Seok Chang Kim

Scrambling techniques for digital transmission

I Preliminaries.- 1 Digital Transmission and Scrambling.- 1.1 Digital Transmission Systems.- 1.2 Scrambling Functions in Digital Transmission.- 1.3 Digital Signals and Scrambling.- 1.4 Packet-Mode Data Transmission and Scrambling.- 2 Fundamentals of Scrambling Techniques.- 2.1 Frame Synchronous Scrambling.- 2.2 Distributed Sample Scrambling.- 2.3 Self Synchronous Scrambling.- 2.4 Serial Scrambling.- 2.5 Parallel Scrambling.- 2.6 Multibit-Parallel Scrambling.- II Frame Synchronous Scrambling.- 3 Introduction to Frame Synchronous Scrambling.- 3.1 Operation of FSS.- 3.2 Scrambling Sequences.- 3.3 Shift Register Generators.- 3.4 Organization of the Part.- 4 Sequence Spaces.- 4.1 Definition of Sequence Space.- 4.2 Elementary Basis.- 4.3 Primary Basis.- 4.4 Polynomial Expression of Sequences.- 4.5 Sequence Subspaces.- 4.6 Minimal Sequence Spaces.- 5 Shift Register Generators.- 5.1 Shift Register Generator.- 5.2 Minimal Spaces for SRG Sequences.- 5.3 SRG Spaces.- 5.4 SRG Maximal Spaces.- 5.5 Basic SRGs.- 5.6 Simple and Modular SRGs.- 6 Serial Frame Synchronous Scrambling.- 6.1 Pseudo-Random Binary Sequences.- 6.2 Primitive Sequence Spaces.- 6.3 PRBS Generators.- 7 Parallel Frame Synchronous Scrambling.- 7.1 Parallel Scrambling Sequences.- 7.2 Decimated Sequences.- 7.3 Decomposition of Sequences.- 7.4 Decimation of Irreducible Sequences.- 7.5 Decimation of Power Sequences.- 7.6 Decimation of PRBS.- 7.7 Decimation of Sum Sequences.- 7.8 Parallel Shift Register Generators.- 7.9 Minimal Realizations of PSRG.- 7.10 Simple Realizations of Minimal PSRG.- 8 Multibit-Parallel Frame Synchronous Scrambling.- 8.1 Multibit-Parallel Sequences.- 8.2 Interleaved Sequences.- 8.3 Minimal Space for Parallel Sequences.- 8.4 Parallel Sequences for Irreducible Sequences.- 8.5 Realizations of PSRGs for MPFSS.- 9 Applications to Scrambling in SDH/SONET Transmission.- 9.1 Scrambling of SDH/SONET Signals.- 9.2 Bit-Parallel Scrambling of STM-1/STS-1 Signals.- 9.3 Byte-Parallel Scrambling of STM-N Signal.- 9.3.1 Byte-Parallel Scrambling of STM-4 Signal.- 9.3.2 Byte-Parallel Scrambling of STM-16 Signal.- 9.4 Byte-Parallel Scrambling of STS-N Signal.- 9.4.1 Byte-Parallel Scrambling of STS-3 Signal.- 9.4.2 Byte-Parallel Scrambling of STS-12 Signal.- III Distributed Sample Scrambling.- 10 Introduction to Distributed Sample Scrambling.- 10.1 Operation of DSS.- 10.2 Three-State Synchronization Mechanism for DSS.- 10.3 Organization of the Part.- 11 Prediction of Scrambling Sequences.- 11.1 Scrambling Space.- 11.2 Scrambling Maximal Space.- 11.3 Scrambling Maximal Spaces for BSRGs.- 11.4 Prediction of Scrambling Sequences.- 12 Serial Distributed Sample Scrambling.- 12.1 Mathematical Modeling.- 12.2 Scramblers for DSS.- 12.2.1 Scrambler SRGs.- 12.2.2 Sampling Times.- 12.3 Descramblers for DSS.- 12.3.1 Descrambler SRGs.- 12.3.2 Correction Times and Correction Vectors.- 12.3.3 Efficient Realization Methods.- 12.4 DSS with Minimized Timing Circuitry.- 12.4.1 Concurrent Sampling.- 12.4.2 Immediate Correction.- 13 Parallel Distributed Sample Scrambling.- 13.1 Considerations for Parallel DSS.- 13.2 PSRGs for PDSS.- 13.3 Parallel Sampling for PDSS.- 13.4 Parallel Correction for PDSS.- 13.4.1 Single Correction.- 13.4.2 Double Correction.- 13.4.3 Multiple Correction.- 14 Multibit-Parallel Distributed Sample Scrambling.- 14.1 Considerations for MPDSS.- 14.2 PSRGs for MPDSS.- 14.3 Parallel Sampling for MPDSS.- 14.4 Parallel Correction for MPDSS.- 15 Three-State Synchronization Mechanism under Sample Errors.- 15.1 Three-State Synchronization Mechanism.- 15.2 Effects of Errored Samples in Acquisition State.- 15.3 Synchronization Verification in Verification State.- 15.4 Synchronization Confirmation in Steady State.- 16 Applications to Cell-Based ATM and High-Speed Data Networks.- 16.1 Scrambling of Cell-Based ATM Signals.- 16.2 Equivalent DSS with Minimized Timing Circuitry.- 16.3 An Optimal DSS Design.- 16.4 Parallel DSS for Cell-Based ATM Signals.- 16.5 Design of Three-State Synchronization Mechanisms.- 16.5.1 Windowed-Observation State Transition Scheme.- 16.5.2 Thresholded-Counting State Transition Scheme.- 16.5.3 Performance Evaluation.- 16.6 Applications to High-Speed Data Networks.- IV Self Synchronous Scrambling.- 17 Introduction to Self Synchronous Scrambling.- 17.1 Operation of SSS.- 17.2 Signal Alignment.- 17.3 Organization of the Part.- 18 Serial Self Synchronous Scrambling.- 18.1 Scrambled Signals.- 18.2 Descrambled Signals.- 18.3 Self-Synchronization.- 18.4 Error-Multiplication.- 19 Parallel Self Synchronous Scrambling.- 19.1 Parallel-Scrambled and -Descrambled Signals.- 19.2 Parallel Self Synchronous Scrambler.- 19.3 Parallel Self Synchronous Descrambler.- 20 Applications to Scrambling in SDH-Based ATM Transmission.- 20.1 Scrambling of SDH-Based ATM Signals.- 20.2 Parallel SSS for Cell Scrambling in SDH-Based ATM Transmission.- 21 Signal-Alignment with Parallel Self Synchronous Scrambling.- 21.1 Operators for Functional Processors.- 21.2 Number-Operators for Operators.- 21.3 Signal-Detection Tables.- 21.4 Signal-Detection Table Characteristic Expressions.- 21.5 Signal-Detection Tables for Various System Configurations.- 21.5.1 Scrambler Based Systems.- 21.5.2 Permuter Based Systems.- 21.5.3 Permuter-Scrambler Based Systems.- 21.5.4 Scrambler-Permuter Based Systems.- 21.5.5 Scrambler-Permuter-Scrambler Based Systems.- 21.5.6 Permuter-Scrambler-Permuter Based Systems.- 21.5.7 Summary of Signal-Detection Tables.- 21.6 Applications of Signal-Detection Tables to Signal-Alignment.- Appendices.- A Facts from Abstract Algebra.- A.1 Field.- A.2 Extension of Fields.- A.3 Irreducible Polynomials.- A.4 Primitive Polynomials.- A.5 Others.- B Facts from Linear Algebra.- B.1 Vector Space.- B.2 Minimal Polynomials of Matrices.- B.3 Properties of Companion Matrix.- B.4 Similarity of Matrices.- References.

Synchronization of shift register generators in general distributed sample scramblers

In this paper, a theory is developed to support the synchronization of shift register generators (SRGs) in the general class of distributed sample scramblers (DSSs). In the general DSS, the samples transmitted to the descrambler for its synchronization are freely generated out of the scrambler SRG, a special case of which is to take samples directly from the SRG sequence. To describe this general sampling method, the concept of sampling vectors is introduced. The delayed sample-transmission problem, which is a real problem in practical transmission systems, can be resolved by adopting the sampling vectors. This paper provides a systematic solution to the synchronization problem of the general DSS based on mathematical modeling. It first considers the sampling problem of the SRG state information, and then discusses the correction problem of the descrambler SRG state using the transmitted samples. Applications are attached at the end to demonstrate the developed theory for simple realizations of the DSS for use in the cell-based ATM transmission environment.

Low-rate parallel scrambling techniques for today's lightwave transmission

Parallel scrambling techniques enable low-rate realizations of high-speed scrambling processes in todays lightwave transmission, which otherwise might be impossible due to technology limitations. Such parallel scrambling techniques are now available for frame synchronous scrambling (FSS), distributed sample scrambling (DSS), and self-synchronous scrambling (SSS), in bit-interleaved as well as byte-interleaved multiplexing environments. The objective of the article is to introduce the parallel scrambling techniques for FSS, DSS, and SSS, together with their applications to lightwave transmissions such as the SDH/SONET and the ATM network. It first considers the role of scrambling in digital transmission, and provides a brief description of the three scrambling techniques. Then it introduces the corresponding three parallel scrambling techniques, and finally demonstrates how they can be practically applied in low-rate scrambling processing of the SDH/SONET transmission signals, the cell-based ATM signals, and the SDH-based ATM signals. >

A theory on sequence spaces and shift register generators

As a unified approach to the description of various shift register generators, the concept of sequence space is introduced and its properties are examined. A sequence space refers to a vector space whose elements are sequences satisfying the relation specified by a characteristic polynomial. In support of the sequence space, two bases-the elementary basis and the primary basis-are defined, and the polynomial expression of the sequence is defined as a tool for mathematical manipulations within the sequence space. Based on these definitions, various properties of sequence spaces such as sequence subspaces and minimal sequence spaces are investigated and summarized in terms of properties and theorems. The developed sequence theory is then applied to the description of the behaviors of shift register generators (SRGs). An SRG is represented by the state transition matrix, and the relevant SRG sequences are uniquely determined by this state transition matrix and the initial state vector. For an SRG, it is shown how to identify the sequence space generated by the SRG sequences with a fixed initial state vector (or the SRG space), and further, how to find the largest-dimensional sequence space that can be obtained by varying the initial state vectors (or the SRG maximal space). Conversely, for a given sequence space, it is shown how to find the minimum-sized SRGs that can generate the sequence space (or the basic SRGs). Finally, it is shown that the two typical SRGs-simple SRG and modular SRG-are special cases of basic SRGs that can generate the primary and the elementary bases, respectively.

Recent advances in theory and applications of scrambling techniques for lightwave transmission

This paper discusses recent advances in the theory and applications of scrambling techniques for digital lightwave transmission. It introduces the theories of sequence space and shift register generator (SRG) space which enable systematic analysis and mathematical manipulation of the behavior of sequences in general and the related SRGs. It discusses the behavior and realization of frame synchronous scrambling (FSS) and distributed sample scrambling (DSS) with emphasis on parallel sequences and the related parallel SRGs (PSRG). In addition, it describes self synchronous scrambling (SSS). Then the paper applies the theories to todays lightwave transmission systems by demonstrating practical parallel designs of FSS for SDH/SONET transmission, DSS for cell-based ATM transmission, and SSS for SDH-based ATM transmission. It finally considers how DSS can be used for scrambling of mixed isochronous and nonisochronous data in future high-speed data networks. The paper employs various new concepts and terminology, such as PSRG engine, generating vector discrimination matrix, (M,N) PSRG, sampling vector, correction vector, correction matrix, predictable scrambling concurrent sampling, and immediate correction. >

A signal-alignment theory in rolling-based lightwave transmission systems

A theory to support signal alignment in rolling-based lightwave transmission systems is developed. The theory originates from the transmission system environment, which consists of three basic building blocks-multiplexer, scrambler, and permuter. These building blocks are represented by mathematical operators, on the basis of which mathematical expressions of the whole transmission system become possible. The mathematical operators are directly translated into number operators which help detect and identify the received signals in the form of a table-the signal-detection table. The signal-detection tables play a central role in the signal-alignment theory, since any transmission system can be represented by its corresponding signal-detection table. The entries in the signal-detection tables are closely correlated so that the tables can be uniquely characterized by their corresponding characteristic expressions. Various types of signal-detection tables are examined, and solutions to align transmitted signals and to reduce signal-alignment time in rolling-based lightwave transmission systems are exemplified through scrambler-permuter configurations. >

Shift Register Generators

Shift register generator (SRG) is an autonomous system consisting of shift registers and exclusive-OR gates. In this chapter, we investigate the behaviors of SRGs in view of the sequence space theory developed in the previous chapter. For a given SRG, we first consider how to determine the sequence space generated by SRG sequences with a fixed initial state vector (SRG space), and then consider how to find the largest-dimensional sequence space that can be obtained by varying the initial state vectors (SRG maximal space). Conversely, for a given sequence space we consider how to find the minimum-sized SRGs that can generate the sequence space (basic SRG). Finally, we examine the two typical SRGs, namely the simple SRG and the modular SRG, in view of the concept of basic SRGs.

Applications to Cell-Based ATM and High-Speed Data Networks

We now consider how to apply the serial, parallel and multibit-parallel DSS techniques along with synchronization mechanisms we have developed in the previous chapters to scrambling in practical transmission networks. We first describe the DSS operation used in the cell-based ATM transmission for BISDN, which is the most typical lightwave transmission system employing the DSS. Then, we consider how to achieve concurrent sampling and immediate correction for eliminating additional timing circuits in this application. Also we consider how to apply the parallel DSS techniques to the cell-based ATM scrambling in conjunction with concurrent parallel sampling and immediate parallel correction. Further, we examine the synchronization mechanisms of the ATM scrambling and analyze their performances. Finally, as an extension to the ATM applications, we discuss how to design DSS scrambler and descrambler for use in future high-speed data networks.

Multibit-Parallel Distributed Sample Scrambling

The multibit-parallel distributed sample scrambling (MPDSS)is an extension of the PDSS in which parallel sequences are generated to match the multibit-interleaved multiplexed bitstream. So, in the MPDSS, the parallel input data bitstreams are scrambled before multibit-interleaved multiplexing, and the scrambled data bitstream is descrambled after multibit-interleaved demultiplexing. In this chapter, we discuss issues involved with the multibit-parallel realizations of DSSs. We first consider how to realize the PSRGs for MPDSS along with the minimal realizations of PSRGs. Then, we examine how to achieve the multibit-parallel sampling for MPDSS along with the concurrent multibit-parallel sampling. Finally, we consider the multibit-parallel correction for MPDSS.

Signal-Alignment with Parallel Self Synchronous Scrambling

The SSS has the unique property that it can scramble and descramble data sequences without looking into the internal contents of the data. Inherited from this property, the PSSS has the capability to scramble and descramble multiple base-rate signals without overlaying any frame structure. However, there is one problem appearing in this case, which is the proper distribution of the base-rate signals to their destined output lines, or the proper signal alignment. In this chapter, we consider such an signal-alignment issue in the transmission systems employing the PSSS, and discuss how to resolve the issue by employing the concept of permuting. We first represent three basic building blocks of the systems -- multiplexer, scrambler and permuter -- in terms of mathematical operators, which are directly translated into number-operators. Based on these operators, we consider how to identify the received signals in the form of a table called the signal-detection table, and examine how to characterize the signal-detection table by employing the signal-detection table characteristic expression. For various system configurations, we determine their signal-detection tables, and investigate their properties. Finally, we demonstrate how to apply the signal-detection table to the signal-alignments of the PSSS-scrambled transmission signals.