arXiv subjects

Hessam Mahdavifar

Publications and source records attributed to Hessam Mahdavifar.

At least 73 records · Page 4Linked to original sources

arXiv2021

Threshold-Secure Coding with Shared Key

Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such as encoders and decoders, together with shared keys to provide a threshold-type security scheme. To this end, we first consider a scenario where the effect of the physical layer is omitted and all the channels between the involved parties are assumed to be noiseless. We introduce a model for threshold-secure coding, where the legitimate parties communicate using a shared key such that an eavesdropper does not get any information, in an information-theoretic sense, about the key as well as about any subset of the input symbols of size up to a certain threshold. Then, a framework is provided for constructing threshold-secure codes from linear block codes while characterizing the requirements to satisfy the reliability and security conditions. Moreover, we propose a threshold-secure coding scheme, based on Reed-Muller (RM) codes, that meets security and reliability conditions. It is shown that the encoder and the decoder of the scheme can be implemented efficiently with quasi-linear time complexity. In particular, a successive cancellation decoder is shown for the RM-based coding scheme. Then we extend the setup to the scenario where the channel between the legitimate parties is no longer noiseless. The reliability condition for noisy channels is then modified accordingly, and a method is described to construct codes attaining threshold security as well as desired reliability. Also, we propose a coding scheme based on RM codes for threshold security and robustness designed for binary erasure channels along with a unified successive cancellation decoder. The proposed threshold-secure coding schemes are flexible and can be adapted for different key lengths.

cs.IT↗

arXiv2020

Polar Coded Repetition for Low-Capacity Channels

Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding have become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT) networks. To this end, schemes based on concatenating the state-of-the-art codes at moderate rates with repetition codes have emerged as practical solutions deployed in various standards. In this paper, we propose a novel mechanism for concatenating outer polar codes with inner repetition codes which we refer to as polar coded repetition. More specifically, we propose to transmit a slightly modified polar codeword by deviating from Arikan's standard 2 x 2 Kernel in a certain number of polarization recursions at each repetition block. We show how this modification can improve the asymptotic achievable rate of the polar-repetition scheme, while ensuring that the overall encoding and decoding complexity is kept almost the same. The achievable rate is analyzed for the binary erasure channels (BEC).

cs.IT↗

arXiv2020

Distributed Multi-User Secret Sharing

We consider a distributed secret sharing system that consists of a dealer, $n$ storage nodes, and $m$ users. Each user is given access to a certain subset of storage nodes, where it can download the stored data. The dealer wants to securely convey a specific secret $s_j$ to user $j$ via storage nodes, for $j=1,2,...,m$. More specifically, two secrecy conditions are considered in this multi-user context. The weak secrecy condition is that each user does not get any information about the individual secrets of other users, while the perfect secrecy condition implies that a user does not get any information about the collection of all other users' secrets. In this system, the dealer encodes secrets into several secret shares and loads them into the storage nodes. Given a certain number of storage nodes we find the maximum number of users that can be served in such a system and construct schemes that achieve this with perfect secrecy. Lower bounds on the minimum communication complexity and the storage overhead are characterized given any $n$ and $m$. We construct distributed secret sharing protocols, under certain conditions on the system parameters, that attain the lower bound on the communication complexity while providing perfect secrecy. Furthermore, we construct protocols, again under certain conditions, that simultaneously attain the lower bounds on the communication complexity and the storage overhead while providing weak secrecy, thereby demonstrating schemes that are optimal in terms of both the parameters. It is shown how to modify the proposed protocols in order to construct schemes with balanced storage load and communication complexity.

cs.IT↗

arXiv2020

Numerically Stable Binary Gradient Coding

A major hurdle in machine learning is scalability to massive datasets. One approach to overcoming this is to distribute the computational tasks among several workers. \textit{Gradient coding} has been recently proposed in distributed optimization to compute the gradient of an objective function using multiple, possibly unreliable, worker nodes. By designing distributed coded schemes, gradient coded computations can be made resilient to \textit{stragglers}, nodes with longer response time comparing to other nodes in a distributed network. Most such schemes rely on operations over the real or complex numbers and are inherently numerically unstable. We present a binary scheme which avoids such operations, thereby enabling numerically stable distributed computation of the gradient. Also, some restricting assumptions in prior work are dropped, and a more efficient decoding is given.

cs.IT↗

arXiv2020

Polar Coding for Non-Stationary Channels

The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the transmitter and the receiver (a coherent scenario). Also, at each code block transmission, each of the channels is used only once. In other words, a codeword of length $N$ is constructed and then the $i$-th encoded bit is transmitted over $W_i$. The goal is to operate at a rate $R$ close to the average of the symmetric capacities of $W_i$'s, denoted by $\overline{I}_N$. To this end, we construct a polar coding scheme using Arikan's channel polarization transform in combination with certain permutations at each polarization level and certain skipped operations. In particular, given a non-stationary sequence of BMS channels $\left\{W_i\right\}_{i=1}^{N}$ and $P_e$, where $0 < P_e <1$, we construct a polar code of length $N$ and rate $R$ guaranteeing a block error probability of at most $P_e$ for transmission over $\left\{W_i\right\}_{i=1}^{N}$ such that $$ N \leq \fracκ{(\overline{I}_N - R)^μ}, $$ where $μ$ is a constant and $κ$ is a constant depending on $P_e$ and $μ$. We further show a numerical upper bound on $μ$ that is: $μ\leq 7.34$ for non-stationary binary erasure channels and $μ\leq 8.54$ for general non-stationary BMS channels. The encoding and decoding complexities of the constructed polar code preserve $O(N \log N)$ complexity of Arikan's polar codes. In an asymptotic sense, when coded bits are transmitted over a non-stationary sequence of BMS channels $\left\{W_i\right\}_{i=1}^{\infty}$, our proposed scheme achieves the average symmetric capacity $$ \overline{I}(\left\{W_i\right\}_{i=1}^{\infty}) := \lim_{N\rightarrow \infty} \frac{1}{N}\sum_{i=1}^N I(W_i), $$ assuming that the limit exists.

cs.IT↗

arXiv2020

Privacy-Preserving Distributed Learning in the Analog Domain

We consider the critical problem of distributed learning over data while keeping it private from the computational servers. The state-of-the-art approaches to this problem rely on quantizing the data into a finite field, so that the cryptographic approaches for secure multiparty computing can then be employed. These approaches, however, can result in substantial accuracy losses due to fixed-point representation of the data and computation overflows. To address these critical issues, we propose a novel algorithm to solve the problem when data is in the analog domain, e.g., the field of real/complex numbers. We characterize the privacy of the data from both information-theoretic and cryptographic perspectives, while establishing a connection between the two notions in the analog domain. More specifically, the well-known connection between the distinguishing security (DS) and the mutual information security (MIS) metrics is extended from the discrete domain to the continues domain. This is then utilized to bound the amount of information about the data leaked to the servers in our protocol, in terms of the DS metric, using well-known results on the capacity of single-input multiple-output (SIMO) channel with correlated noise. It is shown how the proposed framework can be adopted to do computation tasks when data is represented using floating-point numbers. We then show that this leads to a fundamental trade-off between the privacy level of data and accuracy of the result. As an application, we also show how to train a machine learning model while keeping the data as well as the trained model private. Then numerical results are shown for experiments on the MNIST dataset. Furthermore, experimental advantages are shown comparing to fixed-point implementations over finite fields.

cs.LG↗

arXiv2020

Uplink Non-Orthogonal Multiple Access over Mixed RF-FSO Systems

In this paper, we consider a relay-assisted uplink non-orthogonal multiple access (NOMA) system. In this system, two radio frequency (RF) users are grouped for simultaneous transmissions, over each resource block, to an intermediate relay. The relay then forwards the amplified version of the users' aggregated signals, in the presence of multiuser interference, to a relatively far destination. In order to cope with the users' ever-increasing desire for higher data rates, a high-throughput free-space optics (FSO) link is employed as the relay-destination backhaul link. It is assumed that the FSO backhaul link is subject to Gamma-Gamma turbulence with pointing error. Also, a Rayleigh fading model is considered for the user-relay access links. Under these assumptions, we derive closed-form expressions for the outage probability and tractable forms, involving only one-dimensional integrals, for the ergodic capacity. Moreover, the outage probability and ergodic capacity analysis are extended to the conventional RF-backhauled systems in the presence of multiuser interference to both relay and destination nodes, and Rician fading for the relay-destination RF link. Our results reveal the superiority of FSO backhauling for high-throughput and high-reliability NOMA systems compared to RF backhauling. This work can be considered as a general analysis of dual-hop uplink NOMA systems as well as the first attempt to incorporate power-domain NOMA in mixed RF-FSO systems.

cs.IT↗

arXiv2020

Physical Layer Secret Key Generation in Static Environments

Two legitimate parties, referred to as Alice and Bob, wish to generate secret keys from the wireless channel in the presence of an eavesdropper, referred to as Eve, in order to use such keys for encryption and decryption. In general, the secret key rate highly depends on the coherence time of the channel. In particular, a straightforward method of generating secret keys in static environments results in ultra-low rates. In order to resolve this problem, we introduce a low-complexity method called induced randomness. In this method, Alice and Bob independently generate local randomness to be used together with the uniqueness of the wireless channel coefficients in order to enable high-rate secret key generation. In this work, two scenarios are considered: first, when Alice and Bob share a direct communication channel, and second, when Alice and Bob do not have a direct link and communicate through an untrusted relay. After exchanging the induced randomness, post-processing is done by Alice and Bob to generate highly-correlated samples that are used for the key generation. Such samples are then converted into bits, disparities between the sequences generated by Alice and Bob are mitigated, and the resulting sequences are then hashed to compensate for the information leakage to the eavesdropper and to allow consistency checking of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be $2^{-31}$ and $2^{-10.57}$ in the first and the second scenario, respectively.

cs.IT↗

arXiv2020

Coding for Crowdsourced Classification with XOR Queries

This paper models the crowdsourced labeling/classification problem as a sparsely encoded source coding problem, where each query answer, regarded as a code bit, is the XOR of a small number of labels, as source information bits. In this paper we leverage the connections between this problem and well-studied codes with sparse representations for the channel coding problem to provide querying schemes with almost optimal number of queries, each of which involving only a constant number of labels. We also extend this scenario to the case where some workers can be unresponsive. For this case, we propose querying schemes where each query involves only log n items, where n is the total number of items to be labeled. Furthermore, we consider classification of two correlated labeling systems and provide two-stage querying schemes with almost optimal number of queries each involving a constant number of labels.

stat.ML↗

arXiv2020

Capacity-achieving Polar-based LDGM Codes with Crowdsourcing Applications

In this paper we study codes with sparse generator matrices. More specifically, codes with a certain constraint on the weight of all the columns in the generator matrix are considered. The end result is the following. For any binary-input memoryless symmetric (BMS) channel and any epsilon > 2 epsilon*, where epsilon^* = \frac{1}{6}-\frac{5}{3}\log{\frac{4}{3}} \approx 0.085, we show an explicit sequence of capacity-achieving codes with all the column wights of the generator matrix upper bounded by (\log N)^{1+epsilon}, where N is the code block length. The constructions are based on polar codes. Applications to crowdsourcing are also shown.

eess.SP↗

arXiv2019

Cell Association via Boundary Detection: A Scalable Approach Based on Data-Driven Random Features

The problem of cell association is considered for cellular users present in the field. This has become a challenging problem with the deployment of 5G networks which will share the sub-6 GHz bands with the legacy 4G networks. Instead of taking a network-controlled approach, which may not be scalable with the number of users and may introduce extra delays into the system, we propose a scalable solution in the physical layer by utilizing data that can be collected by a large number of spectrum sensors deployed in the field. More specifically, we model the cell association problem as a nonlinear boundary detection problem and focus on solving this problem using randomized shallow networks for determining the boundaries for location of users associated to each cell. We exploit the power of data-driven modeling to reduce the computational cost of training in the proposed solution for the cell association problem. This is equivalent to choosing the right basis functions in the shallow architecture such that the detection is done with minimal error. Our experiments demonstrate the superiority of this method compared to its data-independent counterparts as well as its computational advantage over kernel methods.

eess.SP↗

arXiv2019

Secret Key Generation via Pulse-Coupled Synchronization

A novel framework for sharing common randomness and generating secret keys in wireless networks is considered. In particular, a network of users equipped with pulse oscillators (POs) and coupling mechanisms in between is considered. Such mechanisms exist in synchronized biological and natural systems, and have been exploited to provide synchronization in distributed networks. We show that naturally-existing initial random phase differences between the POs in the network can be utilized to provide almost identical common randomness to the users. This randomness is extracted from the synchronization time in the network. Bounds on the entropy of such randomness are derived for a two-user system and a conjecture is made for a general $n$-user system. Then, a three-terminal scenario is considered including two legitimate users and a passive eavesdropper, referred to as Eve. Since in a practical setting Eve receives pulses with propagation delays, she can not identify the exact synchronization time. A simplified model is then considered for Eve's receiver and then a bound on the rate of secret key generation is derived. Also, it is shown, under certain conditions, that the proposed protocol is resilient to an active jammer equipped with a similar pulse generation mechanism.

cs.IT↗

arXiv2019

Covert Millimeter-Wave Communication via a Dual-Beam Transmitter

In this paper, we investigate covert communication over millimeter-wave (mmWave) frequencies. In particular, a dual-beam mmWave transmitter, comprised of two independent antenna arrays, attempts to reliably communicate to a receiver Bob when hiding the existence of transmission from a warden Willie. In this regard, operating over mmWave bands not only increases the covertness thanks to directional beams, but also increases the transmission data rates given much more available bandwidths and enables ultra-low form factor transceivers due to the lower wavelengths used compared to the conventional radio frequency (RF) counterpart. We assume that the transmitter Alice employs one of its antenna arrays to form a directive beam for transmission to Bob. The other antenna array is used by Alice to generate another beam toward Willie as a jamming signal with its transmit power changing independently from a transmission block to another block. We characterize Willie's detection performance with the optimal detector and the closed-form of its expected value from Alice's perspective. We further derive the closed-form expression for the outage probability of the Alice-Bob link, which enables characterizing the optimal covert rate that can be achieved using the proposed setup. Our results demonstrate the superiority of mmWave covert communication, in terms of covertness and rate, compared to the RF counterpart.

cs.IT↗

arXiv2019

Coded Distributed Computing: Performance Limits and Code Designs

We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed nodes. The goal is to reduce the average execution time of the computational job. We provide a connection between the problem of characterizing the average execution time of a coded distributed computing system and the problem of analyzing the error probability of codes of length $n$ used over erasure channels. Accordingly, we present closed-form expressions for the execution time using binary random linear codes and the best execution time any linear-coded distributed computing system can achieve. It is also shown that there exist good binary linear codes that attain, asymptotically, the best performance any linear code, not necessarily binary, can achieve. We also investigate the performance of coded distributed computing systems using polar and Reed-Muller (RM) codes that can benefit from low-complexity decoding, and superior performance, respectively, as well as explicit constructions. The proposed framework in this paper can enable efficient designs of distributed computing systems given the rich literature in the channel coding theory.

cs.IT↗

arXiv2018

Outage Probability Analysis of Uplink NOMA over Ultra-High-Speed FSO-Backhauled Systems

In this paper, we consider a relay-assisted uplink non-orthogonal multiple access (NOMA) system where two radio frequency (RF) users are grouped for simultaneous transmission, over each resource block, to an intermediate relay which forwards the amplified version of the users' aggregated signals in the presence of multiuser interference to a relatively far destination. In order to cope with the users' ever-increasing desire for higher data rates, a high-throughput free-space optics (FSO) link is employed as the relay-destination backhaul link. Dynamic-order decoding is employed at the destination to determine the priority of the users based on their instantaneous channel state information (CSI). Closed-form expressions for the individual- and sum-rate outage probability formulas are derived in the case of independent Rayleigh fading for the users-relay access links when the FSO backhaul link is subject to Gamma-Gamma turbulence with pointing error. This work can be regarded as an initial attempt to incorporate power-domain NOMA over ultra-high-speed FSO-backhauled systems, known as mixed RF-FSO systems.

cs.IT↗

arXiv2018

A Low-Complexity Recursive Approach Toward Code-Domain NOMA for Massive Communications

Nonorthogonal multiple access (NOMA) is a promising technology to meet the demands of the next generation wireless networks on massive connectivity, high throughput and reliability, improved fairness, and low latency. In this context, code-domain NOMA which attempts to serve $K$ users in $M\leq K$ orthogonal resource blocks, using a pattern matrix, is of utmost interest. However, extending the pattern matrix dimensions severely increases the detection complexity and hampers on the significant advantages that can be achieved using large pattern matrices. In this paper, we propose a novel approach toward code-domain NOMA which factorizes the pattern matrix as the Kronecker product of some other factor matrices each with a smaller dimension. Therefore, both the pattern matrix design at the transmitter side and the mixed symbols' detection at the receiver side can be performed over much smaller dimensions and with a remarkably reduced complexity and latency. As a consequence, the system can significantly be overloaded to effectively support the requirements of the next generation wireless networks without any considerable increase on the system complexity.

cs.IT↗

arXiv2017

Global Games with Noisy Information Sharing

Global games form a subclass of games with incomplete information where a set of agents decide actions against a regime with an underlying fundamental $θ$ representing its power. Each agent has access to an independent noisy observation of $θ$. In order to capture the behavior of agents in a social network of information exchange we assume that agents share their observation in a noisy environment prior to making their decision. We show that global games with noisy sharing of information do not admit an intuitive type of threshold policy which only depends on agents' belief about the underlying $θ$. This is in contrast to the existing results on the threshold policy for the conventional set-up of global games. Motivated by this result, we investigate the existence of equilibrium strategies in a more general collection of threshold-type policies and show that such equilibrium strategies exist and are unique if the sharing of information happens over a sufficiently noisy environment.

cs.SI↗

arXiv2016

Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding

We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a multi-user successive cancellation decoder is deployed at the receiver. The encoding is done separately across the users and is independent of the target achievable rate. For the code construction, the positions of information bits and frozen bits for each of the users are decided jointly. This is done by treating the polar transformations across all the $m$ users as a single polar transformation with a certain \emph{polarization base}. We characterize the resolution of achievable rates on the dominant face of the uniform rate region in terms of the number of users $m$ and the length of the polarization base $L$. In particular, we prove that for any target rate on the dominant face, there exists an achievable rate, also on the dominant face, within the distance at most $\frac{(m-1)\sqrt{m}}{L}$ from the target rate. We then prove that the proposed MAC polar coding scheme achieves the whole uniform rate region with fine enough resolution by changing the decoding order in the multi-user successive cancellation decoder, as $L$ and the code block length $N$ grow large. The encoding and decoding complexities are $O(N \log N)$ and the asymptotic block error probability of $O(2^{-N^{0.5 - ε}})$ is guaranteed. Examples of achievable rates for the $3$-user multiple access channel are provided.

cs.IT↗