# Mathematics - Information Theory Publications (50)

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## Mathematics - Information Theory Publications

New lower and upper bounds on the reliability function of typewriter channels are given. Our lower bounds improve upon the (multiletter) expurgated bound of Gallager, furnishing a new and simple counterexample to a conjecture made in 1967 by Shannon, Gallager and Berlekamp on its tightness. The only other known counterexample is due to Katsman, Tsfasman and Vl\u{a}du\c{t} who used algebraic-geometric codes on a $q$-ary symmetric channels, $q\geq 49$. Read More

We consider the Rudin-Shapiro-like polynomials, whose $L^4$ norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial $f(z)=f_0+f_1 z + \cdots + f_d z^d$ is identified with the sequence $(f_0,f_1,\ldots,f_d)$ of its coefficients. From the $L^4$ norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. Read More

We analyze the problem of learning a single user's preferences in an active learning setting, sequentially and adaptively querying the user over a finite time horizon. Learning is conducted via choice-based queries, where the user selects her preferred option among a small subset of offered alternatives. These queries have been shown to be a robust and efficient way to learn an individual's preferences. Read More

In this paper, we derive upper and lower bounds as well as a simple closed-form approximation for the capacity of the continuous-time, bandlimited, additive white Gaussian noise channel in a three-dimensional free-space electromagnetic propagation environment subject to constraints on the total effective antenna aperture area of the link and a total transmitter power constraint. We assume that the communication range is much larger than the radius of the sphere containing the antennas at both ends of the link, and we show that, in general, the capacity can only be achieved by transmitting multiple spatially-multiplexed data streams simultaneously over the channel. Furthermore, the lower bound on capacity can be approached asymptotically by transmitting the data streams between a pair of physically-realizable distributed antenna arrays at either end of the link. Read More

We consider the cell-free massive multiple-input multiple-output (MIMO) downlink, where a very large number of distributed multiple-antenna access points (APs) serve many single-antenna users in the same time-frequency resource. A simple (distributed) conjugate beamforming scheme is applied at each AP via the use of local channel state information (CSI). This CSI is acquired through time-division duplex operation and the reception of uplink training signals transmitted by the users. Read More

Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce a recurrent neural network architecture for decoding linear block codes. Read More

Energy beamforming (EB) is a key technique to significantly enhance the efficiency of wireless power transfer (WPT). In this paper, we study optimal EB under per-antenna power constraint (PAC) which is more practical than conventional sum-power constraint (SPC) at multi antenna energy transmitter (ET). We consider a broadcast network, where one multi antenna ET with PAC, transfers wireless energy for energy receivers (ER)s which are randomly placed within the cell area. Read More

Product distribution matching (PDM) is proposed to generate target distributions over large alphabets by combining the output of several parallel distribution matchers (DMs) with smaller output alphabets. The parallel architecture of PDM enables low-complexity and high-throughput implementation. PDM is used as a shaping device for probabilistic amplitude shaping (PAS). Read More

This paper considers the security issue of practical distributed storage systems (DSSs) which consist of multiple clusters of storage nodes. Noticing that actual storage nodes constituting a DSS are distributed in multiple clusters, two novel eavesdropper models - the node-restricted model and the cluster-restricted model - are suggested which reflect the clustered nature of DSSs. In the node-restricted model, an eavesdropper cannot access the individual nodes, but can eavesdrop incoming/outgoing data for $L_c$ compromised clusters. Read More

For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. Read More

Founsure is an open-source software library, distributed under LGPLv3 license and implements a multi-dimensional graph-based erasure coding entirely based on fast exclusive OR (XOR) logic. Its implementation uses compiler optimizations to generate the right assembly for the given SIMD-enabled architectures. Founsure 1. Read More

This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the R\'{e}nyi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. Read More

Today's data centers have an abundance of computing resources, hosting server clusters consisting of as many as tens or hundreds of thousands of machines. To execute a complex computing task over a data center, it is natural to distribute computations across many nodes to take advantage of parallel processing. However, as we allocate more and more computing resources to a computation task and further distribute the computations, large amounts of (partially) computed data must be moved between consecutive stages of computation tasks among the nodes, hence the communication load can become the bottleneck. Read More

This paper proposes a novel achievable scheme for the index problem and applies it to the caching problem. Index coding and caching are noiseless broadcast channel problems where receivers have message side information.In the index coding problem the side information sets are fixed, while in the caching problem the side information sets correspond the cache contents, which are under the control of the system designer. Read More

We consider a massive MIMO system, based on Time Division Duplexing (TDD) and channel reciprocity, where the base stations learn the channel vectors of their users via the pilots transmitted by the users in the uplink time-frequency slots. It has been observed that, in the limit of very large number of antennas, the only factor limiting the achievable throughput of such a system is pilot contamination, which arises since the same set of orthogonal pilots is eventually reused in multiple cells. In the regime of moderately large number of antennas, another source of degradation is channel interpolation since, due to limited pilot dimension, the pilot signal of each user probes only a limited number OFDM subcarriers and the channel must be interpolated in the remaining subcarriers over which no pilot symbol is transmitted. Read More

Enhanced mobile broadband (eMBB) is one of the key use-cases for the development of the new standard 5G New Radio for the next generation of mobile wireless networks. Large-scale antenna arrays, a.k. Read More

In this paper, we introduce the concept of space-time channel modulation (STCM), which extends the classical space-time block codes into a new third dimension: channel states (transmission media) dimension. Three novel STCM schemes, which provide interesting trade-offs among decoding complexity, error performance and data rate, are proposed. It is shown via computer simulations that the proposed STCM schemes achieve considerably better error performance than the existing media-based modulation (MBM) and classical systems. Read More

In this paper, we consider a cognitive indoor visible light communications (VLC) system, comprised of multiple access points serving primary and secondary users through the orthogonal frequency division multiple access method. A cognitive lighting cell is divided into two non-overlapping regions that distinguish the primary and secondary users based on the region they are located in. Under the assumption of equal-power allocation among subcarriers, each region is defined in terms of its physical area and the number of allocated subcarriers within that region. Read More

To alleviate the high cost of hardware in mmWave systems, hybrid analog/digital precoding is typically employed. In the conventional two-stage feedback scheme, the analog beamformer is determined by beam search and feedback to maximize the desired signal power of each user. The digital precoder is designed based on quantization and feedback of effective channel to mitigate multiuser interference. Read More

LTE in unlicensed spectrum (LTE-U) is a promising approach to overcome the wireless spectrum scarcity. However, to reap the benefits of LTE-U, a fair coexistence mechanism with other incumbent WiFi deployments is required. In this paper, a novel deep learning approach is proposed for modeling the resource allocation problem of LTE-U small base stations (SBSs). Read More

In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can, in particular, reconstruct a ${d\times d\times d}$ tensor of multilinear ranks $(r,r,r)$ with high probability from as few as $O(r^{7/2}d^{3/2}\log^{7/2}d+r^7d\log^6d)$ entries. In the case when the ranks $r=O(1)$, our sample size requirement matches those for nuclear norm minimization (Yuan and Zhang, 2016a), or alternating least squares assuming orthogonal decomposability (Jain and Oh, 2014). Read More

The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Read More

This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are subjected to Brownian motion in addition to the diffusive motion of the information molecules used for communication. Due to the stochastic movements of the transmitter and receiver nano-machines, the statistics of the channel impulse response change over time. Read More

Spectrally efficient multi-antenna wireless communications is a key challenge as service demands continue to increase. At the same time, powering up radio access networks increases $CO_2$ footprint. Hence, for an efficient radio access design, we design a directional modulation precoder for $M$-QAM modulation with $M=4,8,16,32$. Read More

In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding optimization problems can quickly grow to large scale with increasing the code length and number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. Read More

We consider the problem of determining the asymptotic order of the Gelfand numbers of mixed-(quasi-)norm embeddings $\ell^b_p(\ell^d_q) \hookrightarrow \ell^b_r(\ell^d_u)$ given that $p \leq r$ and $q \leq u$, with emphasis on cases with $p\leq 1$ and/or $q\leq 1$. These cases turn out to be related to structured sparsity. We obtain sharp bounds in a number of interesting parameter constellations. Read More

CSMA (Carrier Sense Multiple Access) algorithms based on Gibbs sampling can achieve throughput optimality if certain parameters called the fugacities are appropriately chosen. However, the problem of computing these fugacities is NP-hard. In this work, we derive estimates of the fugacities by using a framework called the regional free energy approximations. Read More

In this paper, we provide a comprehensive system model of a wireless-powered sensor network (WPSN) based on experimental results on a real-life testbed. In the WPSN, a sensor node is wirelessly powered by the RF energy transfer from a dedicated RF power source. We define the behavior of each component comprising the WPSN and analyze the interaction between these components to set up a realistic WPSN model from the systematic point of view. Read More

In this paper, we revisit the high-dimensional content identification with lossy recovery problem (Tuncel and G\"und\"uz, 2014). We first present a non-asymptotic converse bound. Invoking the non-asymptotic converse bound, we derive a lower bound on the exponent of the probability of correct decoding (the strong converse exponent) and show the lower bound is strictly positive if the rate-distortion tuple falls outside the rate-distortion region by Tuncel and G\"und\"uz. Read More

We consider the practical photon-counting receiver in optical scattering communication. In the receiver side, the detected signal can be characterized as discrete photoelectrons, a series of pulses is generated by photon-multiplier (PMT) detector, held by the pulse-holding circuits, sampled in analog-to-digit convertor (ADC) and then be counted by a rising-edge pulse detector. However, the pulse width incurs the dead time effect that may lead to the sub-Poisson characteristic. Read More

A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density functions onto the real line. For example, information divergence functions measure the dissimilarity between two probability density functions and are particularly useful in a number of applications. Read More

In this paper, we propose a method for acquiring accurate and timely channel state information (CSI) by leveraging full-duplex transmission. Specifically, we propose a mobile communication system in which base stations continuously transmit a pilot sequence in the uplink frequency band, while terminals use self-interference cancellation capabilities to obtain CSI at any time. Our proposal outperforms its half-duplex counterpart by at least 50% in terms of throughput while ensuring the same (or even lower) outage probability. Read More

Several new constructions of 3-dimensional optical orthogonal codes are presented here. In each case the codes have ideal autocorrelation $\mathbf{ \lambda_a=0} $, and in all but one case a cross correlation of $ \mathbf{\lambda_c=1} $. All codes produced are optimal with respect to the applicable Johnson bound either presented or developed here. Read More

The construction of permutation trinomials over finite fields attracts people's interest recently due to their simple form and some additional properties. Motivated by some results on the construction of permutation trinomials with Niho exponents, by constructing some new fractional polynomials that permute the set of the $(q+1)$-th roots of unity in $\mathbb F_{q^2}$, we present several classes of permutation trinomials with Niho exponents over $\mathbb F_{q^2}$, where $q=5^k$. Read More

Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements on the whole Euclidean space and from their phaseless samples taken on a discrete set with finite sampling density. We introduce an undirected graph to a signal and use connectivity of the graph to characterize whether the signal can be determined, up to a sign, from its magnitude measurements on the whole Euclidean space. Read More

We study a spectral initialization method that serves as a key ingredient in recent work on using efficient iterative algorithms for estimating signals in nonconvex settings. Unlike previous analysis in the literature, which is restricted to the phase retrieval setting and which provides only performance bounds, we consider arbitrary generalized linear sensing models and present a precise asymptotic characterization of the performance of the spectral method in the high-dimensional regime. Our analysis reveals a phase transition phenomenon that depends on the sampling ratio. Read More

In this paper, energy-efficient transmission schemes achieving maximal throughput over a finite time interval are studied in a problem setting including energy harvests, data arrivals and channel variation. The goal is to express the offline optimal policy in a way that facilitates a good online solution. We express any throughput maximizing energy efficient offline schedule (EE-TM-OFF) explicitly in terms of water levels. Read More

We propose an intelligent proactive content caching scheme to reduce the energy consumption in wireless downlink. We consider an online social network (OSN) setting where new contents are generated over time, and remain \textit{relevant} to the user for a random lifetime. Contents are downloaded to the user equipment (UE) through a time-varying wireless channel at an energy cost that depends on the channel state and the number of contents downloaded. Read More

This paper considers the channel estimation (CE) and multi-user detection (MUD) problems in cloud radio access network (C-RAN). Assuming that active users are sparse in the network, we solve CE and MUD problems with compressed sensing (CS) technology to greatly reduce the long identification pilot overhead. A mixed L{2,1}-regularization functional for extended sparse group-sparsity recovery is proposed to exploit the inherently sparse property existing both in user activities and remote radio heads (RRHs) that active users are attached to. Read More

We analyze and optimize a wireless system with energy transfer in the downlink and information transfer in the uplink, under quasi-static Nakagami-m fading. We consider ultra-reliable communication scenarios representative of the fifth-generation of wireless systems, with strict error and latency requirements. The error probability and delay are investigated, and an approximation for the former is given and validated through simulations. Read More

We introduce an inequality which may be viewed as a generalization of both the Brascamp-Lieb inequality and its reverse (Barthe's inequality), and prove its information-theoretic (i.e.\ entropic) formulation. Read More

We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in $\mathbb R^n$ from $r\cdot \tilde O(n^{1.5})$ randomly observed entries of the tensor. Read More

Existing works on building a soliton transmission system only encode information using the imaginary part of the eigenvalue, which fails to make full use of the signal degree-of-freedoms. Motivated by this observation, we make the first step of encoding information using (discrete) spectral amplitudes by proposing analytical noise models for the spectral amplitudes of $N$-solitons ($N\geq 1$). To our best knowledge, this is the first work in building an analytical noise model for spectral amplitudes, which leads to many interesting information theoretic questions, such as channel capacity analysis, and has a potential of increasing the transmission rate. Read More

**Authors:**Mahdi Soltanolkotabi

This paper concerns the problem of recovering an unknown but structured
signal $x \in R^n$ from $m$ quadratic measurements of the form
$y_r=|

Millimeter wave communications rely on narrow-beam transmissions to cope with the strong signal attenuation at these frequencies, thus demanding precise beam alignment between transmitter and receiver. The communication overhead incurred to achieve beam alignment may become a severe impairment in mobile networks. This paper addresses the problem of optimizing beam alignment acquisition, with the goal of maximizing throughput. Read More

An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality. Read More

If we assume line-of-sight propagation and perfect channel state information at the base station -- consistent with slow moving terminals -- then a direct performance comparison between single-cell Massive MIMO at PCS and mmWave frequency bands is straightforward and highly illuminating. Line-of-sight propagation is considered favorable for mmWave because of minimal attenuation, and its facilitation of hybrid beamforming to reduce the required number of active transceivers. We quantify the number of mmWave (60 GHz) service antennas that are needed to duplicate the performance of a specified number of PCS (1. Read More

Redundancy is abundant in Fog networks (i.e., many computing and storage points) and grows linearly with network size. Read More

We propose a family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence $k$-concurrence), which has a close relation with the generalized entanglement concurrence. The coherence $k$-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than $k$, and a state can be converted to a state with nonzero entanglement $k$-concurrence via incoherent operations if and only if the state has nonzero coherence $k$-concurrence. The generalized coherence concurrence can be considered as the entanglement-based coherence monotone. Read More

Dynamic time-division duplexing (TDD) is considered a promising solution to deal with fast-varying traffic often found in ultra-densely deployed networks. At the same time, it generates more interference which may degrade the performance of some user equipment (UE). When base station (BS) utilization is low, some BSs may not have an UE to serve. Read More