arXiv subjects

Krishna R. Narayanan

Publications and source records attributed to Krishna R. Narayanan.

At least 37 records · Page 2Linked to original sources

arXiv2020

Sparse IDMA: A Joint Graph-Based Coding Scheme for Unsourced Random Access

This article introduces a novel communication paradigm for the unsourced, uncoordinated Gaussian multiple access problem. The major components of the envisioned framework are as follows. The encoded bits of every message are partitioned into two groups. The first portion is transmitted using a compressive sensing scheme, whereas the second set of bits is conveyed using a multi-user coding scheme. The compressive sensing portion is key in sidestepping some of the challenges posed by the unsourced aspect of the problem. The information afforded by the compressive sensing is employed to create a sparse random multi-access graph conducive to joint decoding. This construction leverages the lessons learned from traditional IDMA into creating low-complexity schemes for the unsourced setting and its inherent randomness. Under joint message-passing decoding, the proposed scheme offers comparable performance to existing low-complexity alternatives. Findings are supported by numerical simulations.

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arXiv2020

A Hybrid Approach to Coded Compressed Sensing where Coupling Takes Place via the Outer Code

This article seeks to advance coded compressed sensing (CCS) as a practical scheme for unsourced random access. The original CCS algorithm features a concatenated structure where an inner code is tasked with support recovery, and an outer tree code conducts message disambiguation. Recently, a link between CCS and sparse regression codes was established, leading to the application of approximate message passing (AMP) to CCS. This connection was subsequently strengthened by integrating AMP and belief propagation on the outer code through a dynamic denoiser. Along these lines, this work shows how block diagonal sensing matrices akin to those used in traditional CCS, together with the aforementioned dynamic denoiser, form an effective means to get good performance at low-complexity. This novel architecture can be used to scale this scheme to dimensions that were previously impractical. Findings are supported by numerical simulations.

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arXiv2020

Unsourced Random Access with Coded Compressed Sensing: Integrating AMP and Belief Propagation

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced random access with coded compressed sensing (CCS), as first demonstrated by Fengler, Jung, and Caire. Specifically, their approach employs a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In their original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer tree decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. This scheme necessitates the redesign of the tree code as to enable belief propagation in a computationally tractable manner. The enhanced architecture exhibits significant performance benefits over a range of system parameters. The error performance of the proposed scheme can be accurately predicted through a set of equations, known as state evolution of AMP. These findings are supported both analytically and through numerical methods.

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arXiv2020

Two-Stage Adaptive Pooling with RT-qPCR for COVID-19 Screening

We propose two-stage adaptive pooling schemes, 2-STAP and 2-STAMP, for detecting COVID-19 using real-time reverse transcription quantitative polymerase chain reaction (RT-qPCR) test kits. Similar to the Tapestry scheme of Ghosh et al., the proposed schemes leverage soft information from the RT-qPCR process about the total viral load in the pool. This is in contrast to conventional group testing schemes where the measurements are Boolean. The proposed schemes provide higher testing throughput than the popularly used Dorfman's scheme. They also provide higher testing throughput, sensitivity and specificity than the state-of-the-art non-adaptive Tapestry scheme. The number of pipetting operations is lower than state-of-the-art non-adaptive pooling schemes, and is higher than that for the Dorfman's scheme. The proposed schemes can work with substantially smaller group sizes than non-adaptive schemes and are simple to describe. Monte-Carlo simulations using the statistical model in the work of Ghosh et al. (Tapestry) show that 10 infected people in a population of size 961 can be identified with 70.86 tests on the average with a sensitivity of 99.50% and specificity of 99.62. This is 13.5x, 4.24x, and 1.3x the testing throughput of individual testing, Dorfman's testing, and the Tapestry scheme, respectively.

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arXiv2020

Semi-Implicit Graph Variational Auto-Encoders

Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithful modeling of implicit posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and rich dependency structures. Compared to VGAE, the derived graph latent representations by SIG-VAE are more interpretable, due to more expressive generative model and more faithful inference enabled by the flexible semi-implicit construction. Extensive experiments with a variety of graph data show that SIG-VAE significantly outperforms state-of-the-art methods on several different graph analytic tasks.

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arXiv2020

On Accelerated Testing for COVID-19 Using Group Testing

COVID-19 has resulted in a global health crisis that may become even more acute over the upcoming months. One of the main reasons behind the current rapid growth of COVID-19 in the U.S. population is the limited availability of testing kits and the relatively-high cost of screening tests. In this draft, we demonstrate the effectiveness of group testing (pooling) ideas to accelerate testing for COVID-19. This draft is semi-tutorial in nature and is written for a broad audience with interest in mathematical formulations relevant to COVID-19 testing. Therefore, ideas are presented through illustrative examples rather than through purely theoretical formulations. The focus is also on pools of size less than 64 such as what is practical with current RT-PCR technology.

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arXiv2020

On Approximate Message Passing for Unsourced Access with Coded Compressed Sensing

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced access with coded compressed sensing (CCS), as first pointed out by Fengler, Jung, and Caire. More specifically, their approach uses a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In the original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer tree decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. The enhanced architecture exhibits significant performance benefit over a range of system parameters. Simulation results are provided to demonstrate the performance benefit offered by the proposed access scheme over existing schemes in the literature.

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arXiv2019

Polar Coding and Random Spreading for Unsourced Multiple Access

This article presents a novel transmission scheme for the unsourced, uncoordinated Gaussian multiple access problem. The proposed scheme leverages notions from single-user coding, random spreading, minimum-mean squared error (MMSE) estimation, and successive interference cancellation. Specifically, every message is split into two parts: the first fragment serves as the argument to an injective function that determines which spreading sequence should be employed, whereas the second component of the message is encoded using a polar code. The latter coded bits are then spread using the sequence determined during the first step. The ensuing signal is transmitted through a Gaussian multiple-access channel (GMAC). On the receiver side, active sequences are detected using a correlation-based energy detector, thereby simultaneously recovering individual signature sequences and their generating information bits in the form of preimages of the sequence selection function. Using the set of detected active spreading sequences, an MMSE estimator is employed to produce log-likelihood ratios (LLRs) for the second part of the messages corresponding to these detected users. The LLRs associated with each detected user are then passed to a list decoder of the polar code, which performs single-user decoding to decode the second portion of the message. This decoding operation proceeds iteratively by subtracting the interference due to the successfully decoded messages from the received signal, and repeating the above steps on the residual signal. At this stage, the proposed algorithm outperforms alternate existing low-complexity schemes when the number of active uses is below 225.

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arXiv2019

An enhanced decoding algorithm for coded compressed sensing

Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to machine-type communications. Coded compressed sensing uses a divide-and-conquer approach to break the sparse recovery task into sub-components whose dimensions are amenable to conventional compressed sensing solvers. The recovered fragments are then stitched together using a low complexity decoder. This article introduces an enhanced decoding algorithm for coded compressed sensing where fragment recovery and the stitching process are executed in tandem, passing information between them. This novel scheme leads to gains in performance and a significant reduction in computational complexity. This algorithmic opportunity stems from the realization that the parity structure inherent to coded compressed sensing can be used to dynamically restrict the search space of the subsequent recovery algorithm.

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arXiv2019

Non-adaptive Quantitative Group Testing Using Irregular Sparse Graph Codes

This paper considers the problem of Quantitative Group Testing (QGT) where there are some defective items among a large population of $N$ items. We consider the scenario in which each item is defective with probability $K/N$, independently from the other items. In the QGT problem, the goal is to identify all or a sufficiently large fraction of the defective items by testing groups of items, with the minimum possible number of tests. In particular, the outcome of each test is a non-negative integer which indicates the number of defective items in the tested group. In this work, we propose a non-adaptive QGT scheme for the underlying randomized model for defective items, which utilizes sparse graph codes over irregular bipartite graphs with optimized degree profiles on the left nodes of the graph as well as binary $t$-error-correcting BCH codes. We show that in the sub-linear regime, i.e., when the ratio $K/N$ vanishes as $N$ grows unbounded, the proposed scheme with ${m=c(t,d)K(t\log (\frac{\ell N}{c(t,d)K}+1)+1)}$ tests can identify all the defective items with probability approaching $1$, where $d$ and $\ell$ are the maximum and average left degree, respectively, and $c(t,d)$ depends only on $t$ and $d$ (and does not depend on $K$ and $N$). For any $t\leq 4$, the testing and recovery algorithms of the proposed scheme have the computational complexity of $\mathcal{O}(N\log \frac{N}{K})$ and $\mathcal{O}(K\log \frac{N}{K})$, respectively. The proposed scheme outperforms two recently proposed non-adaptive QGT schemes for the sub-linear regime, including our scheme based on regular bipartite graphs and the scheme of Gebhard et al., in terms of the number of tests required to identify all defective items with high probability.

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arXiv2019

Piecewise Stationary Modeling of Random Processes Over Graphs With an Application to Traffic Prediction

Stationarity is a key assumption in many statistical models for random processes. With recent developments in the field of graph signal processing, the conventional notion of wide-sense stationarity has been extended to random processes defined on the vertices of graphs. It has been shown that well-known spectral graph kernel methods assume that the underlying random process over a graph is stationary. While many approaches have been proposed, both in machine learning and signal processing literature, to model stationary random processes over graphs, they are too restrictive to characterize real-world datasets as most of them are non-stationary processes. In this paper, to well-characterize a non-stationary process over graph, we propose a novel model and a computationally efficient algorithm that partitions a large graph into disjoint clusters such that the process is stationary on each of the clusters but independent across clusters. We evaluate our model for traffic prediction on a large-scale dataset of fine-grained highway travel times in the Dallas--Fort Worth area. The accuracy of our method is very close to the state-of-the-art graph based deep learning methods while the computational complexity of our model is substantially smaller.

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arXiv2019

Factored LT and Factored Raptor Codes for Large-Scale Distributed Matrix Multiplication

We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These coding schemes are adaptations of LT codes and Raptor codes to distributed matrix multiplication and are termed \emph{factored LT (FLT) codes} and \emph{factored Raptor (FR) codes}. Empirically, we show that FLT codes have near-optimal recovery thresholds when the number of worker nodes is very large, and that FR codes have excellent recovery thresholds while the number of worker nodes is moderately large. FLT and FR codes have better recovery thresholds when compared to Product codes and they are expected to have better numerical stability when compared to Polynomial codes, while they can also be decoded with a low-complexity decoding algorithm.

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arXiv2019

Random Khatri-Rao-Product Codes for Numerically-Stable Distributed Matrix Multiplication

We propose a class of codes called random Khatri-Rao-Product (RKRP) codes for distributed matrix multiplication in the presence of stragglers. The main advantage of the proposed codes is that decoding of RKRP codes is highly numerically stable in comparison to decoding of Polynomial codes and decoding of the recently proposed OrthoPoly codes. We show that RKRP codes are maximum distance separable with probability 1. The communication cost and encoding complexity for RKRP codes are identical to that of OrthoPoly codes and Polynomial codes and the average decoding complexity of RKRP codes is lower than that of OrthoPoly codes. Numerical results show that the average relative $L_2$-norm of the reconstruction error for RKRP codes is substantially better than that of OrthoPoly codes.

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arXiv2019

Spatially-Coupled Neural Network Architectures

In this work, we leverage advances in sparse coding techniques to reduce the number of trainable parameters in a fully connected neural network. While most of the works in literature impose $\ell_1$ regularization, DropOut or DropConnect techniques to induce sparsity, our scheme considers feature importance as a criterion to allocate the trainable parameters (resources) efficiently in the network. Even though sparsity is ensured, $\ell_1$ regularization requires training on all the resources in a deep neural network. The DropOut/DropConnect techniques reduce the number of trainable parameters in the training stage by dropping a random collection of neurons/edges in the hidden layers. However, both these techniques do not pay heed to the underlying structure in the data when dropping the neurons/edges. Moreover, these frameworks require a storage space equivalent to the number of parameters in a fully connected neural network. We address the above issues with a more structured architecture inspired from spatially-coupled sparse constructions. The proposed architecture is shown to have a performance akin to a conventional fully connected neural network with dropouts, and yet achieving a $94\%$ reduction in the training parameters. Extensive simulations are presented and the performance of the proposed scheme is compared against traditional neural network architectures.

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arXiv2019

A Coded Compressed Sensing Scheme for Uncoordinated Multiple Access

This article introduces a novel communication scheme, termed coded compressed sensing, for unsourced multiple-access communication. The proposed divide-and-conquer approach leverages recent advances in compressed sensing and forward error correction to produce a novel uncoordinated access paradigm, along with a computationally efficient decoding algorithm. Within this framework, every active device partitions its data into several sub-blocks and, subsequently, adds redundancy using a systematic linear block code. Compressed sensing techniques are then employed to recover sub-blocks up to a permutation of their order, and the original messages are obtained by stitching fragments together using a tree-based algorithm. The error probability and computational complexity of this access paradigm are characterized. An optimization framework, which exploits the tradeoff between performance and computational complexity, is developed to assign parity-check bits to each sub-block. In addition, two emblematic parity bit allocation strategies are examined and their performances are analyzed in the limit as the number of active users and their corresponding payloads tend to infinity. The number of channel uses needed and the computational complexity associated with these allocation strategies are established for various scaling regimes. Numerical results demonstrate that coded compressed sensing outperforms other existing practical access strategies over a range of operational scenarios.

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arXiv2019

Collaborative Decoding of Polynomial Codes for Distributed Computation

We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes return erroneous values. For an additive random Gaussian error model, we show that for all $t < N-K$, errors can be corrected with probability 1. Further, numerical results show that in the presence of additive errors, when $L$ Reed-Solomon codes are collaboratively decoded, the numerical stability in recovering the error locator polynomial improves with increasing $L$.

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arXiv2019

Sparse Graph Codes for Non-adaptive Quantitative Group Testing

This paper considers the problem of Quantitative Group Testing (QGT). Consider a set of $N$ items among which $K$ items are defective. The QGT problem is to identify (all or a sufficiently large fraction of) the defective items, where the result of a test reveals the number of defective items in the tested group. In this work, we propose a non-adaptive QGT algorithm using sparse graph codes over bi-regular bipartite graphs with left-degree $\ell$ and right degree $r$ and binary $t$-error-correcting BCH codes. The proposed scheme provides exact recovery with probabilistic guarantee, i.e. recovers all the defective items with high probability. In particular, we show that for the sub-linear regime where $\frac{K}{N}$ vanishes as $K,N\rightarrow\infty$, the proposed algorithm requires at most ${m=c(t)K\left(t\log_2\left(\frac{\ell N}{c(t)K}+1\right)+1\right)+1}$ tests to recover all the defective items with probability approaching one as ${K,N\rightarrow\infty}$, where $c(t)$ depends only on $t$. The results of our theoretical analysis reveal that the minimum number of required tests is achieved by $t=2$. The encoding and decoding of the proposed algorithm for any $t\leq 4$ have the computational complexity of $\mathcal{O}(K\log^2 \frac{N}{K})$ and $\mathcal{O}(K\log \frac{N}{K})$, respectively. Our simulation results also show that the proposed algorithm significantly outperforms a non-adaptive semi-quantitative group testing algorithm recently proposed by Abdalla \emph{et al.} in terms of the required number of tests for identifying all the defective items with high probability.

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arXiv2018

Asynchronous Neighbor Discovery Using Coupled Compressive Sensing

The neighbor discovery paradigm finds wide application in Internet of Things networks, where the number of active devices is orders of magnitude smaller than the total device population. Designing low-complexity schemes for asynchronous neighbor discovery has recently gained significant attention from the research community. Concurrently, a divide-and-conquer framework, referred to as coupled compressive sensing, has been introduced for the synchronous massive random access channel. This work adapts this novel algorithm to the problem of asynchronous neighbor discovery with unknown transmission delays. Simulation results suggest that the proposed scheme requires much fewer transmissions to achieve a performance level akin to that of state-of-the-art techniques.

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