Combining the Burrows-Wheeler Transform and RCM-LDGM Codes for the Transmission of Sources with Memory at High Spectral Efficiencies

In this paper, we look at the problem of implementing high-throughput Joint SourceChannel (JSC) coding schemes for the transmission of binary sources with memory over AWGN channels. The sources are modeled either by a Markov chain (MC) or a hidden Markov model (HMM). We propose a coding scheme based on the Burrows-Wheeler Transform (BWT) and the parallel concatenation of Rate-Compatible Modulation and Low-Density Generator Matrix (RCM-LDGM) codes. The proposed scheme uses the BWT to convert the original source with memory into a set of independent non-uniform Discrete Memoryless (DMS) binary sources, which are then separately encoded, with optimal rates, using RCM-LDGM codes

When Machine Learning Meets Information Theory: Some Practical Applications to Data Storage

Machine learning and information theory are closely inter-related areas. In this dissertation, we explore topics in their intersection with some practical applications to data storage. Firstly, we explore how machine learning techniques can be used to improve data reliability in non-volatile memories (NVMs). NVMs, such as flash memories, store large volumes of data. However, as devices scale down towards small feature sizes, they suffer from various kinds of noise and disturbances, thus significantly reducing their reliability. This dissertation explores machine learning techniques to design decoders that make use of natural redundancy (NR) in data for error correction. By NR, we mean redundancy inherent in data, which is not added artificially for error correction. This work studies two different schemes for NR-based error-correcting decoders. In the first scheme, the NR-based decoding algorithm is aware of the data representation scheme (e.g., compression, mapping of symbols to bits, meta-data, etc.), and uses that information for error correction. In the second scenario, the NR-decoder is oblivious of the representation scheme and uses deep neural networks (DNNs) to recognize the file type as well as perform soft decoding on it based on NR. In both cases, these NR-based decoders can be combined with traditional error correction codes (ECCs) to substantially improve their performance. Secondly, we use concepts from ECCs for designing robust DNNs in hardware. Non-volatile memory devices like memristors and phase-change memories are used to store the weights of hardware implemented DNNs. Errors and faults in these devices (e.g., random noise, stuck-at faults, cell-level drifting etc.) might degrade the performance of such DNNs in hardware. We use concepts from analog error-correcting codes to protect the weights of noisy neural networks and to design robust neural networks in hardware. To summarize, this dissertation explores two important directions in the intersection of information theory and machine learning. We explore how machine learning techniques can be useful in improving the performance of ECCs. Conversely, we show how information-theoretic concepts can be used to design robust neural networks in hardware

Proceedings of the 35th WIC Symposium on Information Theory in the Benelux and the 4th joint WIC/IEEE Symposium on Information Theory and Signal Processing in the Benelux, Eindhoven, the Netherlands May 12-13, 2014

Compressive sensing (CS) as an approach for data acquisition has recently received much attention. In CS, the signal recovery problem from the observed data requires the solution of a sparse vector from an underdetermined system of equations. The underlying sparse signal recovery problem is quite general with many applications and is the focus of this talk. The main emphasis will be on Bayesian approaches for sparse signal recovery. We will examine sparse priors such as the super-Gaussian and student-t priors and appropriate MAP estimation methods. In particular, re-weighted l2 and re-weighted l1 methods developed to solve the optimization problem will be discussed. The talk will also examine a hierarchical Bayesian framework and then study in detail an empirical Bayesian method, the Sparse Bayesian Learning (SBL) method. If time permits, we will also discuss Bayesian methods for sparse recovery problems with structure; Intra-vector correlation in the context of the block sparse model and inter-vector correlation in the context of the multiple measurement vector problem

A Unified Coded Deep Neural Network Training Strategy Based on Generalized PolyDot Codes for Matrix Multiplication

This paper has two contributions. First, we propose a novel coded matrix multiplication technique called Generalized PolyDot codes that advances on existing methods for coded matrix multiplication under storage and communication constraints. This technique uses "garbage alignment," i.e., aligning computations in coded computing that are not a part of the desired output. Generalized PolyDot codes bridge between Polynomial codes and MatDot codes, trading off between recovery threshold and communication costs. Second, we demonstrate that Generalized PolyDot can be used for training large Deep Neural Networks (DNNs) on unreliable nodes prone to soft-errors. This requires us to address three additional challenges: (i) prohibitively large overhead of coding the weight matrices in each layer of the DNN at each iteration; (ii) nonlinear operations during training, which are incompatible with linear coding; and (iii) not assuming presence of an error-free master node, requiring us to architect a fully decentralized implementation without any "single point of failure." We allow all primary DNN training steps, namely, matrix multiplication, nonlinear activation, Hadamard product, and update steps as well as the encoding/decoding to be error-prone. We consider the case of mini-batch size $B=1$, as well as $B>1$, leveraging coded matrix-vector products, and matrix-matrix products respectively. The problem of DNN training under soft-errors also motivates an interesting, probabilistic error model under which a real number $(P,Q)$ MDS code is shown to correct $P-Q-1$ errors with probability $1$ as compared to $\lfloor \frac{P-Q}{2} \rfloor$ for the more conventional, adversarial error model. We also demonstrate that our proposed strategy can provide unbounded gains in error tolerance over a competing replication strategy and a preliminary MDS-code-based strategy for both these error models.Comment: Presented in part at the IEEE International Symposium on Information Theory 2018 (Submission Date: Jan 12 2018); Currently under review at the IEEE Transactions on Information Theor

Compressed sensing with approximate message passing: measurement matrix and algorithm design

Compressed sensing (CS) is an emerging technique that exploits the properties of a sparse or compressible signal to efficiently and faithfully capture it with a sampling rate far below the Nyquist rate. The primary goal of compressed sensing is to achieve the best signal recovery with the least number of samples. To this end, two research directions have been receiving increasing attention: customizing the measurement matrix to the signal of interest and optimizing the reconstruction algorithm. In this thesis, contributions in both directions are made in the Bayesian setting for compressed sensing. The work presented in this thesis focuses on the approximate message passing (AMP) schemes, a new class of recovery algorithm that takes advantage of the statistical properties of the CS problem. First of all, a complete sample distortion (SD) framework is presented to fundamentally quantify the reconstruction performance for a certain pair of measurement matrix and recovery scheme. In the SD setting, the non-optimality region of the homogeneous Gaussian matrix is identified and the novel zeroing matrix is proposed with an improved performance. With the SD framework, the optimal sample allocation strategy for the block diagonal measurement matrix are derived for the wavelet representation of natural images. Extensive simulations validate the optimality of the proposed measurement matrix design. Motivated by the zeroing matrix, we extend the seeded matrix design in the CS literature to the novel modulated matrix structure. The major advantage of the modulated matrix over the seeded matrix lies in the simplicity of its state evolution dynamics. Together with the AMP based algorithm, the modulated matrix possesses a 1-D performance prediction system, with which we can optimize the matrix configuration. We then focus on a special modulated matrix form, designated as the two block matrix, which can also be seen as a generalization of the zeroing matrix. The effectiveness of the two block matrix is demonstrated through both sparse and compressible signals. The underlining reason for the improved performance is presented through the analysis of the state evolution dynamics. The final contribution of the thesis explores improving the reconstruction algorithm. By taking the signal prior into account, the Bayesian optimal AMP (BAMP) algorithm is demonstrated to dramatically improve the reconstruction quality. The key insight for its success is that it utilizes the minimum mean square error (MMSE) estimator for the CS denoising. However, the prerequisite of the prior information makes it often impractical. A novel SURE-AMP algorithm is proposed to address the dilemma. The critical feature of SURE-AMP is that the Stein’s unbiased risk estimate (SURE) based parametric least square estimator is used to replace the MMSE estimator. Given the optimization of the SURE estimator only involves the noisy data, it eliminates the need for the signal prior, thus can accommodate more general sparse models

Intra-Key-Frame Coding and Side Information Generation Schemes in Distributed Video Coding

In this thesis investigation has been made to propose improved schemes for intra-key-frame coding and side information (SI) generation in a distributed video coding (DVC) framework. From the DVC developments in last few years it has been observed that schemes put more thrust on intra-frame coding and better quality side information (SI) generation. In fact both are interrelated as SI generation is dependent on decoded key frame quality. Hence superior quality key frames generated through intra-key frame coding will in turn are utilized to generate good quality SI frames. As a result, DVC needs less number of parity bits to reconstruct the WZ frames at the decoder. Keeping this in mind, we have proposed two schemes for intra-key frame coding namely, (a) Borrows Wheeler Transform based H.264/AVC (Intra) intra-frame coding (BWT-H.264/AVC(Intra)) (b) Dictionary based H.264/AVC (Intra) intra-frame coding using orthogonal matching pursuit (DBOMP-H.264/AVC (Intra)) BWT-H.264/AVC (Intra) scheme is a modified version of H.264/AVC (Intra) scheme where a regularized bit stream is generated prior to compression. This scheme results in higher compression efficiency as well as high quality decoded key frames. DBOMP-H.264/AVC (Intra) scheme is based on an adaptive dictionary and H.264/AVC (Intra) intra-frame coding. The traditional transform is replaced with a dictionary trained with K-singular value decomposition (K-SVD) algorithm. The dictionary elements are coded using orthogonal matching pursuit (OMP). Further, two side information generation schemes have been suggested namely, (a) Multilayer Perceptron based side information generation (MLP - SI) (b) Multivariable support vector regression based side information generation (MSVR-SI) MLP-SI scheme utilizes a multilayer perceptron (MLP) to estimate SI frames from the decoded key frames block-by-block. The network is trained offline using training patterns from different frames collected from standard video sequences. MSVR-SI scheme uses an optimized multi variable support vector regression (M-SVR) to generate SI frames from decoded key frames block-by-block. Like MLP, the training for M-SVR is made offline with known training patterns apriori. Both intra-key-frame coding and SI generation schemes are embedded in the Stanford based DVC architecture and studied individually to compare performances with their competitive schemes. Visual as well as quantitative evaluations have been made to show the efficacy of the schemes. To exploit the usefulness of intra-frame coding schemes in SI generation, four hybrid schemes have been formulated by combining the aforesaid suggested schemes as follows: (a) BWT-MLP scheme that uses BWT-H.264/AVC (Intra) intra-frame coding scheme and MLP-SI side information generation scheme. (b) BWT-MSVR scheme, where we utilize BWT-H.264/AVC (Intra) for intra-frame coding followed by MSVR-SI based side information generation. (c) DBOMP-MLP scheme is an outcome of putting DBOMP-H.264/AVC (Intra) intra-frame coding and MLP-SI side information generation schemes. (d) DBOMP-MSVR scheme deals with DBOMP-H.264/AVC (Intra) intra-frame coding and MSVR-SI side information generation together. The hybrid schemes are also incorporated into the Stanford based DVC architecture and simulation has been carried out on standard video sequences. The performance analysis with respect to overall rate distortion, number requests per SI frame, temporal evaluation, and decoding time requirement has been made to derive an overall conclusion

Journal of Telecommunications and Information Technology, 2006, nr 1

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