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Kamyar Moshksar

Publications and source records attributed to Kamyar Moshksar.

10 recordsLinked to original sources
arXiv2026

Refining Concentration Bounds for Gaussian Quadratic Chaos with Applications

This paper studies concentration of measure for Gaussian quadratic chaos in the non-asymptotic regime. We begin by tightening the classic Hanson-Wright inequality, where we increase its absolute constant $κ$ from 0.125 to at least 0.1457 in the symmetric case. We present a sharper version of Laurent-Massart inequality (LMI), which increases $κ$ from the largest available value of $1-\frac{\sqrt{3}}{2}\approx 0.134$ to $\frac{9-\sqrt{17}}{32}\approx 0.152$ in the positive-semidefinite case. We develop a sequence of inequalities indexed by $m\ge1$ that involve Schatten norms of the underlying matrix. The case $m=1$ recovers HWI. The bounds undergo a phase transition in the sense that if the tail parameter is smaller than a critical threshold $τ_c$, then $m=1$ is the tightest, whereas if it is larger than $τ_c$, then $m=\infty$ is the tightest. This leads to a novel bound called the $m_\infty$ bound. All HWI, LMI and the $m_\infty$ inequality rely on Markov's inequality. By avoiding Markov's inequality, we introduce the strong and weak $χ^2$ inequalities. We provide a list of concentration bounds that depend only on the operator norm in the positive-definite case, namely, the $m_\infty$ bound, the weak $χ^2$ bound, relaxed versions of HWI and LMI, and the so-called large-deviations bound. The sharpest among these is shown to be always either the $m_\infty$ bound or the weak $χ^2$ bound. By utilizing conditioning, modified versions of $m_\infty$, $χ^2$, and HW inequalities of various orders are proposed, all of which can be significantly tighter than the original inequalities. At the expense of higher computational cost, the sharpness of these modified bounds improves dramatically as the order increases. The paper concludes with two applications in statistical signal processing and wireless communications where the modified bounds prove highly effective.

math.PR↗
arXiv2022

On a Class of Time-Varying Gaussian ISI Channels

This paper studies a class of stochastic and time-varying Gaussian intersymbol interference~(ISI) channels. The probability law for the~$i^{th}$ channel tap during time slot~$t$ is supported over an interval of centre $c_i$ and radius~$ r_{i}$. The transmitter and the receiver only know the centres $c_i$ and the radii $r_i$. The joint distribution for the array of channel taps and their realizations are unknown to both the transmitter and the receiver. A lower bound (achievability result) is presented on the channel capacity which results in an upper bound on the capacity loss compared to when all radii are zeros. The lower bound on the channel capacity saturates at a positive value as the maximum average input power $P$ increases beyond what is referred to as the saturation power $P_{sat}$. Roughly speaking, $P_{sat}$ is inversely proportional to the sum of the squares of the radii $r_i$. A partial converse result is provided in the worst-case scenario where the array of channel taps varies independently along both indices $t$ and $i$ with uniform marginals. It is shown that for every sequence of codebooks with vanishing probability of error, if the size of each symbol in every codeword is bounded away from zero by an amount proportional to $\sqrt{P}$, then the rate of that sequence of codebooks does not scale with~$P$. Tools in matrix analysis such as matrix norms and Weyl's inequality on perturbation of eigenvalues of symmetric matrices are used in order to analyze the probability of error.

cs.IT↗
arXiv2021

On Interference Channels with Gradual Data Arrival

We study memoryless interference channels with gradual data arrival in the absence of feedback. The information bits arrive at the transmitters according to independent and asynchronous~(Tx-Tx asynchrony) Bernoulli processes with average data rate $λ$. Each information source turns off after generating a number of $n$ bits. In a scenario where the transmitters are unaware of the amount of Tx-Tx asynchrony, we say $ε$ is an \textit{achievable outage level} in the asymptote of large~$n$ if (i) the average transmission rate at each transmitter is $λ$ and (ii) the probability that the bit-error-rate at each receiver does not eventually vanish is not larger than~$ε$. Denoting the infimum of all achievable outage levels by $ε(λ)$, the contribution of this paper is an upper bound (achievability result) on $ε(λ)$. The proposed method of communication is a simple block transmission scheme where a transmitter sends a random point-to-point codeword upon availability of enough bits in its buffer. Both receivers that treat interference as noise or decode interference are addressed.

cs.IT↗
arXiv2016

Asynchronous Transmission over Gaussian Interference Channels with Stochastic Data Arrival

This paper addresses a Gaussian interference channel with two transmitter-receiver~(Tx-Rx) pairs under stochastic data arrival~(GIC-SDA). Information bits arrive at the transmitters according to independent and asynchronous Bernoulli processes~(Tx-Tx~asynchrony). Each information source turns off after generating a given total number of bits. The transmissions are \textit{asynchronous} (Tx-Rx~asynchrony) in the sense that each Tx sends a codeword to its Rx immediately after there are enough bits available in its buffer. Such asynchronous style of transmission is shown to significantly reduce the transmission delay in comparison with the existing Tx-Rx synchronous transmission schemes. The receivers learn the activity frames of both transmitters by employing sequential joint-typicality detection. As a consequence, the GIC-SDA under Tx-Rx asynchrony is represented by a standard GIC with state known at the receivers. The cardinality of the state space is $\binom{2N_1+2N_2}{2N_2}$ in which $N_1, N_2$ are the numbers of transmitted codewords by the two transmitters. Each realization of the state imposes two sets of constraints on $N_1, N_2$ referred to as the geometric and reliability constraints. In a scenario where the transmitters are only aware of the statistics of Tx-Tx~asynchrony, it is shown how one designs $N_1,N_2$ to achieve target transmission rates for both users and minimize the probability of unsuccessful decoding.

cs.IT↗
arXiv2010

Totally Asynchronous Interference Channels

This paper addresses an interference channel consisting of $\mathbf{n}$ active users sharing $u$ frequency sub-bands. Users are asynchronous meaning there exists a mutual delay between their transmitted codes. A stationary model for interference is considered by assuming the starting point of an interferer's data is uniformly distributed along the codeword of any user. The spectrum is divided to private and common bands each containing $v_{\mathrm{p}}$ and $v_{\mathrm{c}}$ frequency sub-bands respectively. We consider a scenario where all transmitters are unaware of the number of active users and the channel gains. The optimum $v_{\mathrm{p}}$ and $v_{\mathrm{c}}$ are obtained such that the so-called outage capacity per user is maximized. If $\Pr\{\mathbf{n}\leq 2\}=1$, upper and lower bounds on the mutual information between the input and output of the channel for each user are derived using a genie-aided technique. The proposed bounds meet each other as the code length grows to infinity yielding a closed expression for the achievable rates. If $\Pr\{\mathbf{n}>2\}>0$, all users follow a locally Randomized On-Off signaling scheme on the common band where each transmitter quits transmitting its Gaussian signals independently from transmission to transmission. Using a conditional version of Entropy Power Inequality (EPI) and an upper bound on the differential entropy of a mixed Gaussian random variable, lower bounds on the achievable rates of users are developed. Thereafter, the activation probability on each transmission slot is designed resulting in the largest outage capacity.

cs.IT↗
arXiv2010

Wireless Networks with Asynchronous Users

This paper addresses an interference channel consisting of $\mathbf{n}$ active users sharing $u$ frequency sub-bands. Users are asynchronous meaning there exists a mutual delay between their transmitted codes. A stationary model for interference is considered by assuming the starting point of an interferer's data is uniformly distributed along the codeword of any user. This model is not ergodic, however, we show that the noise plus interference process satisfies an Asymptotic Equipartition Property (AEP) under certain conditions. This enables us to define achievable rates in the conventional Shannon sense. The spectrum is divided to private and common bands. Each user occupies its assigned private band and the common band upon activation. In a scenario where all transmitters are unaware of the number of active users and the channel gains, the optimum spectrum assignment is obtained such that the so-called outage capacity per user is maximized. If $\Pr\{\mathbf{n}>2\}>0$, all users follow a locally Randomized On-Off signaling scheme on the common band where each transmitter quits transmitting its Gaussian signals independently from transmission to transmission. Achievable rates are developed using a conditional version of Entropy Power Inequality (EPI) and an upper bound on the differential entropy of a mixed Gaussian random variable. Thereafter, the activation probability on each transmission slot together with the spectrum assignment are designed resulting in the largest outage capacity.

cs.IT↗
arXiv2010

On The Design of Signature Codes in Decentralized Wireless Networks

This paper addresses a unified approach towards communication in decentralized wireless networks of separate transmitter-receiver pairs. In general, users are unaware of each other's codebooks and there is no central controller to assign the resources in the network to the users. A randomized signaling scheme is introduced in which each user locally spreads its Gaussian signal along a randomly generated spreading code comprised of a sequence of nonzero elements over a certain alphabet. Along with spreading, each transmitter also masks its output independently from transmission to transmission. Using a conditional version of entropy power inequality and a key lemma on the differential entropy of mixed Gaussian random vectors, achievable rates are developed for the users. It is seen that as the number of users increases, the achievable Sum Multiplexing Gain of the network approaches that of a centralized orthogonal scheme where multiuser interference is completely avoided. An interesting observation is that in general the elements of a spreading code are not equiprobable over the underlying alphabet. Finally, using the recently developed extremal inequality of Liu-Viswanath, we present an optimality result showing that transmission of Gaussian signals via spreading and masking yields higher achievable rates than the maximum achievable rate attained by applying masking only.

cs.IT↗
arXiv2009

Randomized vs. orthogonal spectrum allocation in decentralized networks: Outage Analysis

We address a decentralized wireless communication network with a fixed number $u$ of frequency sub-bands to be shared among $N$ transmitter-receiver pairs. It is assumed that the number of users $N$ is a random variable with a given distribution and the channel gains are quasi-static Rayleigh fading. The transmitters are assumed to be unaware of the number of active users in the network as well as the channel gains and not capable of detecting the presence of other users in a given frequency sub-band. Moreover, the users are unaware of each other's codebooks and hence, no multiuser detection is possible. We consider a randomized Frequency Hopping (FH) scheme in which each transmitter randomly hops over a subset of the $u$ sub-bands from transmission to transmission. Developing a new upper bound on the differential entropy of a mixed Gaussian random vector and using entropy power inequality, we offer a series of lower bounds on the achievable rate of each user. Thereafter, we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given Signal-to-Noise Ratio (SNR) level. We demonstrate that the so-called outage capacity can be considerably higher in the FH scheme than in the Frequency Division (FD) scenario for reasonable distributions on the number of active users. This guarantees a higher spectral efficiency in FH compared to FD.

cs.IT↗
arXiv2009

A model for randomized resource allocation in decentralized wireless networks

In this paper, we consider a decentralized wireless communication network with a fixed number $u$ of frequency sub-bands to be shared among $N$ transmitter-receiver pairs. It is assumed that the number of active users is a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized Frequency Hopping (FH) scheme in which each transmitter randomly hops over a subset of $u$ sub-bands from transmission to transmission. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large Signal-to-Noise Ratio (SNR) values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system with that of the Frequency Division (FD) system in terms of several performance measures and show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement implying a more efficient usage of the spectrum.

cs.IT↗