Topics on Register Synthesis Problems

Pseudo-random sequences are ubiquitous in modern electronics and information technology. High speed generators of such sequences play essential roles in various engineering applications, such as stream ciphers, radar systems, multiple access systems, and quasi-Monte-Carlo simulation. Given a short prefix of a sequence, it is undesirable to have an efficient algorithm that can synthesize a generator which can predict the whole sequence. Otherwise, a cryptanalytic attack can be launched against the system based on that given sequence. Linear feedback shift registers (LFSRs) are the most widely studied pseudorandom sequence generators. The LFSR synthesis problem can be solved by the Berlekamp-Massey algorithm, by constructing a system of linear equations, by the extended Euclidean algorithm, or by the continued fraction algorithm. It is shown that the linear complexity is an important security measure for pseudorandom sequences design. So we investigate lower bounds of the linear complexity of different kinds of pseudorandom sequences. Feedback with carry shift registers (FCSRs) were first described by Goresky and Klapper. They have many good algebraic properties similar to those of LFSRs. FCSRs are good candidates as building blocks of stream ciphers. The FCSR synthesis problem has been studied in many literatures but there are no FCSR synthesis algorithms for multi-sequences. Thus one of the main contributions of this dissertation is to adapt an interleaving technique to develop two algorithms to solve the FCSR synthesis problem for multi-sequences. Algebraic feedback shift registers (AFSRs) are generalizations of LFSRs and FCSRs. Based on a choice of an integral domain R and π ∈ R, an AFSR can produce sequences whose elements can be thought of elements of the quotient ring R/(π). A modification of the Berlekamp-Massey algorithm, Xu\u27s algorithm solves the synthesis problem for AFSRs over a pair (R, π) with certain algebraic properties. We propose two register synthesis algorithms for AFSR synthesis problem. One is an extension of lattice approximation approach but based on lattice basis reduction and the other one is based on the extended Euclidean algorithm

A fast-initializing digital equalizer with on-line tracking for data communications

A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix

Single-Laser Multi-Terabit/s Systems

Optical communication systems carry the bulk of all data traffic worldwide. This book introduces multi-Terabit/s transmission systems and three key technologies for next generation networks. A software-defined multi-format transmitter, an optical comb source and an optical processing scheme for the fast Fourier transform for Tbit/s signals. Three world records demonstrate the potential: The first single laser 10 Tbit/s and 26 Tbit/s OFDM and the first 32.5 Tbit/s Nyquist WDM experiments

Single-Laser Multi-Terabit/s Systems

Optical communication systems carry the bulk of all data traffic worldwide. This book introduces multi-Terabit/s transmission systems and three key technologies for next generation networks. A software-defined multi-format transmitter, an optical comb source and an optical processing scheme for the fast Fourier transform for Tbit/s signals. Three world records demonstrate the potential: The first single laser 10 Tbit/s and 26 Tbit/s OFDM and the first 32.5 Tbit/s Nyquist WDM experiments

Performance Evaluation of Phase Optimized Spreading Codes in Non Linear DS-CDMA Receiver

Spread spectrum (SS) is a modulation technique in which the signal occupies a bandwidth much larger than the minimum necessary to send the information. A synchronized reception with the code at the receiver is used for despreading the information before data recovery. Bandspread is accomplished by means of a code which is independent of the data. Bandspreading code is pseudo-random, thus the spread signal resembles noise. The coded modulation characteristic of SS system uniquely qualifies it for navigation applications. Any signal used in ranging is subject to time/distance relations. A SS signal has advantage that its phase is easily resolvable. Direct-sequence (DS) form of modulation is mostly preferred over Frequency Hopping system (FH) as FH systems do not normally possess high resolution properties. Higher the chip rate, the better the measurement capability. The basic resolution is one code chip. Initially, some existing code families e.g. Gold, Kasami (large and smal..

Threshold decoding

"April 5, 1963." Issued also as a thesis, M.I.T. Dept. of Electrical Engineering, August 20, 1962.Bibliography: p. 122-123.Army Signal Corps Contract DA36-039-sc-78108. Dept. of the Army Task 3-99-25-001-08.James L. Massey

Dynamic element matching techniques for data converters

Analog to digital converter (ADC) circuit component errors create nonuniform quantization code widths and create harmonic distortion in an ADC\u27s output. In this dissertation, two techniques for estimating an ADC\u27s output spectrum from the ADC\u27s transfer function are determined. These methods are compared to a symmetric power function and asymmetric power function approximations. Standard ADC performance metrics, such as SDR, SNDR, SNR, and SFDR, are also determined as a function of the ADC\u27s transfer function approximations. New dynamic element matching (DEM) flash ADCs are developed. An analysis of these DEM flash ADCs is developed and shows that these DEM algorithms improve an ADC\u27s performance. The analysis is also used to analyze several existing DEM ADC architectures; Digital to analog converter (DAC) circuit component errors create nonuniform quantization code widths and create harmonic distortion in a DAC\u27s output. In this dissertation, an exact relationship between a DAC\u27s integral nonlinearity (INL) and its output spectrum is determined. Using this relationship, standard DAC performance metrics, such as SDR, SNDR, SNR, and SFDR, are calculated from the DAC\u27s transfer function. Furthermore, an iterative method is developed which determines an arbitrary DAC\u27s transfer function from observed output magnitude spectra. An analysis of DEM techniques for DACs, including the determination of several suitable metrics by which DEM techniques can be compared, is derived. The performance of a given DEM technique is related to standard DAC performance metrics, such as SDR, SNDR, and SFDR. Conditions under which DEM techniques can guarantee zero average INL and render the distortion due to mismatched components as white noise are developed. Several DEM circuits proposed in the literature are shown to be equivalent and have hardware efficient implementations based on multistage interconnection networks. Example DEM circuit topologies and their hardware efficient VLSI implementations are also presented