Scrambling Techniques for Digital Transmission

Digital transmission is a technique that transmits information signals in a stream of digital pulses. The original signals may be in analog or digital form, and the transmission medium may be copper wire or optical fiber based. In either case, as long as the signals are conveyed in digital pulse stream over the transmission medium, it is called digital transmission.

Scrambling is a binary bit-level processing applied to the transmission rate signal in order to make the resulting binary sequence appear more random. The scrambler performing this scrambling function can be implemented simply using a few shift registers and exclusive-OR gates; and the descramblers reconstructing the original bitstream out of the scrambled data stream has the same structure but with the reversed data flow. For a proper reconstruction of the original bitstream the shift registers in the descrambler should get synchronized to their counterparts in the scrambler. Depending on the synchronization method used, scrambling techniques are classified into three categories, namely the frame-synchronous scrambling(FSS), the distributed sample scrambling(DSS), and the self-synchronous scrambling(SSS).¹ In the FSS, the states of the scrambler and the descrambler shift registers get synchronized by being simultaneously reset to the prespecified states at the start of each frame; in the DSS, samples taken from the scrambler shift registers are transmitted to the descrambler in a distributed manner for use in synchronizing the descrambler shift registers; and in the SSS, the states of the scrambler and descrambler shift registers are automatically synchronized without any additional synchronization processes.

In the frame synchronous scrambling (FSS), the input data bitstream is scrambled by adding a pseudo-random binary sequence (PRBS) to this, and the scrambled data bitstream is descrambled by adding the same PRBS to this. In this chapter, we examine the behaviors of PRBSs in view of the sequence space theory developed in Chapter 4, and consider how to realize SRGs that generate PRBSs based on the SRG theory developed in Chapter 5. We will first define PRBS systematically using the mathematical definitions of weight, run and autocorrelation of sequences. Then, we will consider a special class of sequence spaces, namely the primitive sequence spaces, whose characteristic polynomials are primitive, showing that the sequences in the primitive sequence spaces are PRBSs. Finally, we will consider how to realize SRGs that generate PRBSs in the primitive sequence spaces.

In the parallel frame synchronous scrambling (PFSS), the parallel input data bitstreams are scrambled before multiplexing, and the scrambled data bitstream is descrambled after demultiplexing. In this chapter, we discuss the behaviors of parallel scrambling sequences for use in the parallel scrambling in view of the sequence space theory developed in Chapter 4, and consider how to realize SRGs generating parallel scrambling sequences using the SRG theory developed in Chapter 5. We will first show that the parallel scrambling sequences are the decimated sequences of the serial scrambling sequence. Then, we will discuss how to decompose the serial sequence into a linear sum of the so-called irreducible sequence and power sequence, and consider how to determine the decimated sequences of the irreducible and power sequences. We will also examine how to obtain the decimated sequences of the original serial sequences decomposed into the irreducible and power sequences. Finally, we will discuss how to realize parallel SRGs to generate parallel sequences, and consider how to achieve their minimal realizations.

Multibit-parallel frame synchronous scrambling (MPFSS) is a generalization of the parallel frame synchronous scrambling (PFSS) in which multiplexing is done multibit based. In this sense the PFSS we have considered so far is a special case of the MPFSS since in the PFSS multiplexing is done single bit based. Multibit-interleaved multiplexing is a scheme widely used these days in lightwave-based digital transmissions such as SDH/SONET (see Chapter 9), and therefore the parallel scrambling in this environment -- that is, the MPFSS -- becomes very important. As in the case of the PFSS, the parallel input data bitstreams are scrambled before multiplexing, and the scrambled data bitstream is descrambled after demultiplexing in the MPFSS. However, since the multiplexer and demultiplexer employed in the MPFSS operate multibit based, the parallel scrambling sequences for use in the MPFSS is quite different from those employed in the PFSS.

In this chapter, we consider how to apply the serial, parallel and multibitparallel FSS techniques developed in the previous chapters to the SDH and SONET systems, which are the most typical lightwave transmission systems employing the FSS. We first describe the FSS operations used in the SDH and SONET systems along with the frame formats of their transmission signals STM-N and STS-N. Then, we consider how to apply the parallel FSS techniques to the scrambling of the STM-1 and the STS-1 signals such that the scrambling rates can drop to one-eighth of the transmission rates. Finally, we examine how to apply the byteparallel FSS techniques to the scrambling of the various STM-N and STS-N signals to reduce their rates to the STM-1 and the STS-1 rates respectively.

The DSS is distinctively different from the FSS in that it takes samples out of the scrambler SRG sequences and conveys them to the descrambier for use in determining the state of the descrambler SRG. In this regard, it is important to clearly understand the properties of the scrambling sequences and the relations between the scrambling sequences and their samples.

Synchronization is a critical issue especially in the DSS since it solely relies on the transmitted samples for synchronization as opposed to the FSS case in which synchronization is achieved by resetting the shift registers to some prespecified states. The transmitted samples, however, could get corrupted by errors during transmission, while the prespecified initial state vector never gets errored. If guided by such errored samples, the DSS descrambler can not reach the synchronization state, and therefore synchronization becomes a very critical issue in the DSS.

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.

Self synchronous scrambling (SSS) is a scrambling technique which employs a kind of SRGs for use in scrambling as well as in descrambling of data bitstream. The transmission data stream is scrambled by passing through a scrambler composed of shift register generators and exclusive-OR gates, and the scrambled signal is descrambled by passing through a descrambler which is the same as the scrambler but the input and the output are reversed. In the SSS, the states of the scrambler and descrambler shift registers are automatically synchronized without any additional synchronization process. Scrambling effect of the SSS is good in general, but a bit error in the scrambled bitstream can cause multibit errors after descrambling. For the SSS, parallel scrambling techniques are available in the multiplexed environment, as for the FSS and the DSS. However, differently from these two cases, the parallel SSS (PSSS) can be applied to the parallel input signals without requiring any overlaid multiplexing frame. Instead, it requires an appropriate means to properly align the order of the descrambled parallel output signals.

In this chapter, we consider how to apply the serial and the parallel SSS techniques developed in the previous chapters to the ATM-cell scrambling in the SDH-based ATM transmission, which is the most typical lightwave transmission employing the SSS. We first describe the scrambling operations used for cell scrambling in the SDH-based ATM transmission. Then, we consider how to apply the parallel SSS techniques to the ATM-cell 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.