arXiv subjects

Emre Telatar

Publications and source records attributed to Emre Telatar.

At least 19 recordsLinked to original sources

arXiv2026

Tail exponents of conditional guesswork via the method of types

We study the problem of guessing a realization of an i.i.d. random sequence given element-wise correlated side-information. We use type-counting to provide estimates of the tail probabilities of the number of guesses for the case without side-information, which was shown earlier through large-deviation techniques. We then extend the same counting argument to the conditional setting, obtaining new explicit expressions for the corresponding guesswork exponents as divergences involving conditional tilted distributions. Finally, we provide an application of these exponents to brute-force password guessing with side-information.

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arXiv2026

Space Upper Bounds for $\alpha$-Perfect Hashing

In the problem of minimal perfect hashing, we are given a size $k$ subset $\mathcal{A}$ of a universe of keys $[n] = \{1,2, \cdots, n\}$, for which we wish to construct a hash function $h: [n] \to [k]$ such that $h(\cdot)$ maps $\mathcal{A}$ to $[k]$ with no collisions, i.e., the restriction of $h(\cdot)$ to $\mathcal{A}$ is injective. In this paper, we extend the study of minimal perfect hashing to the approximate setting. For an $\alpha \in [0, 1]$, we say that a randomized hashing scheme is $\alpha$-perfect if for any input $\mathcal{A}$ of size $k$, it outputs a hash function which exhibits at most $(1-\alpha)k$ collisions on $\mathcal{A}$ in expectation. One important performance consideration for any hashing scheme is the space required to store the hash functions. For minimal perfect hashing, it is well known that approximately $k\log(e)$ bits, or $\log(e)$ bits per key, is required to store the hash function. In this paper, we propose schemes for constructing minimal $\alpha$-perfect hash functions and analyze their space requirements. We begin by presenting a simple base-line scheme which randomizes between perfect hashing and zero-bit random hashing. We then present a more sophisticated hashing scheme based on sampling which significantly improves upon the space requirement of the aforementioned strategy for all values of $\alpha$.

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arXiv2026

On the suboptimality of linear codes for binary distributed hypothesis testing

We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression schemes and show that simple truncation is the best linear scheme in two cases: (1) testing opposite signs of the same magnitude of correlation, and (2) testing for or against independence. We conjecture, supported by numerical evidence, that truncation is the best linear code for testing any correlations of opposite signs. Further, for testing against independence, we also compute classical random coding exponents and show that truncation, and consequently any linear code, is strictly suboptimal.

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arXiv2026

High signal-to-noise ratio asymptotics of entropy-constrained Gaussian channel capacity

We study the input-entropy-constrained Gaussian channel capacity problem in the asymptotic high signal-to-noise ratio (SNR) regime. We show that the capacity-achieving distribution as SNR goes to infinity is given by a discrete Gaussian distribution supported on a scaled integer lattice. Further, we show that the gap between the input entropy and the capacity decreases to zero exponentially in SNR, and characterize this exponent.

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arXiv2025

On entropy-constrained Gaussian channel capacity via the moment problem

We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a corollary of the following general result on a moment matching problem: We show that for any continuous random variable with finite moments, the largest number of initial moments that can be matched by a discrete random variable of sufficiently small but positive entropy is three.

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arXiv2023

On the Fusion Strategies for Federated Decision Making

We consider the problem of information aggregation in federated decision making, where a group of agents collaborate to infer the underlying state of nature without sharing their private data with the central processor or each other. We analyze the non-Bayesian social learning strategy in which agents incorporate their individual observations into their opinions (i.e., soft-decisions) with Bayes rule, and the central processor aggregates these opinions by arithmetic or geometric averaging. Building on our previous work, we establish that both pooling strategies result in asymptotic normality characterization of the system, which, for instance, can be utilized to derive approximate expressions for the error probability. We verify the theoretical findings with simulations and compare both strategies.

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arXiv2022

Optimal Policies for Age and Distortion in a Discrete-Time Model

We study a discrete-time model where each packet has a cost of not being sent -- this cost might depend on the packet content. We study the tradeoff between the age and the cost where the sender is confined to packet-based strategies. The optimal tradeoff is found by an appropriate formulation of the problem as a Markov Decision Process (MDP). We show that the optimal tradeoff can be attained with finite-memory policies and we devise an efficient policy iteration algorithm to find these optimal policies. We further study a related problem where the transmitted packets are subject to erasures. We show that the optimal policies for our problem are also optimal for this new setup. Allowing coding across packets significantly extends the packet-based strategies. We show that when the packet payloads are small, the performance can be improved by coding.

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arXiv2022

A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization

We study a distributed hypothesis testing setup where peripheral nodes send quantized data to the fusion center in a memoryless fashion. The \emph{expected} number of bits sent by each node under the null hypothesis is kept limited. We characterize the optimal decay rate of the mis-detection (type-II error) probability provided that false alarms (type-I error) are rare, and study the tradeoff between the communication rate and maximal type-II error decay rate. We resort to rate-distortion methods to provide upper bounds to the tradeoff curve and show that at high rates lattice quantization achieves near-optimal performance. We also characterize the tradeoff for the case where nodes are allowed to record and quantize a fixed number of samples. Moreover, under sum-rate constraints, we show that an upper bound to the tradeoff curve is obtained with a water-filling solution.

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arXiv2022

On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference

We study the asymptotic learning rates under linear and log-linear combination rules of belief vectors in a distributed hypothesis testing problem. We show that under both combination strategies, agents are able to learn the truth exponentially fast, with a faster rate under log-linear fusion. We examine the gap between the rates in terms of network connectivity and information diversity. We also provide closed-form expressions for special cases involving federated architectures and exchangeable networks.

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arXiv2022

Social Learning under Randomized Collaborations

We study a social learning scheme where at every time instant, each agent chooses to receive information from one of its neighbors at random. We show that under this sparser communication scheme, the agents learn the truth eventually and the asymptotic convergence rate remains the same as the standard algorithms which use more communication resources. We also derive large deviation estimates of the log-belief ratios for a special case where each agent replaces its belief with that of the chosen neighbor.

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arXiv2020

Finite-Level Quantization Procedures for Construction and Decoding of Polar Codes

We consider finite-level, symmetric quantization procedures for construction and decoding of polar codes. Whether polarization occurs in the presence of quantization is not known in general. Hassani and Urbanke have shown that a simple three-level quantization procedure polarizes and they have proposed a calculation method to obtain a lower bound for achievable rates. We find an improved calculation method for achievable rates and also the exact asymptotic behavior of the block error probability under the aforementioned simple case. We then prove that certain D-level quantization schemes polarize and give a lower bound on achievable rates. Furthermore, we show that a broad class of quantization procedures result in a weaker form of the polarization phenomenon.

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arXiv2019

Content Based Status Updates

Consider a stream of status updates generated by a source, where each update is of one of two types: high priority or ordinary (low priority). These updates are to be transmitted through a network to a monitor. However, the transmission policy of each packet depends on the type of stream it belongs to. For the low priority stream, we analyze and compare the performances of two transmission schemes: (i) Ordinary updates are served in a First-Come-First-Served (FCFS) fashion, whereas, in (ii), the ordinary updates are transmitted according to an M/G/1/1 with preemption policy. In both schemes, high priority updates are transmitted according to an M/G/1/1 with preemption policy and receive preferential treatment. An arriving priority update discards and replaces any currently-in-service high priority update, and preempts (with eventual resume for scheme (i)) any ordinary update. We model the arrival processes of the two kinds of updates, in both schemes, as independent Poisson processes. For scheme (i), we find the arrival and service rates under which the system is stable and give closed-form expressions for average peak age and a lower bound on the average age of the ordinary stream. For scheme (ii), we derive closed-form expressions for the average age and average peak age of the high priority and low priority streams. We finally show that, if the service time is exponentially distributed, the M/M/1/1 with preemption policy leads to an average age of the low priority stream higher than the one achieved using the FCFS scheme. Therefore, the M/M//1/1 with preemption policy, when applied on the low priority stream of updates and in the presence of a higher priority scheme, is not anymore the optimal transmission policy from an age point of view.

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arXiv2019

Optimal Age over Erasure Channels

Previous works on age of information and erasure channels have dealt with specific models and computed the average age or average peak age for certain settings. In this paper, given a source that produces a letter every $T_s$ seconds and an erasure channel that can be used every $T_c$ seconds, we ask what is the coding strategy that minimizes the time-average age of information that an observer of the channel output incurs. We first analyze the case where the source alphabet and the channel-input alphabet have the same size. We show that a trivial coding strategy is optimal and a closed form expression for the age can be derived. We then analyze the case where the alphabets have different sizes. We use a random coding argument to bound the average age and show that the average age achieved using random codes converges to the optimal average age of linear block codes as the source alphabet becomes large.

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arXiv2018

Status Updates in a multi-stream M/G/1/1 preemptive queue

We consider a source that collects a multiplicity of streams of updates and sends them through a network to a monitor. However, only a single update can be in the system at a time. Therefore, the transmitter always preempts the packet being served when a new update is generated. We consider Poisson arrivals for each stream and a common general service time, and refer to this system as the multi-stream M/G/1/1 queue with preemption. Using the detour flow graph method, we compute a closed form expression for the average age and the average peak age of each stream. Moreover, we deduce that although all streams are treated equally from a transmission point of view (they all preempt each other), one can still prioritize a stream from an age point of view by simply increasing its generation rate. However, this will increase the sum of the ages which is minimized when all streams have the same update rate.

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arXiv2017

Fourier Analysis of MAC Polarization

One problem with MAC polar codes that are based on MAC polarization is that they may not achieve the entire capacity region. The reason behind this problem is that MAC polarization sometimes induces a loss in the capacity region. This paper provides a single letter necessary and sufficient condition which characterizes all the MACs that do not lose any part of their capacity region by polarization.

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arXiv2016

On Channel Resolvability in Presence of Feedback

We study the problem of generating an approximately i.i.d. string at the output of a discrete memoryless channel using a limited amount of randomness at its input in presence of causal noiseless feedback. Feedback does not decrease the channel resolution, the minimum entropy rate required to achieve an accurate approximation of an i.i.d. output string. However, we show that, at least over a binary symmetric channel, a significantly larger resolvability exponent (the exponential decay rate of the divergence between the output distribution and product measure), compared to the best known achievable resolvability exponent in a system without feedback, is possible. We show that by employing a variable-length resolvability scheme and using an average number of coin-flips per channel use, the average divergence between the distribution of the output sequence and product measure decays exponentially fast in the average length of output sequence with an exponent equal to $[R-I(U;V)]^+$ where $I(U;V)$ is the mutual information developed across the channel.

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arXiv2016

Exact Random Coding Secrecy Exponents for the Wiretap Channel

We analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in Wyner's wiretap channel setting using wiretap channel codes constructed from both i.i.d. and constant-composition random codes. Our analysis for those sampled from i.i.d. random coding ensemble shows that the previously-known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble. Furthermore, our analysis on wiretap channel codes constructed from the ensemble of constant-composition random codes leads to an exponent which, in addition to being the exact exponent for an average code, is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble (which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i.i.d. random coding ensemble). We show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant-composition codes is larger than that of those constructed from i.i.d. random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i.i.d. random codes is larger than that of those constructed from constant-composition random codes. We, hence, conclude that, unlike the error correction problem, there is no general ordering between the two random coding ensembles in terms of their secrecy exponent.

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arXiv2015

On the Secrecy Exponent of the Wire-tap Channel

We derive an exponentially decaying upper-bound on the unnormalized amount of information leaked to the wire-tapper in Wyner's wire-tap channel setting. We characterize the exponent of the bound as a function of the randomness used by the encoder. This exponent matches that of the recent work of Hayashi (2011) which is, to the best of our knowledge, the best exponent that exists in the literature. Our proof---like those of Han et al. (2014) and Hayashi (2015)---is exclusively based on an i.i.d. random coding construction while that of Hayashi (2011), in addition, requires the use of random universal hash functions.

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