version of the state, in addition to transmitting the information messages through a generalized Gel'fand-Pinsker binning. Particularly important in this problem are the questions of 1) optimal ways of performing the state compression and 2) whether or not the compression indices should be decoded uniquely. We show that both compression à-la noisy network coding, i.e., with no binning, and compression using Wyner-Ziv binning are optimal. The scheme that uses Wyner-Ziv binning shares elements with Cover and El Gamal original compress-and-forward, but differs from it mainly in that backward decoding is employed instead of forward decoding and the compression indices are not decoded uniquely. Finally, by exploring the properties of our outer bound, we show that, although not required in general, the compression indices can in fact be decoded uniquely essentially without altering the capacity region, but at the expense of larger alphabets sizes for the auxiliary random variables.

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arXiv2012

On X-Channels with Feedback and Delayed CSI

The sum degrees of freedom (DoF) of the two-user MIMO X-channel is characterized in the presence of output feedback and delayed channel state information (CSI). The number of antennas at each transmitters is assumed to be M and the number of antennas at each of the receivers is assumed to be N. It is shown that the sum DoF of the two-user MIMO X-channel is the same as the sum DoF of a two-user MIMO broadcast channel with 2M transmit antennas, and N antennas at each receiver. Hence, for this symmetric antenna configuration, there is no performance loss in the sum degrees of freedom due to the distributed nature of the transmitters. This result highlights the usefulness of feedback and delayed CSI for the MIMO X-channel. The K-user X-channel with single antenna at each transmitter and each receiver is also studied. In this network, each transmitter has a message intended for each receiver. For this network, it is shown that the sum DoF with partial output feedback alone is at least 2K/(K+1). This lower bound is strictly better than the best lower bound known for the case of delayed CSI assumption for all values of K.

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arXiv2012

Capacity Region of Multiple Access Channel with States Known Noncausally at One Encoder and Only Strictly Causally at the Other Encoder

We consider a two-user state-dependent multiaccess channel in which the states of the channel are known non-causally to one of the encoders and only strictly causally to the other encoder. Both encoders transmit a common message and, in addition, the encoder that knows the states non-causally transmits an individual message. We find explicit characterizations of the capacity region of this communication model in both discrete memoryless (DM) and memoryless Gaussian cases. In particular the capacity region analysis demonstrates the utility of the knowledge of the states only strictly causally at the encoder that sends only the common message in general. More specifically, in the DM setting we show that such a knowledge is beneficial and increases the capacity region in general. In the Gaussian setting, we show that such a knowledge does not help, and the capacity is same as if the states were completely unknown at the encoder that sends only the common message. The analysis also reveals optimal ways of exploiting the knowledge of the state only strictly causally at the encoder that sends only the common message when such a knowledge is beneficial. The encoders collaborate to convey to the decoder a lossy version of the state, in addition to transmitting the information messages through a generalized Gel'fand-Pinsker binning. Particularly important in this problem are the questions of 1) optimal ways of performing the state compression and 2) whether or not the compression indices should be decoded uniquely. We show that both compression à-la noisy network coding, i.e., with no binning and non-unique decoding, and compression using Wyner-Ziv binning with backward decoding and non-unique or unique decoding are optimal.

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arXiv2012

Secret Writing on Dirty Paper: A Deterministic View

Recently there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as "secret writing on dirty paper") to within half a bit.

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arXiv2011

Secrecy Degrees of Freedom of MIMO Broadcast Channels with Delayed CSIT

The degrees of freedom (DoF) of the two-user Gaussian multiple-input and multiple-output (MIMO) broadcast channel with confidential message (BCC) is studied under the assumption that delayed channel state information (CSI) is available at the transmitter. We characterize the optimal secrecy DoF (SDoF) region and show that it can be achieved by a simple artificial noise alignment (ANA) scheme. The proposed scheme sends the confidential messages superposed with the artificial noise over several time slots. Exploiting delayed CSI, the transmitter aligns the signal in such a way that the useful message can be extracted at the intended receiver but is completely drowned by the artificial noise at the unintended receiver. The proposed scheme can be interpreted as a non-trivial extension of Maddah-Ali Tse (MAT) scheme and enables us to quantify the resource overhead, or equivalently the DoF loss, to be paid for the secrecy communications.

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arXiv2011

Hybrid Digital/Analog Schemes for Secure Transmission with Side Information

Recent results on source-channel coding for secure transmission show that separation holds in several cases under some less-noisy conditions. However, it has also been proved through a simple counterexample that pure analog schemes can be optimal and hence outperform digital ones. According to these observations and assuming matched-bandwidth, we present a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. An application example to binary symmetric sources with side information is also investigated.

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