arXiv subjects

Hessam Mahdavifar

Publications and source records attributed to Hessam Mahdavifar.

At least 55 records · Page 3Linked to original sources

arXiv2023

Capacity-achieving Polar-based Codes with Sparsity Constraints on the Generator Matrices

In this paper, we leverage polar codes and the well-established channel polarization to design capacity-achieving codes with a certain constraint on the weights of all the columns in the generator matrix (GM) while having a low-complexity decoding algorithm. We first show that given a binary-input memoryless symmetric (BMS) channel $W$ and a constant $s \in (0, 1]$, there exists a polarization kernel such that the corresponding polar code is capacity-achieving with the \textit{rate of polarization} $s/2$, and the GM column weights being bounded from above by $N^s$. To improve the sparsity versus error rate trade-off, we devise a column-splitting algorithm and two coding schemes for BEC and then for general BMS channels. The \textit{polar-based} codes generated by the two schemes inherit several fundamental properties of polar codes with the original $2 \times 2$ kernel including the decay in error probability, decoding complexity, and the capacity-achieving property. Furthermore, they demonstrate the additional property that their GM column weights are bounded from above sublinearly in $N$, while the original polar codes have some column weights that are linear in $N$. In particular, for any BEC and $β<0.5$, the existence of a sequence of capacity-achieving polar-based codes where all the GM column weights are bounded from above by $N^λ$ with $λ\approx 0.585$, and with the error probability bounded by $O(2^{-N^β} )$ under a decoder with complexity $O(N\log N)$, is shown. The existence of similar capacity-achieving polar-based codes with the same decoding complexity is shown for any BMS channel and $β<0.5$ with $λ\approx 0.631$.

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arXiv2023

Channel Coding at Low Capacity

Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. Moreover, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundamental limits at finite length and code constructions. We first specify what a low-capacity regime means. We then characterize finite-length fundamental limits of channel coding in the low-capacity regime for various types of channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), and additive white Gaussian noise (AWGN) channels. From the code construction perspective, we characterize the optimal number of repetitions for transmission over binary memoryless symmetric (BMS) channels, in terms of the code blocklength and the underlying channel capacity, such that the capacity loss due to the repetition is negligible. Furthermore, it is shown that capacity-achieving polar codes naturally adopt the aforementioned optimal number of repetitions.

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arXiv2023

Federated Learning with Heterogeneous Differential Privacy

Federated learning (FL) takes a first step towards privacy-preserving machine learning by training models while keeping client data local. Models trained using FL may still leak private client information through model updates during training. Differential privacy (DP) may be employed on model updates to provide privacy guarantees within FL, typically at the cost of degraded performance of the final trained model. Both non-private FL and DP-FL can be solved using variants of the federated averaging (FedAvg) algorithm. In this work, we consider a heterogeneous DP setup where clients require varying degrees of privacy guarantees. First, we analyze the optimal solution to the federated linear regression problem with heterogeneous DP in a Bayesian setup. We find that unlike the non-private setup, where the optimal solution for homogeneous data amounts to a single global solution for all clients learned through FedAvg, the optimal solution for each client in this setup would be a personalized one even for homogeneous data. We also analyze the privacy-utility trade-off for this setup, where we characterize the gain obtained from heterogeneous privacy where some clients opt for less strict privacy guarantees. We propose a new algorithm for FL with heterogeneous DP, named FedHDP, which employs personalization and weighted averaging at the server using the privacy choices of clients, to achieve better performance on clients' local models. Through numerical experiments, we show that FedHDP provides up to $9.27\%$ performance gain compared to the baseline DP-FL for the considered datasets where $5\%$ of clients opt out of DP. Additionally, we show a gap in the average performance of local models between non-private and private clients of up to $3.49\%$, empirically illustrating that the baseline DP-FL might incur a large utility cost when not all clients require the stricter privacy guarantees.

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arXiv2022

Capacity-achieving Polar-based LDGM Codes

In this paper, we study codes with sparse generator matrices. More specifically, low-density generator matrix (LDGM) codes with a certain constraint on the weight of the columns in the generator matrix are considered. In this paper, it is first shown that when a BMS channel W and a constant s>0 are given, there exists a polarization kernel such that the corresponding polar code is capacity-achieving and the column weights of the generator matrix (GM) are bounded from above by $N^s$. Then, a general construction based on a concatenation of polar codes and a rate-$1$ code, and a new column-splitting algorithm that guarantees a much sparser GM, is given. More specifically, for any BMS channel and any $ε> 2ε^*$, where $ε^* \approx 0.085$, an existence of a sequence of capacity-achieving codes with all the GM column weights upper bounded by $(\log N)^{1+ε}$ is shown. Furthermore, two coding schemes for BEC and BMS channels, based on a second column-splitting algorithm, are devised with low-complexity decoding that uses successive-cancellation. The second splitting algorithm allows for the use of a low-complexity decoder by preserving the reliability of the bit-channels observed by the source bits, and by increasing the code block length. The concatenation-based construction can also be applied to the random linear code ensemble to yield capacity-achieving codes with all the GM column weights being $O(\log N)$ and with (large-degree) polynomial decoding complexity.

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arXiv2022

ML-Aided Collision Recovery for UHF-RFID Systems

We propose a collision recovery algorithm with the aid of machine learning (ML-aided) for passive Ultra High Frequency (UHF) Radio Frequency Identification (RFID) systems. The proposed method aims at recovering the tags under collision to improve the system performance. We first estimate the number of tags from the collided signal by utilizing machine learning tools and show that the number of colliding tags can be estimated with high accuracy. Second, we employ a simple yet effective deep learning model to find the experienced channel coefficients. The proposed method allows the reader to separate each tag's signal from the received one by applying maximum likelihood decoding. We perform simulations to illustrate that the use of deep learning is highly beneficial and demonstrate that the proposed approach boosts the throughput performance of the standard framed slotted ALOHA (FSA) protocol from 0.368 to 1.837, where the receiver is equipped with a single antenna and capable of decoding up to 4 tags.

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arXiv2022

Hybrid Non-Binary Repeated Polar Codes

Concatenating the state-of-the-art codes at moderate rates with repetition codes has emerged as a practical solution deployed in various standards for ultra-low-power devices such as in Internet-of-Things (IoT) networks. In this paper, we propose a novel concatenation mechanism for such applications which need to operate at very low signal-to-noise ratio (SNR) regime. In the proposed scheme, the outer code is a hybrid polar code constructed in two stages, one with a binary kernel and another also with a binary kernel but applied over a binary extension field. The inner code is a non-binary multiplicative repetition code. This particular structure inherits low-complexity decoding structures of polar codes while enabling concatenation with an inner non-binary multiplicative repetition scheme. The decoding for the proposed scheme is done using cyclic redundancy check (CRC) aided successive cancellation list (SCL) decoder over AWGN channel. Simulation results demonstrate that the proposed hybrid non-binary repeated polar code provides performance gain compared to a polar-repetition scheme with comparable decoding complexity.

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arXiv2022

Orthonormal Sketches for Secure Coded Regression

In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a random orthonormal matrix and then subsample in \textit{blocks}, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the transformation corresponds to an encoded encryption in an \textit{approximate} gradient coding scheme, and the subsampling corresponds to the responses of the non-straggling workers; in a centralized coded computing network. We focus on the special case of the \textit{Subsampled Randomized Hadamard Transform}, which we generalize to block sampling; and discuss how it can be used to secure the data. We illustrate the performance through numerical experiments.

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arXiv2022

Low-Complexity Decoding of a Class of Reed-Muller Subcodes for Low-Capacity Channels

We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically, the input sequence is shaped as a multi-dimensional array, and the encoding over each dimension is done separately via a smaller RM encoder. Similarly, the decoding is performed over each dimension via a low-complexity decoder for smaller RM codes. The proposed construction is of particular interest to low-capacity channels that are relevant to emerging low-rate communication scenarios. We present an efficient soft-input soft-output (SISO) iterative decoding algorithm for the product of RM codes and demonstrate its superiority compared to hard decoding over RM code components. The proposed coding scheme has decoding (as well as encoding) complexity of $\mathcal{O}(n\log n)$ and latency of $\mathcal{O}(\log n)$ for blocklength $n$. This research renders a general framework toward efficient decoding of RM codes.

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arXiv2022

Analog Subspace Coding: A New Approach to Coding for Non-Coherent Wireless Networks

We provide a novel framework to study subspace codes for non-coherent communications in wireless networks. To this end, an analog operator channel is defined with inputs and outputs being subspaces of $\mathbb{C}^n$. Then a certain distance is defined to capture the performance of subspace codes in terms of their capability to recover from interference and rank-deficiency of the network. We also study the robustness of the proposed model with respect to an additive noise. Furthermore, we propose a new approach to construct subspace codes in the analog domain, also regarded as Grassmann codes, by leveraging polynomial evaluations over finite fields together with characters associated to finite fields that map their elements to the unit circle in the complex plane. The constructed codes, referred to as character-polynomial (CP) codes, are shown to perform better comparing to other existing constructions of Grassmann codes in terms of the trade-off between the rate and the normalized minimum distance, for a wide range of values for $n$.

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arXiv2021

Covert Millimeter-Wave Communication: Design Strategies and Performance Analysis

In this paper, we investigate covert communication over millimeter-wave (mmWave) frequencies. In particular, a mmWave transmitter, referred to as Alice, attempts to reliably communicate to a receiver, referred to as Bob, while hiding the existence of communication from a warden, referred to as Willie. In this regard, operating over the 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 first assume that the transmitter Alice employs two independent antenna arrays in which one of the arrays is to form a directive beam for data transmission to Bob. The other antenna array is used by Alice to generate another beam toward Willie as a jamming signal while changing the transmit power independently across the transmission blocks in order to achieve the desired covertness. For this dual-beam setup, we characterize Willie's detection error rate with the optimal detector and the closed-form of its expected value from Alice's perspective. We then 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. We further obtain tractable forms for the ergodic capacity of the Alice-Bob link involving only one-dimensional integrals that can be computed in closed forms for most ranges of the channel parameters. Finally, we highlight how the results can be extended to more practical scenarios, particularly to the cases where perfect information about the location of the passive warden is not available.

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arXiv2021

Coded Computing via Binary Linear Codes: Designs and Performance Limits

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 \textit{good} binary linear codes that not only attain (asymptotically) the best performance that any linear code (not necessarily binary) can achieve but also are numerically stable against the inevitable rounding errors in practice. We then develop a low-complexity algorithm for decoding Reed-Muller (RM) codes over erasure channels. Our decoder only involves additions, subtractions, {and inversion of relatively small matrices of dimensions at most $\log n+1$}, and enables coded computation over real-valued data. Extensive numerical analysis of the fundamental results as well as RM- and polar-coded computing schemes demonstrate the excellence of the RM-coded computation in achieving close-to-optimal performance while having a low-complexity decoding and explicit construction. The proposed framework in this paper enables efficient designs of distributed computing systems given the rich literature in the channel coding theory.

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arXiv2021

ApproxIFER: A Model-Agnostic Approach to Resilient and Robust Prediction Serving Systems

Due to the surge of cloud-assisted AI services, the problem of designing resilient prediction serving systems that can effectively cope with stragglers/failures and minimize response delays has attracted much interest. The common approach for tackling this problem is replication which assigns the same prediction task to multiple workers. This approach, however, is very inefficient and incurs significant resource overheads. Hence, a learning-based approach known as parity model (ParM) has been recently proposed which learns models that can generate parities for a group of predictions in order to reconstruct the predictions of the slow/failed workers. While this learning-based approach is more resource-efficient than replication, it is tailored to the specific model hosted by the cloud and is particularly suitable for a small number of queries (typically less than four) and tolerating very few (mostly one) number of stragglers. Moreover, ParM does not handle Byzantine adversarial workers. We propose a different approach, named Approximate Coded Inference (ApproxIFER), that does not require training of any parity models, hence it is agnostic to the model hosted by the cloud and can be readily applied to different data domains and model architectures. Compared with earlier works, ApproxIFER can handle a general number of stragglers and scales significantly better with the number of queries. Furthermore, ApproxIFER is robust against Byzantine workers. Our extensive experiments on a large number of datasets and model architectures also show significant accuracy improvement by up to 58% over the parity model approaches.

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arXiv2021

KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning

Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes: each is a linear code and represents a mathematical breakthrough. The impact on humanity is huge: each of these codes has been used in global wireless communication standards (satellite, WiFi, cellular). Reliability of communication over the classical additive white Gaussian noise (AWGN) channel enables benchmarking and ranking of the different codes. In this paper, we construct KO codes, a computationaly efficient family of deep-learning driven (encoder, decoder) pairs that outperform the state-of-the-art reliability performance on the standardized AWGN channel. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding, in the challenging short-to-medium block length regime on the AWGN channel. We show that the gains of KO codes are primarily due to the nonlinear mapping of information bits directly to transmit real symbols (bypassing modulation) and yet possess an efficient, high performance decoder. The key technical innovation that renders this possible is design of a novel family of neural architectures inspired by the computation tree of the {\bf K}ronecker {\bf O}peration (KO) central to Reed-Muller and Polar codes. These architectures pave way for the discovery of a much richer class of hitherto unexplored nonlinear algebraic structures. The code is available at \href{https://github.com/deepcomm/KOcodes}{https://github.com/deepcomm/KOcodes}

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arXiv2021

List-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier

We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously known in coded computing. More specifically, we leverage list-decoding techniques for folded Reed-Solomon codes and propose novel algorithms to recover the correct codeword using side information. In the coded computing setting, we show how the master node can perform certain carefully designed extra computations to obtain the side information. The workload of computing this side information is negligible compared to the computations done by each worker. This side information is then utilized to prune the output of the list decoder and uniquely recover the true outcome. We further propose folded Lagrange coded computing (FLCC) to incorporate the developed techniques into a specific coded computing setting. Our results show that FLCC outperforms LCC by breaking the barrier on the number of adversaries that can be tolerated. In particular, the corresponding threshold in FLCC is improved by a factor of two asymptotically compared to that of LCC.

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arXiv2021

Coded Machine Unlearning

There are applications that may require removing the trace of a sample from the system, e.g., a user requests their data to be deleted, or corrupted data is discovered. Simply removing a sample from storage units does not necessarily remove its entire trace since downstream machine learning models may store some information about the samples used to train them. A sample can be perfectly unlearned if we retrain all models that used it from scratch with that sample removed from their training dataset. When multiple such unlearning requests are expected to be served, unlearning by retraining becomes prohibitively expensive. Ensemble learning enables the training data to be split into smaller disjoint shards that are assigned to non-communicating weak learners. Each shard is used to produce a weak model. These models are then aggregated to produce the final central model. This setup introduces an inherent trade-off between performance and unlearning cost, as reducing the shard size reduces the unlearning cost but may cause degradation in performance. In this paper, we propose a coded learning protocol where we utilize linear encoders to encode the training data into shards prior to the learning phase. We also present the corresponding unlearning protocol and show that it satisfies the perfect unlearning criterion. Our experimental results show that the proposed coded machine unlearning provides a better performance versus unlearning cost trade-off compared to the uncoded baseline.

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arXiv2021

Massive Coded-NOMA for Low-Capacity Channels: A Low-Complexity Recursive Approach

In this paper, we present a low-complexity recursive approach for massive and scalable code-domain nonorthogonal multiple access (NOMA) with applications to emerging low-capacity scenarios. The problem definition in this paper is inspired by three major requirements of the next generations of wireless networks. Firstly, the proposed scheme is particularly beneficial in low-capacity regimes which is important in practical scenarios of utmost interest such as the Internet-of-Things (IoT) and massive machine-type communication (mMTC). Secondly, we employ code-domain NOMA to efficiently share the scarce common resources among the users. Finally, the proposed recursive approach enables code-domain NOMA with low-complexity detection algorithms that are scalable with the number of users to satisfy the requirements of massive connectivity. To this end, we propose a novel encoding and decoding scheme for code-domain NOMA based on factorizing the pattern matrix, for assigning the available resource elements to the users, as the Kronecker product of several smaller factor matrices. As a result, both the pattern matrix design at the transmitter side and the mixed symbols' detection at the receiver side can be performed over matrices with dimensions that are much smaller than the overall pattern matrix. Consequently, this leads to significant reduction in both the complexity and the latency of the detection. We present the detection algorithm for the general case of factor matrices. The proposed algorithm involves several recursions each involving certain sets of equations corresponding to a certain factor matrix. We then characterize the system performance in terms of average sum rate, latency, and detection complexity. Our latency and complexity analysis confirm the superiority of our proposed scheme in enabling large pattern matrices.

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arXiv2021

Reed-Muller Subcodes: Machine Learning-Aided Design of Efficient Soft Recursive Decoding

Reed-Muller (RM) codes are conjectured to achieve the capacity of any binary-input memoryless symmetric (BMS) channel, and are observed to have a comparable performance to that of random codes in terms of scaling laws. On the negative side, RM codes lack efficient decoders with performance close to that of a maximum likelihood decoder for general parameters. Also, they only admit certain discrete sets of rates. In this paper, we focus on subcodes of RM codes with flexible rates that can take any code dimension from 1 to n, where n is the blocklength. We first extend the recursive projection-aggregation (RPA) algorithm proposed recently by Ye and Abbe for decoding RM codes. To lower the complexity of our decoding algorithm, referred to as subRPA in this paper, we investigate different ways for pruning the projections. We then derive the soft-decision based version of our algorithm, called soft-subRPA, that is shown to improve upon the performance of subRPA. Furthermore, it enables training a machine learning (ML) model to search for \textit{good} sets of projections in the sense of minimizing the decoding error rate. Training our ML model enables achieving very close to the performance of full-projection decoding with a significantly reduced number of projections. For instance, our simulation results on a (64,14) RM subcode show almost identical performance for full-projection decoding and pruned-projection decoding with 15 projections picked via training our ML model. This is equivalent to lowering the complexity by a factor of more than 4 without sacrificing the decoding performance.

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arXiv2021

Analog Lagrange Coded Computing

A distributed computing scenario is considered, where the computational power of a set of worker nodes is used to perform a certain computation task over a dataset that is dispersed among the workers. Lagrange coded computing (LCC), proposed by Yu et al., leverages the well-known Lagrange polynomial to perform polynomial evaluation of the dataset in such a scenario in an efficient parallel fashion while keeping the privacy of data amidst possible collusion of workers. This solution relies on quantizing the data into a finite field, so that Shamir's secret sharing, as one of its main building blocks, can be employed. Such a solution, however, is not properly scalable with the size of dataset, mainly due to computation overflows. To address such a critical issue, we propose a novel extension of LCC to the analog domain, referred to as analog LCC (ALCC). All the operations in the proposed ALCC protocol are done over the infinite fields of R/C but for practical implementations floating-point numbers are used. We characterize the privacy of data in ALCC, against any subset of colluding workers up to a certain size, in terms of the distinguishing security (DS) and the mutual information security (MIS) metrics. Also, the accuracy of outcome is characterized in a practical setting assuming operations are performed using floating-point numbers. Consequently, a fundamental trade-off between the accuracy of the outcome of ALCC and its privacy level is observed and is numerically evaluated. Moreover, we implement the proposed scheme to perform matrix-matrix multiplication over a batch of matrices. It is observed that ALCC is superior compared to the state-of-the-art LCC, implemented using fixed-point numbers, assuming both schemes use an equal number of bits to represent data symbols.

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