Entanglement-assisted (EA) quantum codes relax the condition of dual-containment property on the classical codes by using pre-shared Bell pairs across the quantum transceiver. We design an encoder for the EA Calderbank-Shor-Steane (CSS) quantum codes by utilizing the operators from the Clifford group. We also present a fault-tolerant measurement strategy for obtaining syndromes by incorporating an extra resource state while working with a faulty measurement device.

We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. By carefully designing the parity-check matrix, our approach ensures both structural flexibility and improved error-correction capabilities. We evaluate the performance of these codes under the additive white Gaussian noise (AWGN) channel. Simulation results demonstrate that the proposed QC-LDPC codes outperform the protograph LDPC codes included in the Consultative Committee for Space Data Systems (CCSDS) telecommand standards. Additionally, we benchmark our proposed codes against existing short-length codes with girth 8, observing improvements in the decoding performance while ensuring suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs for the Internet of Things (IoT), machine-to-machine (M2M), and satellite communications.

Magic state distillation (MSD) is a procedure to purify noisy non-stabilizer states from a quantum code, useful towards fault-tolerant quantum computing. Quantum circuits requiring non-Clifford gates can be realized using special states called magic states that are the eigenstates of both non-Clifford and Clifford gates. The purification of noisy states is realized by projecting these magic states onto the space spanned by the eigenstates of the projection operator of the stabilizer code. Given a noisy non- stabilizer state from a given stabilizer code, not all states can be distilled towards magic states. In this paper, we provide the condition for distillability of magic states specific to the choice of qudit stabilizer codes. We derive the noise threshold for magic state distillation depending on the code parameters. We prove that magic state distillation is a convergent map in the entropic sense. We also give an efficient decoding circuit for the best-known code to distill the$\left|H_i\right\rangle$state, which is an eigenstate of the qutrit Hadamard gate.

We provide code constructions along with code properties for a few families of entanglement-assisted (EA) Calderbank-Shor-Steane (CSS) codes derived from quasi-cyclic (QC) low-density parity check (LDPC) codes. These codes require only a minimum number of Bell pairs to be shared between the transmitter and the receiver. The Tanner graph of the proposed EA QC LDPC code has girth$> 4$. We evaluate the performance of these codes using both random and Markovian noise models to assess random and burst error performance using a modified-version of the min-sum algorithm.

We propose quantum circuit architectures for convolutional neural networks based on generalized 3-qubit and 2-qubit quantum gates for the multiclass classification problem. The quantum architecture is equivalent to a classical convolutional neural network with fully connected layers and densely connected layers. The quantum circuit parameters are optimized by minimizing the cross-entropy loss function. We validate the classification performance over several model configurations on the MNIST, Fashion-MNIST and Kuzushiji-MNIST datasets. Our proposed architecture shows classification accuracies that are comparable to classical CNNs with a similar number of parameters. In addition to this, we find that circuit depth is greatly decreased by a logarithmic factor compared to classical CNNs. We study the performance and complexity tradeoffs over several model configurations within the proposed quantum CNN architecture.

Transformer-based architectures using attention mechanisms are a class of learning architectures for sequence processing tasks. These include architectures such as the generative pretrained transformer (GPT) and the bidirectional encoder representations from transformers (BERT). GPT-2 is a popular sequence learning architecture that uses transformer architecture. GPT-2 is trained on text prediction, and the network parameters obtained during this training process can be used in various other tasks like text classification and premise-hypothesis testing. Edge computing is an recent trend in which training is done on cloud or server with multiple GPUs, but inference is done on edge devices like mobile phones to reduce latency and improve privacy. This necessitates a study of GPT-2 performance and complexity to distill hardware-based architectures for their usability on edge devices. In this paper, a single layer of GPT-2 based inference architecture is implemented on Virtex-7 xc7vx485tffg1761-2 FPGA board. The inference engine has model dimensionality of 128 and latency of 1.637 ms while operating at 142.44 MHz, consuming 85.6K flip-flops and 96.8K lookup tables, achieving 1.73x speedup compared to previously reported work on transformer-based architecture. The approach proposed in this paper is scalable to models of higher dimensionality.

We develop a systematic theory to reconstruct missing samples in a time series using a spatiotemporal memory based on artificial neural networks. The Markov order of the input process is learned and subsequently used for learning temporal correlations from data difference sequences. We enforce the Lipschitz continuity criterion in our algorithm, leading to a regularized optimization framework for learning. The performance of the algorithm is analyzed using both theory and simulations. The efficacy of the technique is tested on synthetic and real life data sets. Our technique is analytic and uses nonlinear feedback within an optimization setup. Simulation results show that the algorithm presented in this article significantly outperforms the state-of-the-art algorithms for missing samples reconstruction with the same data set and similar training conditions.

Self-organizing maps (SOM) are popularly used for applications in learning features, vector quantization and recalling spatial input patterns. The adaptation rule in SOM is based on the Euclidean distance between the input vector and the neuronal weight vector along with a neighborhood function that brings in topological arrangement of the neurons. It is capable of learning the spatial correlations among the data but fails to capture temporal correlations present in a sequence of inputs. We formulate a potential function based on a spatio-temporal metric and create hierarchical vector quantization feature maps by embedding memory structures similar to long short-term memories (LSTM) across the feature maps to learn the spatiotemporal correlations in the data across clusters. We derive the learning rule from first principles and estimate the computational complexity. Simulation results over a synthetic data set and a real world climate data set show that our algorithm is capable of learning the spatio-temporal mappings.

Learning rate is a crucial parameter governing the convergence rate of any learning algorithm. Most of the learning algorithms based on stochastic gradient descent (SGD) method depend on heuristic choice of learning rate. In this paper, we derive bounds on the learning rate of SGD based adaptive learning algorithms by analyzing the largest eigenvalue of the Hessian matrix from first principles. The proposed approach is analytical. To illustrate the efficacy of the analytical approach, we considered several high-dimensional data sets and compared the rate of convergence of error for the neural gas algorithm and showed that the proposed bounds on learning rate result in a faster rate of convergence than AdaDec, Adam, and AdaDelta approaches which require hyper-parameter tuning.

Self-organizing maps (SOMs) find numerous applications in learning, clustering, and recalling spatial input patterns. The traditional approach in learning spatiotemporal patterns is to incorporate time on the output space of a SOM along with heuristic update rules that work well in practice. Inspired by the pioneering work of Alan Turing, who used reaction-diffusion equations to explain spatial pattern formation, we develop an analogous theoretical model for a spatiotemporal memory to learn and recall temporal patterns. The contribution of the paper is threefold: 1) using coupled reaction-diffusion equations, we develop a theory from first principles for constructing a spatiotemporal SOM and derive an update rule for learning based on the gradient of a potential function; 2) we analyze the dynamics of our algorithm and derive conditions for optimally setting the model parameters; and 3) we mathematically quantify the temporal plasticity effect observed during recall in response to the input dynamics. The simulation results show that the proposed algorithm outperforms the SOM with temporal activity diffusion, neural gas with temporal activity diffusion and spatiotemporal map formation based on a potential function in the presence of correlated noise for the same data set and similar training conditions.

Vector quantization techniques using self-organizing maps (SOM) and its variants are popularly used for applications in contextual data clustering, data visualization and high-dimensional data exploration. The update rule in a SOM is based on competitive learning using a neighborhood function that measures the Euclidean distance between an input vector and a non-linear processing element without any consideration of selective priority for a specific feature in the input data. Certain applications may require unsupervised learning of high-dimensional data with a priori knowledge on the priority of certain features, leading to resolution dependent contextual maps. With this in mind, we propose a vector quantization technique called priority based soft vector quantization feature maps (PSVQFM) for creating contextual feature maps by learning priorities. In this paper, we formulate the cost function based on the priorities over the feature coordinates and derive a learning rule from first principles. We present an analysis on the misclassification error and prove that the proposed algorithm is asymptotically optimal. Simulation results over a synthetic data set and a high-dimensional banking corpus data set show that the PSVQFM algorithm is able to learn the input data based on priority of features very well.

Two-dimensional magnetic recording (TDMR) is an emerging storage technology that aims to achieve areal densities on the order of 10 Tb/in2, mainly driven by innovative channels engineering with minimal changes to existing head/media designs within a systems framework. Significant additive areal density gains can be achieved by using TDMR over bit patterned media (BPM) and energy-assisted magnetic recording (EAMR). In TDMR, the sectors are inherently 2-D with reduced track pitch and bit widths, leading to severe 2-D intersymbol interference (ISI). This necessitates the development of powerful 2-D signal processing and coding algorithms for mitigating 2-D ISI, timing artifacts, jitter, and electronics noise resulting from irregular media grain positions and read-head electronics. The algorithms have to be eventually realized within a read/write channel architecture as a part of a system-on-chip (SoC) within the disk controller system. In this work, we provide a wide overview of TDMR technology, channel models and capacity, signal processing algorithms (detection and timing recovery), and error-correcting codes attuned to 2-D channels. The innovations and advances described not only make TDMR a promising future technology, but may serve a broader engineering audience as well.

We introduce a stochastic resonance based decoding paradigm for quantum codes using an error correction circuit made of a combination of noisy and noiseless logic gates. The quantum error correction circuit is based on iterative syndrome decoding of quantum low-density parity check codes, and uses the positive effect of errors in gates to correct errors due to decoherence. We analyze how the proposed stochastic algorithm can escape from short cycle trapping sets present in the dual containing Calderbank, Shor and Steane (CSS) codes. Simulation results show improved performance of the stochastic algorithm over the deterministic decoder.

We propose the construction and error correction procedures of an entanglement assisted binary quantum tensor product code. We devise an efficient procedure to construct the code with complexity O(max{ρ21, ρ22}) compared to O(ρ21ρ22) using symplectic Gram-Schmidt orthogonalization, where ρ1and ρ2are the number of parity bits of the component codes. Our error correction procedures can correct quantum burst errors without destroying the quantum state.

We look at the neural network as a non-linear probability density function (pdf) transformer by stochastic learning cumulative (SLC) technique. We formulate a potential function that drives a neural network to non-linearly transform the input pdf to the desired pdf. We show the working of the algorithm using synthetic data drawn from three different pdfs and estimate the parameters of the distributions. The estimated parameter values match with the true values and the maximum likelihood estimates. We also derive bounds on the number of hidden neurons needed for parametric estimation in terms of the input data statistics.

Two dimensional magnetic recording (TDMR) achieves high areal densities by reducing the size of a bit comparable to the size of the magnetic grains resulting in two dimensional (2D) inter symbol interference (ISI) and very high media noise. Therefore, it is critical to handle the media noise along with the 2D ISI detection. In this paper, we tune the generalized belief propagation (GBP) algorithm to handle the media noise seen in TDMR. We also provide an intuition into the nature of hard decisions provided by the GBP algorithm. The performance of the GBP algorithm is evaluated over a Voronoi based TDMR channel model where the soft outputs from the GBP algorithm are used by a belief propagation (BP) algorithm to decode low-density parity check (LDPC) codes.

The digital universe is doubling every two years and expected to reach an unwieldy 44 zettabytes into the next decade. To cope with the ever increasing need for storing, transmitting and retrieving huge amounts of data, cloud storage, data centers and other massively distributed storage networks have emerged. These rely on efficient memory technologies at the physical level for speed, reliability and energy efficiency.

We revisit the problem of temporal self organization using activity diffusion based on the neural gas (NGAS) algorithm. Using a potential function formulation motivated by a spatio-temporal metric, we derive an adaptation rule for dynamic vector quantization of data. Simulations results show that our algorithm learns the input distribution and time correlation much faster compared to the static neural gas method over the same data sequence under similar training conditions.

We investigate into the loopy belief propagation algorithm for binary low density parity check (LDPC) codes having cycles of small girth. Independence assumption among messages passed, assumed reasonable in all configurations of graphs, fails the most in graphical structures with short cycles. We investigate into this limitation and propose a modified algorithm, by considering dependency in the probability domain. This improves the performance of decoding over such graphs when compared to the original message passing algorithm at higher signal-to-noise ratio (SNR), thereby, yielding lower error floors.

We investigate into the limitations of the sum-product algorithm in the probability domain over graphs with isolated short cycles. By considering the statistical dependency of messages passed in a cycle of length 4, we modify the update equations for the beliefs at the variable and check nodes. We highlight an approximate log domain algebra for the modified variable node update to ensure numerical stability. At higher signal-to-noise ratios (SNR), the performance of decoding over graphs with isolated short cycles using the modified algorithm is improved compared to the original message passing algorithm (MPA).

We develop several novel signal detection algorithms for two-dimensional intersymbol-interference channels. The contribution of the paper is two-fold: (1) We extend the one-dimensional maximum a-posteriori (MAP) detection algorithm to operate over multiple rows and columns in an iterative manner. We study the performance vs. complexity trade-offs for various algorithmic options ranging from single row/column non-iterative detection to a multi-row/column iterative scheme and analyze the performance of the algorithm. (2) We develop a self-iterating 2-D linear minimum mean-squared based equalizer by extending the 1-D linear equalizer framework, and present an analysis of the algorithm. The iterative multi-row/column detector and the self-iterating equalizer are further connected together within a turbo framework. We analyze the combined 2-D iterative equalization and detection engine through analysis and simulations. The performance of the overall equalizer and detector is near MAP estimate with tractable complexity, and beats the Marrow Wolf detector by about at least 0.8 dB over certain 2-D ISI channels. The coded performance indicates about 8 dB of significant SNR gain over the uncoded 2-D equalizer-detector system.

We develop several novel signal detection algorithms for two-dimensional intersymbol-interference channels. The core in all these schemes is a modified one-dimensional maximum aposteriori (MAP) detection algorithm that operates over single and multiple rows providing a balanced performance vs. complexity tradeoff. We explore 2-D iterative algorithms that operate by feeding extrinsic information from multi-row/column detectors in a turbo fashion. Multi-row/column MAP detection using 2-D turbo-processing yields more than 2 dB signal-to-noise ratio (SNR) gain compared to a non-iterative multi-row detector over the additive white Gaussian channel and within 0.1 dB of the ML estimate.

We present bounds on the two-dimensional capacity for two sets of symmetric and asymmetric M-ary runlength-limited constraints based on simple constructions. The bounds extend and generalize previous work on binary constraints.

In this paper, we consider the tradeoffs of binary and M-ary signaling in page-oriented holographic storage systems that multiplex pages using two methods: conventional angle multiplexing throughout the volume and localized recording. We study the mutual information transfer, which is increasingly easy to achieve in practice, between the recorded and recovered data and use it to assess the trade-offs in these systems. We use the transmission model developed by Heanue, Bashaw, and Hesselink [7] for deriving the mutual information bound on capacity and examine the interplay between the storage density and the number of recorded pages within the medium. This result is useful for deciding the number of recorded pages and the desired level of a multi-level modulation code for maximizing the storage density in a volume holographic memory. We analyze our results for localized and angle multiplexed recording and compare the performance in these two cases.

In this paper, we present maximum-likelihood modeling of burst errors in magnetic recording channels using hidden Markov models (HMM). We derive low-complexity and memory efficient algorithms for computing the log-likelihood function for burst sequences, and use this algorithm to optimally determine the model parameters using smart search techniques. Finally, we illustrate a modeling example from real observed data collected from hard disks, and show how the model can be applied for evaluating decoder failure rates using Wolf's method [5].

We present lower bounds on the two-dimensional capacity for two sets of symmetric and asymmetric M-ary runlength-limited constraints. The bounds extend and generalize our previous work on binary constraints. We also give sequential coding algorithms achieving the derived capacity lower bounds

Pixel misalignments such as two-dimensional lateral shifts, rotation and magnification are one of the common sources of distortion in optical data storage systems like volume holographic memories. In this paper, we formulate the channel model for rotational misalignment of the detector grid array with respect to the transmitter, about the center of the optical axis, and derive an expression for the number of transmitted bits that can be recovered losslessly. Finally, we outline an algorithm for recovering the transmitted bits from the detector array in the presence of additive white Gaussian noise and rotational misalignment. The method is applicable to holographic memories and other imaging systems.

We present two enumeration algorithms for a class of (d/sub 1/, /spl infin/, d/sub 2/, /spl infin/) run-length limited (RLL) constrained arrays. Based on the structure of these algorithms, we derive bounds for the maximum information rate of the constraint. We also give encoders and decoders for coded 2D constrained arrays with rates close to the derived bounds.