# Mathematics - Information Theory Publications (50)

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## Mathematics - Information Theory Publications

A smart meter (SM) measures a consumer's electricity consumption and reports it automatically to a utility provider (UP) in almost real time. Despite many advantages of SMs, their use also leads to serious concerns about consumer privacy. In this paper, SM privacy is studied by considering the presence of a renewable energy source (RES) and a battery, which can be used to partially hide the consumer's energy consumption behavior. Read More

Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do this, we generalize the recent contribution of Mesnager given in [Cryptography and Communications 9(1), 71-84, 2017]. Read More

Distributed storage systems are known to be susceptible to long tails in response time. In modern online storage systems such as Bing, Facebook, and Amazon, the long tails of the service latency are of particular concern. with 99. Read More

To exploit the sparsity of the considered system, the diffusion proportionate-type least mean square (PtLMS) algorithms assign different gains to each tap in the convergence stage while the diffusion sparsity-constrained LMS (ScLMS) algorithms pull the components towards zeros in the steady-state stage. In this paper, by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L0 norm of the weighted updated weight vector, we propose a diffusion L0-norm constraint improved proportionate LMS (L0-IPLMS) algorithm, which combines the benefits of the diffusion PtLMS and diffusion ScLMS algorithms and performs the best performance among them. Simulations in a system identification context confirm the improvement of the proposed algorithm. Read More

In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering coverings that are not connected, we classify the metrics satisfying the MacWilliams extension property. Read More

Distance-based attenuation is a critical aspect of wireless communications. As opposed to the ubiquitous power-law path loss model, this paper proposes a stretched exponential path loss model that is suitable for short-range communication. In this model, the signal power attenuates over a distance $r$ as $e^{-\alpha r^{\beta}}$, where $\alpha,\beta$ are tunable parameters. Read More

This paper presents outdoor wideband small-scale spatial fading and autocorrelation measurements and results in the 73 GHz millimeter-wave (mmWave) band conducted in downtown Brooklyn, New York. Both directional and omnidirectional receiver (RX) antennas are studied. Two pairs of transmitter (TX) and RX locations were tested with one line-of-sight (LOS) and one non-lineof- sight (NLOS) environment, where a linear track was employed at each RX to move the antenna in half-wavelength increments. Read More

This paper presents details and applications of a novel channel simulation software named NYUSIM, which can be used to generate realistic temporal and spatial channel responses to support realistic physical- and link-layer simulations and design for fifth-generation (5G) cellular communications. NYUSIM is built upon the statistical spatial channel model for broadband millimeter-wave (mmWave) wireless communication systems developed by researchers at New York University (NYU). The simulator is applicable for a wide range of carrier frequencies (500 MHz to 100 GHz), radio frequency (RF) bandwidths (0 to 800 MHz), antenna beamwidths (7? to 360? for azimuth and 7? to 45? for elevation), and operating scenarios (urban microcell, urban macrocell, and rural macrocell), and also incorporates multiple-input multiple-output (MIMO) antenna arrays at the transmitter and receiver. Read More

Multiple-input multiple-output (MIMO) systems are well suited for millimeter-wave (mmWave) wireless communications where large antenna arrays can be integrated in small form factors due to tiny wavelengths, thereby providing high array gains while supporting spatial multiplexing, beamforming, or antenna diversity. It has been shown that mmWave channels exhibit sparsity due to the limited number of dominant propagation paths, thus compressed sensing techniques can be leveraged to conduct channel estimation at mmWave frequencies. This paper presents a novel approach of constructing beamforming dictionary matrices for sparse channel estimation using the continuous basis pursuit (CBP) concept, and proposes two novel low-complexity algorithms to exploit channel sparsity for adaptively estimating multipath channel parameters in mmWave channels. Read More

Polar codes have gained significant amount of attention during the past few years and have been selected as a coding scheme for the next generation of mobile broadband standard. Among decoding schemes, successive-cancellation list (SCL) decoding provides a reasonable trade-off between the error-correction performance and hardware implementation complexity when used to decode polar codes, at the cost of limited throughput. The simplified SCL (SSCL) and its extension SSCL-SPC increase the speed of decoding by removing redundant calculations when encountering particular information and frozen bit patterns (rate one and single parity check codes), while keeping the error-correction performance unaltered. Read More

We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic analysis, Proc. IEEE, 1982]: assuming bandwidth $W$ and $N$ time domain observations, the average of the square of the first $K=2NW$ Slepian functions approaches, as $K$ grows, an ideal band-pass kernel for the interval $[-W,W]$. Read More

In a former paper the authors introduced two new systematic authentication codes based on the Gray map over a Galois ring. In this paper, it is proved the one-to-one onto correspondence between keys and encoding maps for the second introduced authentication code. Read More

This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of the message. Commercial data compression standards make use of Huffman or arithmetic coding at some stage of the compression process. Read More

**Affiliations:**

^{1}Shitz,

^{2}Shitz,

^{3}Shitz

The capacity of the semi-deterministic relay channel (SD-RC) with non-causal channel state information (CSI) only at the encoder and decoder is characterized. The capacity is achieved by a scheme based on cooperative-bin-forward. This scheme allows cooperation between the transmitter and the relay without the need to decode a part of the message by the relay. Read More

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes. Read More

This paper presents a millimeter-wave (mmWave) wideband sliding correlator channel sounder with flexibility to operate at various transmission rates. The channel sounder can transmit and receive up to 1 GHz of RF null-to-null bandwidth while measuring a 2 nanosecond multipath time resolution. The system architecture takes advantage of field-programmable gate arrays (FPGAs), high-speed digital-to-analog converters (DACs), and low phase noise Rubidium (Rb) references for synchronization. Read More

This paper presents millimeter wave (mmWave) penetration loss measurements and analysis at 73 GHz using a wideband sliding correlator channel sounder in an indoor office environment. Penetration loss was measured using a carefully controlled measurement setup for many common indoor building materials such as glass doors, glass windows, closet doors, steel doors, and whiteboard writing walls. Measurements were conducted using narrowbeam transmitter (TX) and receiver (RX) horn antennas that were boresight-aligned with a test material between the antennas. Read More

We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami--Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The algorithm is based on a recent generalization of the power decoding algorithm for Reed--Solomon codes and does not require an expensive root-finding step. Read More

When Physical Unclonable Functions (PUFs) are used for cryptographic purposes, error correction in combination with a helper data scheme is an essential component due to the fuzzy nature of a PUF. All known schemes require both a code and additional helper data to recover PUF responses. Recently, M\"uelich and Bossert proposed a scheme that only requires a code. Read More

This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by clipping, saturation, impulsive noise, or narrowband interference. We employ the $\ell_q$-norm ($0 \le q < 1$) for sparsity inducing and propose a constrained $\ell_q$-minimization formulation for the recovery and demixing problem. Read More

This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and utilizes a generalized nonconvex penalty for sparsity inducing. The $\ell_1$-loss is less sensitive to outliers in the measurements than the popular $\ell_2$-loss, while the nonconvex penalty has the capability of ameliorating the bias problem of the popular convex LASSO penalty and thus can yield more accurate recovery. Read More

In high-speed railway (HSR) communication systems, distributed antenna is usually employed to support frequent handover and enhance the signal to noise ratio to user equipments. In this case, dynamic time-domain power allocation and antenna selection (PAWAS) could be jointly optimized to improve the system performances. This paper consider this problem in such a simple way where dynamic switching between multiple-input-multiple-output (MIMO) and single-input-multiple-output (SIMO) is allowed and exclusively utilized, while the channel states and traffic demand are taken into account. Read More

This paper revisits polynomial residue codes with non-pairwise coprime moduli by presenting a new decoding, called the minimum degree-weighted distance decoding. This decoding is based on the degree-weighted distance and different from the traditional minimum Hamming distance decoding. It is shown that for the two types of minimum distance decoders, i. Read More

Based on unique decoding of the polynomial residue code with non-pairwise coprime moduli, a polynomial with degree less than that of the least common multiple (lcm) of all the moduli can be accurately reconstructed when the number of residue errors is less than half the minimum distance of the code. However, once the number of residue errors is beyond half the minimum distance of the code, the unique decoding may fail and lead to a large reconstruction error. In this paper, assuming that all the residues are allowed to have errors with small degrees, we consider how to reconstruct the polynomial as accurately as possible in the sense that a reconstructed polynomial is obtained with only the last $\tau$ number of coefficients being possibly erroneous, when the residues are affected by errors with degrees upper bounded by $\tau$. Read More

We establish existence of Stein kernels for probability measures on $\mathbb{R}^d$ satisfying a Poincar\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance $W_2$ with optimal rate and dependence on the dimension. As a byproduct, we obtain a stability version of an estimate of the Poincar\'e constant of probability measures under a second moment constraint. Read More

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. Read More

Minimax robust decentralized detection is studied for parallel sensor networks. Random variables corresponding to sensor observations are assumed to follow a distribution function, which belongs to an uncertainty class. It has been proven that, for some uncertainty classes, if all probability distributions are absolutely continuous with respect to a common measure, the joint stochastic boundedness property, which is the fundamental rule for the derivations in Veerevalli's work, does not hold. Read More

The exponential increase in mobile data traffic forces network operators to deal with a capacity shortage. One of the most promising technologies for 5G networks is proactive caching. Using a network of cache enabled small cells, traffic during peak hours can be reduced through proactively caching the content that is most probable to be requested. Read More

This paper proposes a new algorithm to improve the throughput of the MIMO interference channel, under imperfect channel state information (CSI). Each transmitter and receiver has respectively M and N antennas and network operates in a time division duplex mode. With the knowledge of channel estimation error variance, mean of signal-to-interference-plus-noise ratio (SINR) is approximated. Read More

In this short paper, we develop a probabilistic algorithm for the elliptic curve discrete logarithm problem. This algorithm is not generic in nature, it uses some properties of the elliptic curve. Read More

Outsourcing integrated circuit (IC) manufacturing to offshore foundries has grown exponentially in recent years. Given the critical role of ICs in the control and operation of vehicular systems and other modern engineering designs, such offshore outsourcing has led to serious security threats due to the potential of insertion of hardware trojans - malicious designs that, when activated, can lead to highly detrimental consequences. In this paper, a novel game-theoretic framework is proposed to analyze the interactions between a hardware manufacturer, acting as attacker, and an IC testing facility, acting as defender. Read More

This paper addresses carrier frequency offset (CFO) estimation and training sequence design for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems over frequency selective fading channels. By exploiting the orthogonality of the training sequences in the frequency domain, integer CFO (ICFO) is estimated. {With the uniformly spaced non-zero pilots in the training sequences} and the corresponding geometric mapping, fractional CFO (FCFO) is estimated through the roots of a real polynomial. Read More

Differential privacy is a strong privacy notion based on indistinguishability of outputs of two neighboring datasets, which represent two states of one's information is within or without of a dataset. However, when facing dependent records, the representation would lose its foundation. Motivated by the observation, we introduce a variant of differential privacy notion based on the influence of outputs to an individual's inputs. Read More

In this paper, we study the energy efficiency (EE) maximization problem in multiple-input multiple-output (MIMO) two-way relay networks with simultaneous wireless information and power transfer (SWIPT). The network consists of a multiple-antenna amplify-and-forward relay node which provides bidirectional communications between two multiple-antenna transceiver nodes Read More

**Affiliations:**

^{1}Shitz,

^{2}Shitz,

^{3}Shitz,

^{4}Shitz

The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition for the equality is established by making a connection to the famous Cauchy functional equation. Read More

In this paper, the problem of distributed resource allocation is studied for an Internet of Things (IoT) system, composed of heterogeneous group of nodes compromising both machine-type devices (MTDs) and human-type devices (HTDs). The problem is formulated as a noncooperative game between the heterogeneous IoT devices that seek to find the optimal time allocation so as to meet their qualityof-service (QoS) requirements in terms of energy, rate and latency. Since the strategy space of each device is dependent on the actions of the other devices, the generalized Nash equilibrium (GNE) solution is first characterized, and the conditions for uniqueness of the GNE are derived. Read More

We consider the $K$-User Multiple-Input-Single-Output (MISO) Broadcast Channel (BC) where the transmitter, equipped with $M$ antennas, serves $K$ users, with $K \leq M$. The transmitter has access to a partial channel state information of the users. This is modelled by letting the variance of the Channel State Information at the Transmitter (CSIT) error of user $i$ scale as $O(P^{-\alpha_i}$) for the Signal-to-Noise Ratio (SNR) $P$ and some constant $\alpha_i \geq 0$. Read More

We study the performance of multi-hop networks composed of millimeter wave (MMW)-based radio frequency (RF) and free-space optical (FSO) links. The results are obtained in the cases with and without hybrid automatic repeat request (HARQ). Taking the MMW characteristics of the RF links into account, we derive closed-form expressions for the network outage probability. Read More

A novel frequency domain training sequence and the corresponding carrier frequency offset (CFO) estimator are proposed for orthogonal frequency division multiplexing (OFDM) systems over frequency-selective fading channels. The proposed frequency domain training sequence comprises two types of pilot tones, namely distinctively spaced pilot tones with high energies and uniformly spaced ones with low energies. Based on the distinctively spaced pilot tones, integer CFO estimation is accomplished. Read More

In this paper, we consider a full-duplex (FD) amplify-and-forward (AF) relay system and optimize its power allocation and relay location to minimize the system symbol error rate (SER). We first derive the asymptotic expressions of the outage probability and SER performance by taking into account the residual self interference (RSI) in FD systems. We then formulate the optimization problem based on the minimal SER criterion. Read More

This paper addresses a simplified frequency offset estimator for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems over frequency selective fading channels. By exploiting the good correlation property of the training sequences, which are constructed from the Chu sequence, carrier frequency offset (CFO) estimation is obtained through factor decomposition for the derivative of the cost function with great complexity reduction. The mean-squared error (MSE) of the CFO estimation is derived to optimize the key parameter of the simplified estimator and also to evaluate the estimator performance. Read More

In this letter, signal-to-noise ratio (SNR) performance is analyzed for orthogonal frequency division multiplexing (OFDM) based amplify-and-forward (AF) relay systems in the presence of carrier frequency offset (CFO) for fading channels. The SNR expression is derived under one-relay-node scenario, and is further extended to multiple-relay-node scenario. Analytical results show that the SNR is quite sensitive to CFO and the sensitivity of the SNR to CFO is mainly determined by the power of the corresponding link channel and gain factor. Read More

In this paper, energy efficient power allocation for downlink massive MIMO systems is investigated. A constrained non-convex optimization problem is formulated to maximize the energy efficiency (EE), which takes into account the quality of service (QoS) requirements. By exploiting the properties of fractional programming and the lower bound of the user data rate, the non-convex optimization problem is transformed into a convex optimization problem. Read More

In this paper, energy efficient power allocation for the uplink of a multi-cell massive MIMO system is investigated. With the simplified power consumption model, the problem of power allocation is formulated as a constrained Markov decision process (CMDP) framework with infinite-horizon expected discounted total reward, which takes into account different quality of service (QoS) requirements for each user terminal (UT). We propose an offline solution containing the value iteration and Q-learning algorithms, which can obtain the global optimum power allocation policy. Read More

In this paper, energy efficient power control for the uplink two-tier networks where a macrocell tier with a massive multiple-input multiple-output (MIMO) base station is overlaid with a small cell tier is investigated. We propose a distributed energy efficient power control algorithm which allows each user in the two-tier network taking individual decisions to optimize its own energy efficiency (EE) for the multi-user and multi-cell scenario. The distributed power control algorithm is implemented by decoupling the EE optimization problem into two steps. Read More

In this paper, joint resource allocation and power control for energy efficient device-to-device (D2D) communications underlaying cellular networks are investigated. The resource and power are optimized for maximization of the energy efficiency (EE) of D2D communications. Exploiting the properties of fractional programming, we transform the original nonconvex optimization problem in fractional form into an equivalent optimization problem in subtractive form. Read More

In this paper, pattern division multiple access with large-scale antenna array (LSA-PDMA) is proposed as a novel non-orthogonal multiple access (NOMA) scheme. In the proposed scheme, pattern is designed in both beam domain and power domain in a joint manner. At the transmitter, pattern mapping utilizes power allocation to improve the system sum rate and beam allocation to enhance the access connectivity and realize the integration of LSA into multiple access spontaneously. Read More

This paper investigate the problem of estimating sparse channels in massive MIMO systems. Most wireless channel are sparse with large delay spread, while some channels can be observed have common support within a certain area of the antenna array. This common support property is attractive when it comes to the estimation of large number of channels in massive MIMO systems. Read More

The effective capacity (EC) has been recently established as a rigorous alternative to the classical Shannon' s ergodic capacity since it accounts for the delay constraints imposed by future wireless applications and their impact on the overall system performance. This paper develops a novel unified approach for the EC analysis of dispersed spectrum cognitive radio (CR) with equal gain combining (EGC) and maximal ratio combining (MRC) diversity receivers over generalized fading channels under a maximum delay constraint. The mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results thus confirming the correctness of the proposed unified approach. Read More

In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. In particular, we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver by using a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we derive an optimization problem based on the Bayesian Cram\'er-Rao lower bound (BCRLB) which allows us to solve the transmitter design problem using an Eigenvalue decomposition. Read More