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作者： Soleymani, Mahdi University of Michigan

学位级别：Ph.D., Doctor of Philosophy

Most of the current body of coding theory research has been dedicated to constructing codes in discrete spaces with finite alphabet sizes. The progress accomplished in coding theory over the last decades has been fruitful for various disciplines, from theoretical computer science to wireless communications and storage systems. However, the ever-growing advancements in such areas always give rise to new challenges for which the coding theory is a framework that can offer novel solutions. For instance, analog subspace codes offer a framework for low-latency and reliable communication over a network of many relays operating in non-coherent fashion. Moreover, analog error-correcting codes have been proposed as a framework to overcome inevitable errors in analog resistive devices for vector-matrix multiplication that perform computations over reals without requiring intermediate quantization step. This thesis investigates the advantages of analog codes over the conventional codes constructed over discrete spaces in specific applications. In particular, 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 Cn. In a sense, we develop a counterpart for Koetter-Kschischang's operator channel in the analog domain. 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 additive noise. Furthermore, we propose a new approach to construct subspace codes in the analog domain, also regarded as Grassmann codes. The constructed codes, referred to as character-polynomial (CP) codes, perform better than 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

关键词： Error-correcting codes analog coding Distributed computing Data privacy

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A Simple Family of Non-Linear analog Codes

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IEEE COMMUNICATIONS LETTERS 2023年第11期27卷 2889-2893页

作者： Burich, Mariano Eduardo Garcia-Frias, Javier Micron Technol Inc Irvine CA 92612 USA Univ Delaware Dept Elect & Comp Engn Newark NJ 19716 USA

We propose novel non-linear graph-based analog codes that directly encode $k$ real-valued source samples into $n$ real-valued samples by using (non-linear) sample-by-sample soft quantization of the input samples followed by a linear transformation on the soft-quantized values. Different from existing analog coding schemes, the proposed analog codes are able to produce additional output symbols in a rateless manner and can be decoded utilizing message passing algorithms dealing with real-valued nodes, achieving a performance close to the theoretical limits.

关键词： analog coding non-linear codes sparse codes iterative decoding

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analog Lagrange Coded Computing

IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY

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IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY 2021年第1期2卷 283-295页

作者： Soleymani, Mahdi Mahdavifar, Hessam Avestimehr, A. Salman Univ Michigan Ann Arbor Dept Elect Engn & Comp Sci Ann Arbor MI 48104 USA Univ Southern Calif Dept Elect Engn Los Angeles CA 90089 USA

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.

关键词： Coded computing privacy-preserving computing analog coding

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Computational Imaging for Compressive Synthetic Aperture Interferometric Radiometer

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2018年第10期66卷 5546-5557页

作者： Kpre, Ettien Decroze, Cyril Mouhamadou, Moctar Fromenteze, Thomas Univ Limoges XLIM Lab UMR CNRS 6172 F-87068 Limoges France

Recent work proved the effectiveness of a new concept, namely compressive synthetic aperture interferometric radiometer, which aims to reduce the number of RF chains of an interferometric radiometer by means of a passive microwave component. The device is used for coding M antenna signals into N (N << M) measured waveforms. Thereafter, a decoding process is applied to retrieve the antenna signals necessary to compute the basic observables of an interferometer, namely complex visibilities. Initially, a Fourier algorithm was applied to reconstruct the images, and nonetheless, this kind of imaging algorithm ignores the visibility observation errors, which cause blurring and distortion effects in the images. Herein, a generalized visibility equation is given while considering M antennas associated with N receivers. Then, a linear relationship between these visibility samples and the noise source brightness temperature is established, and a regularization method is applied to compute the source image. Furthermore, the impact of the device on the reconstructed images is studied by means of numerical analysis as well as by experiment measurements performed in the S-band (2-4 GHz). The results confirm that the computational approach provides accurate reconstructed images compared with those obtained with the Fourier algorithm.

关键词： analog coding antenna array interferometric radiometer microwave imaging microwave passive device

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Frame Moments and Welch Bound with Erasures

Frame Moments and Welch Bound with Erasures

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IEEE International Symposium on Information Theory (ISIT)

作者： Haikin, Marina Zamir, Ram Gavish, Matan Tel Aviv Univ EE Syst Dept Tel Aviv Israel Hebrew Univ Jerusalem Sch Comp Sci & Engn Jerusalem Israel

ISBN: (纸本)9781538647813

The Welch (lower) Bound on the mean square cross correlation between n unit-norm vectors f(1), ... , f(n) in the m dimensional space (R-m or C-m), for n >= m, is a useful tool in the analysis and design of spread spectrum communications, compressed sensing and analog coding. Letting F = [f(1)vertical bar ... vertical bar f(n)] denote the m-by-n frame matrix, the Welch bound can be viewed as a lower bound on the second moment of F, namely on the trace of the squared Gram matrix (F' F)(2). We consider an erasure setting, in which a reduced frame, composed of a random subset of Bernoulli selected vectors, is of interest. We present the erasure Welch bound and generalize it to the d-th order moment of the reduced frame, for d = 2, 3, 4. We provide simple, explicit formulae for the generalized bound, which interestingly is equal to the d-th moment of Wachter's classical MANOVA distribution plus a vanishing term (as n goes to infinity with m/n held constant). The bound holds with equality if (and for d = 4 only if) F is an Equiangular Tight Frame (ETF). Hence, our results offer a novel perspective on the superiority of ETFs over other frames, and provide explicit characterization for their subset moments.

关键词： Welch bound equiangular tight frames MANOVA distribution analog coding random matrix theory code division multiple access

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analogCast: Full Linear coding and Pseudo analog Transmission for Satellite Remote-sensing Images 41

AnalogCast: Full Linear Coding and Pseudo Analog Transmissio...

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Li, Jingyu Wen, XiangE Jia, Huizhu Xie, Xiaodong Gao, Wen Peking Univ Inst Digital Media Beijing 100871 Peoples R China Cooperat Medianet Innovat Ctr Beijing 100871 Peoples R China

ISBN: (纸本)9781479999880

In this papa, we propose a novel image coding and transmission scheme called analogCast, which is a pseudo analog coding system for transmitting satellite remote-sensing images to large number of receivers. analogCast follows the idea originally developed for SoftCast [1-3] but with two special techniques, scale factor estimate based on L-shaped chunk division and scale factor fix curve-fitting model, so that there is no need to transmit side information as is required for Soft Cast [1-3]. This improvement can get better mobility, less bandwidth and computational budget than SoftCast [1-3]. For robustness, analogCast adopts a mode of GOP (Group of Pictures) interweave structure to smooth image quality and improve perceptual quality when packet loss happens. Experimental results show that the proposed method can work well in low SNR condition in -7dB to 4dB where SoftCast system and JPEG2000 system fall into "cliff effect". And in high SNR condition, our proposed method works even better than SoftCast system at SNR 1.5 similar to 3dR and a gain of 1 similar to 10dB over JPEG2000 with forward error correction. For robustness, the analogCast works better than SoftCast at SNR 8dB when the burst packet loss rate is higher than 35%. And the scheme gets better perceptual quality under packet loss.

关键词： Image broadcasting satellite images analog coding GoP interweave fix model

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analog Coded SoftCast: A Network Slice Design for Multimedia Broadcast/Multicast

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IEEE TRANSACTIONS ON MULTIMEDIA 2017年第10期19卷 2293-2306页

作者： Tan, Bin Wu, Jun Li, Ying Cui, Hao Yu, Wei Chen, Chang Wen Tongji Univ Coll Elect & Informat Engn Shanghai 201804 Peoples R China Jinggangshan Univ Coll Elect & Informat Engn Jian 343009 Jiangxi Peoples R China Tongji Univ Coll Elect & Informat Engn Key Lab Minist Educ Embedded Syst Shanghai 201804 Peoples R China Tongji Univ Coll Elect & Informat Engn Serv Comp Shanghai 201804 Peoples R China Tongji Univ Coll Elect & Informat Engn Shanghai 201804 Peoples R China SUNY Buffalo Dept Comp Sci & Engn Buffalo NY 14228 USA

This paper presents a network slice design for ultra high definition (UHD) video broadcast/multicast to achieve higher network efficiency and improved quality of experience (QoE). The proposed network slice design consists of a rateless source compression scheme and an analog-coded SoftCast scheme. The rateless Spinal code is adopted to compress the video source at content server and the compressed source is transmitted from content server across wireless core network to the base station. An a priori information-assisted Spinal decoder is designed to utilize the sparsity of bit planes for compression. In the analog-coded SoftCast scheme, we design a new chaotic function-based analog code with negligible power penalty for the generalized Gaussian-distributed source in SoftCast because the existing chaotic functions designed for uniformly distributed sources suffer from serious power penalty in SoftCast. We also design a maximum a posteriori probability decoding algorithm for the proposed analog code in order to exploit the statistics of video source as a priori information to improve the performance. The experimental results show that the proposed rateless code-based compression scheme achieves efficient compression and approaches the bound of binary erasure channel. In particular, the 1/2 analog-coded SoftCast has almost 2 dB gain over conventional SoftCast with two repetitions, and the 1/3 analog-coded SoftCast has almost 3 dB gain over conventional SoftCast with three repetitions. The system simulations for the broadcast system show higher network capacity and improved QoE in the proposed UHD slice, because the reconstructed video quality of each user is commensurate with its channel condition.

关键词： analog coding network slice rateless code SoftCast

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analog Mappings for Flexible Rate Transmission of Gaussian Sources with Side Information

Analog Mappings for Flexible Rate Transmission of Gaussian S...

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48th Annual Conference on Information Sciences and Systems (CISS)

作者： Lu, Bo Garcia-Frias, Javier Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

ISBN: (纸本)9781479930012

This paper considers the problem of designing bandwidth expansion zero-delay analog joint source-channel coding (JSCC) schemes for the transmission of memoryless Gaussian samples over additive white Gaussian noise (AWGN) channels when side information is present at the receiver (Wyner-Ziv scenario). We first propose a 1 : 1 scheme and a 1 : M scheme based on the use of Shannon-Kotel'nikov mappings in a periodic fashion. Then, we combine the two proposed mappings to construct a flexible rate bandwidth expansion mapping whose rate can be anywhere from 1 : 1 to 1 : M. Different from digital systems, the proposed scheme offers low delay, low complexity and high robustness. Simulation results show that the performance of the proposed 1 : 2 scheme is better than that of existing zero-delay systems for a wide range of signal to noise ratios, but especially for high signal to noise ratios and highly correlated side information. The proposed flexible rate bandwidth expansion system also offers satisfactory performance, specially when considering its great flexibleness in terms of rate.

关键词： analog coding space-filling curves bandwidth expansion side information

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Single-Sample Robust Joint Source-Channel coding: Achieving Asymptotically Optimum Scaling of SDR Versus SNR

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第3期58卷 1565-1577页

作者： Taherzadeh, Mahmoud Khandani, Amir Keyvan Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

In this paper, we consider the problem of zero-delay (encoding a single-source sample) robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme that, unlike previously known coding schemes, achieves the optimal scaling of the source signal-to-distortion ratio (SDR) versus channel signal-to-noise ratio (SNR). Also, we propose a family of robust codes, which together maintain a bounded gap with the optimum SDR curve (in terms of decibel). To show the importance of this result, we derive some theoretical bounds on the asymptotic performance of a widely used class of delay-limited hybrid digital-analog (HDA) coding schemes based on superposition of analog and digital components. We show that, unlike the delay-unlimited case, for this class of delay-limited HDA codes, the asymptotic performance loss is unbounded (in terms of decibels). Although the main focus of this paper is on uniform sources, it is also shown that the results are also valid for a more general class of well-behaved distributions.

关键词： analog coding hybrid digital-analog (HDA) coding robust joint source-channel coding scaling of signal-to-distortion ratio (SDR) versus signal-to-noise ratio (SNR) successive refinement zero-delay coding

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analog JOINT SOURCE-CHANNEL coding IN RAYLEIGH FADING CHANNELS

ANALOG JOINT SOURCE-CHANNEL CODING IN RAYLEIGH FADING CHANNE...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： de Oliveira Brante, Glauber Gomes Souza, Richard Demo Garcia-Frias, Javier Fed Univ Technol Parana UTFPR CPGEI Curitiba Parana Brazil

ISBN: (纸本)9781457705397

We consider discrete-time all-analog-processing joint source-channel coding, using non-linear spiral-like curves. We assume a Rayleigh channel, where the receiver may employ or not multiple antennas. Maximum Likelihood (ML) and Minimum Mean Square Error (MMSE) detection are considered. Our results show that MMSE performs much better than ML in high CSNR in single-antenna wireless systems, while diversity combining is able to significantly reduce such performance gap, therefore making the low complexity ML decoding very attractive in the case of multiple receive antennas.

关键词： Joint source-channel coding wireless channel receive diversity analog coding

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