Quantization and erasures in frame representations

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 123-126).Frame representations, which correspond to overcomplete generalizations to basis expansions, are often used in signal processing to provide robustness to errors. In this thesis robustness is provided through the use of projections to compensate for errors in the representation coefficients, with specific focus on quantization and erasure errors. The projections are implemented by modifying the unaffected coefficients using an additive term, which is linear in the error. This low-complexity implementation only assumes linear reconstruction using a pre-determined synthesis frame, and makes no assumption on how the representation coefficients are generated. In the context of quantization, the limits of scalar quantization of frame representations are first examined, assuming the analysis is using inner products with the frame vectors. Bounds on the error and the bit-efficiency are derived, demonstrating that scalar quantization of the coefficients is suboptimal. As an alternative to scalar quantization, a generalization of Sigma-Delta noise shaping to arbitrary frame representations is developed by reformulating noise shaping as a sequence of compensations for the quantization error using projections.(cont.) The total error is quantified using both the additive noise model of quantization, and a deterministic upper bound based on the triangle inequality. It is thus shown that the average and the worst-case error is reduced compared to scalar quantization of the coefficients. The projection principle is also used to provide robustness to erasures. Specifically, the case of a transmitter that is aware of the erasure occurrence is considered, which compensates for the erasure error by projecting it to the subsequent frame vectors. It is further demonstrated that the transmitter can be split to a transmitter/receiver combination that performs the same compensation, but in which only the receiver is aware of the erasure occurrence. Furthermore, an algorithm to puncture dense representations in order to produce sparse approximate ones is introduced. In this algorithm the error due to the puncturing is also projected to the span of the remaining coefficients. The algorithm can be combined with quantization to produce quantized sparse representations approximating the original dense representation.by Petros T. Boufounos.Sc.D

Study and simulation of low rate video coding schemes

The semiannual report is included. Topics covered include communication, information science, data compression, remote sensing, color mapped images, robust coding scheme for packet video, recursively indexed differential pulse code modulation, image compression technique for use on token ring networks, and joint source/channel coder design

Digital Color Imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided

Low Power Analog to Digital Converters in Advanced CMOS Technology Nodes

The dissertation presents system and circuit solutions to improve the power efficiency and address high-speed design issues of ADCs in advanced CMOS technologies. For image sensor applications, a high-performance digitizer prototype based on column-parallel single-slope ADC (SS-ADC) topology for readout of a back-illuminated 3D-stacked CMOS image sensor is presented. To address the high power consumption issue in high-speed digital counters, a passing window (PW) based hybrid counter topology is proposed. To address the high column FPN under bright illumination conditions, a double auto-zeroing (AZ) scheme is proposed. The proposed techniques are experimentally verified in a prototype chip designed and fabricated in the TSMC 40 nm low-power CMOS process. The PW technique saves 52.8% of power consumption in the hybrid digital counters. Dark/bright column fixed pattern noise (FPN) of 0.0024%/0.028% is achieved employing the proposed double AZ technique for digital correlated double sampling (CDS). A single-column digitizer consumes total power of 66.8μW and occupies an area of 5.4 µm x 610 µm. For mobile/wireless receiver applications, this dissertation presents a low-power wide-bandwidth multistage noise-shaping (MASH) continuous-time delta-sigma modulator (CT-ΔΣM) employing finite impulse response (FIR) digital-to-analog converters (DACs) and encoder-embedded loop-unrolling (EELU) quantizers. The proposed MASH 1-1-1 topology is a cascade of three single-loop first-order CT-ΔΣM stages, each of which consists of an active-RC integrator, a current-steering DAC, and an EELU quantizer. An FIR filter in the main 1.5-bit DAC improves the modulator’s jitter sensitivity performance. FIR’s effect on the noise transfer function (NTF) of the modulator is compensated in the digital domain thanks to the MASH topology. Instead of employing a conventional analog direct feedback path, a 1.5-bit EELU quantizer based on multiplexing comparator outputs is proposed; this approach is suitable for highspeed operation together with power and area benefits. Fabricated in a 40-nm low-power CMOS technology, the modulator’s prototype achieves a 67.3 dB of signal-to-noise and distortion ratio (SNDR), 68 dB of signal-to-noise ratio (SNR), and 68.2 dB of dynamic range (DR) within 50.5 MHz of bandwidth (BW), while consuming 19 mW of total power (P). The proposed modulator features 161.5 dB of figure-of-merit (FOM), defined as FOM = SNDR + 10 log10 (BW/P)

The development of speech coding and the first standard coder for public mobile telephony

This thesis describes in its core chapter (Chapter 4) the original algorithmic and design features of the ??rst coder for public mobile telephony, the GSM full-rate speech coder, as standardized in 1988. It has never been described in so much detail as presented here. The coder is put in a historical perspective by two preceding chapters on the history of speech production models and the development of speech coding techniques until the mid 1980s, respectively. In the epilogue a brief review is given of later developments in speech coding. The introductory Chapter 1 starts with some preliminaries. It is de- ??ned what speech coding is and the reader is introduced to speech coding standards and the standardization institutes which set them. Then, the attributes of a speech coder playing a role in standardization are explained. Subsequently, several applications of speech coders - including mobile telephony - will be discussed and the state of the art in speech coding will be illustrated on the basis of some worldwide recognized standards. Chapter 2 starts with a summary of the features of speech signals and their source, the human speech organ. Then, historical models of speech production which form the basis of di??erent kinds of modern speech coders are discussed. Starting with a review of ancient mechanical models, we will arrive at the electrical source-??lter model of the 1930s. Subsequently, the acoustic-tube models as they arose in the 1950s and 1960s are discussed. Finally the 1970s are reviewed which brought the discrete-time ??lter model on the basis of linear prediction. In a unique way the logical sequencing of these models is exposed, and the links are discussed. Whereas the historical models are discussed in a narrative style, the acoustic tube models and the linear prediction tech nique as applied to speech, are subject to more mathematical analysis in order to create a sound basis for the treatise of Chapter 4. This trend continues in Chapter 3, whenever instrumental in completing that basis. In Chapter 3 the reader is taken by the hand on a guided tour through time during which successive speech coding methods pass in review. In an original way special attention is paid to the evolutionary aspect. Speci??cally, for each newly proposed method it is discussed what it added to the known techniques of the time. After presenting the relevant predecessors starting with Pulse Code Modulation (PCM) and the early vocoders of the 1930s, we will arrive at Residual-Excited Linear Predictive (RELP) coders, Analysis-by-Synthesis systems and Regular- Pulse Excitation in 1984. The latter forms the basis of the GSM full-rate coder. In Chapter 4, which constitutes the core of this thesis, explicit forms of Multi-Pulse Excited (MPE) and Regular-Pulse Excited (RPE) analysis-by-synthesis coding systems are developed. Starting from current pulse-amplitude computation methods in 1984, which included solving sets of equations (typically of order 10-16) two hundred times a second, several explicit-form designs are considered by which solving sets of equations in real time is avoided. Then, the design of a speci??c explicitform RPE coder and an associated eÆcient architecture are described. The explicit forms and the resulting architectural features have never been published in so much detail as presented here. Implementation of such a codec enabled real-time operation on a state-of-the-art singlechip digital signal processor of the time. This coder, at a bit rate of 13 kbit/s, has been selected as the Full-Rate GSM standard in 1988. Its performance is recapitulated. Chapter 5 is an epilogue brie y reviewing the major developments in speech coding technology after 1988. Many speech coding standards have been set, for mobile telephony as well as for other applications, since then. The chapter is concluded by an outlook

The Fifth NASA Symposium on VLSI Design

The fifth annual NASA Symposium on VLSI Design had 13 sessions including Radiation Effects, Architectures, Mixed Signal, Design Techniques, Fault Testing, Synthesis, Signal Processing, and other Featured Presentations. The symposium provides insights into developments in VLSI and digital systems which can be used to increase data systems performance. The presentations share insights into next generation advances that will serve as a basis for future VLSI design

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Presented here are the proceedings of the Second International Mobile Satellite Conference (IMSC), held June 17-20, 1990 in Ottawa, Canada. Topics covered include future mobile satellite communications concepts, aeronautical applications, modulation and coding, propagation and experimental systems, mobile terminal equipment, network architecture and control, regulatory and policy considerations, vehicle antennas, and speech compression

Progress in Group Field Theory and Related Quantum Gravity Formalisms

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research