In this paper, we consider how to apply the sequence space and the shift register generator (SRG) theories to distributed sample scrambling (DSS), which exhibits the best performance in scrambling of small frame-sized signals. We first consider how to predict scrambling sequences using their samples, which is a basic problem for a proper synchronization within the DSS systems. Then for DSS scramblers, we consider how to determine the scrambler SRGs and the sampling times for conveying information on the scrambling sequence; and for DSS descramblers, we consider how to determine the descrambler SRGs, the correction times, and the correction vectors for a proper synchronization. We further examine how to realize the scramblers and the descramblers with minimized circuit complexity. Finally, we demonstrate how to apply the results to DSS scramblers and descramblers for application in cell-based asynchronous transfer mode (ATM) transmission.

In this paper, a theory is developed in support of parallel realizations of the distributed sample scramblers (DSS) in the cell-based ATM transmission environment. For the relevant parallel realizations of the SRG (shift register generator) engines and the SRG sequence-generating circuits, the PSRG theory is applied which is readily available for parallel FSS (frame synchronous scrambler). For the synchronization of the parallel DSS, the double-sampling and double-correction schemes are employed as they efficiently match the two adjacently located sample conveyance channels within the ATM cells. The resulting synchronization conditions are described in terms of three theorems-one regarding the sampling time and vector's condition, and the other two regarding the correction time and vector's conditions for even- and odd-lengthened SRGs. Demonstration is given at the end on the use of the developed theory for parallel realizations of DSS in scrambling and descrambling the ITU-T recommended cell-based ATM signals.

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.

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.

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 SRG's. 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 SRG's (PSRG). In addition, it describes self synchronous scrambling (SSS). Then the paper applies the theories to today's 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.>

In this paper a theory is developed to support the synchronization of shift register generators (SRG) in the distributed sample scramblers (DSS). DSSs, recently introduced for the cell-based ATM scrambling, are identical to the frame synchronous scramblers (FSS) in scrambling and descrambling processes, but are different in synchronizing the descrambler SRG states. The paper provides a systematic solution to the DSS synchronization problem based on mathematical modeling. It first considers how to sample the SRG state information of scrambler for transmission. Then it discusses how to use the received SRG state samples for the synchronization of the SRG state of descrambler. Examples are attached at the end to demonstrate the developed theory in the cell-based ATM scrambling environment.>

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.>