Blind detection of LFSR-based Scar Mabel parameters in digital data

Master thesis in the field

Electrical Engineering

Communication-system

Abstract

Blind detection of parameters of LFSR based scramblers, in digital data

by effort

 Zahra Zakari

In digital telecommunication systems, linear scramblers are used both for simple encryption and for breaking a large sequence of identical bits. The bit sequence issue, i.e. a large number of 0's and 1's in a row, usually leads to synchronization problems. In fact, the methods of whitening the statistics of the digital source without using the content data are called scrambling. In telecommunications and decoders, a scrambler is a device that manipulates and changes data before it is sent. These changes are done in reverse in the receiver to reach the primary data.

In this thesis, after introducing the scrambler and its components, the methods of finding the scrambler parameters in two cases of having the input text sequence (Berlkamp-Messi method) and the other case of having only the scrambled sequence (Clausio algorithm) are discussed and the results are analyzed. takes After that, we consider the case where the scrambled data has an error after passing through the channel, and in the presence of channel noise, we identify the scrambler parameters and observe the effect of noise on the output data of two types of scramblers (multiplicative scramblers and collective scramblers). After that, we investigate the feedback polynomial identification method of linear scramblers assuming that the source bits are coded by error correction coding before they are scrambled.

1-1- What is a scrambler and why do we use it?

A digital data transmission system always causes errors and damages when sending data, and the amount of these disturbances and damages changes depending on the statistics of the source. Sometimes synchronization, interference and equalization problems are related to source statistics. Although the use of internals in sending codes makes the system performance independent from the source statistics to some extent, there are always dependencies, in addition, adding internals data causes problems such as increasing the rate of sent symbols or adding alignment in symbols. In a code sending system, if we assume that the symbols sent are statistically independent, it will be much easier to analyze and find errors. We call such a source whose symbols are statistically independent from each other as a white source because its analysis is like Gaussian white noise. Whitening methods of digital source statistics without using content data are described as scrambling[1]. In telecommunications and decoders, a scrambler[2] is a device that manipulates and changes data before it is sent. These changes are done in reverse in the receiver to get the original data. Various scrambling methods are used in satellite and PSTN modems [3]. The scrambler can be placed just before an FEC encoder [4] or it can be placed after the FEC and before the modulation block.

Our effort in this research is to investigate different methods and techniques in identifying the parameters of linear scramblers. This is done by having a string of output bits and based on assumptions on the input bits of the scrambler. Of course, someone who does this using the output bits must consider two categories: first, error correction, and then extracting the scrambler parameters. Considering the linearity of the discussed scramblers, using algebraic methods to estimate the scrambler parameters is the most efficient method. Especially linear shift registers with feedback, whose feedback function is a linear function, which is further explained in this regard.

1-2- Advantages of using scrambling before sending data

With this method, without adding content data to the sent message, the accuracy of Time Recovery can be increased in the receiving equipment.

By spreading the energy throughout the carrier signal, it reduces the possibility of interference between the carrier signals and the dependence of the spectral density between It removes the scrambled data and the real data sent.

It increases the security of sending data and scramblers can be used in encryption. Because the ideal state of a ciphertext is to be a completely random sequence. In other words, the bits of the sequence are completely independent from each other and the probability of being zero and one is equal, and a long and i.i.d sequence can be produced from a limited and short key.

1-3- Pseudo-random sequences

An ideal binary random sequence is actually an independent infinite sequence with a uniform distribution in which the random variables accept any of the values ??0 or 1 with a probability of 0.5. This sequence can be modeled by the data string produced by the binary sources. With linear feedback shift registers, the best approximation for binary random sequences can be achieved. The sequence obtained in this way is called pseudo-random, pseudo-noise, maximum-length, or sequence.

To simulate a random binary sequence, we are looking for a shift register that, if its length is a register, the sequence it produces has the largest possible period, i.e. Such a sequence is called a "maximum length sequence". It can be shown that the shift register produces a sequence with the maximum length, whose connection polynomial (in the next chapter, it is explained about the connection polynomial) is of the fundamental polynomial type. There are fundamental polynomials of any degree. A necessary condition for a polynomial to be fundamental is that it is indecomposable, but this condition is not sufficient. A polynomial with binary coefficients in the binary basis is said to be indecomposable when we cannot decompose it into a binary polynomial with coefficients and at least 1.

1-4- Criteria for the degree of randomness of a sequence

The degree of randomness of a sequence refers to the degree of unpredictability of a sequence. Any random sequence produced by processes used in practical applications is not necessarily random. Here we are going to express some characteristics of random sequences and any sequence that has these characteristics is called random or more precisely pseudo-random.

Criteria and principles provided by Glomb for the randomness of a sequence:

Glomb criteria for sequences with a period of periodicity are from the next vector space in the field, but because The field of work of this thesis is on binary sequences in the field. We express these properties for binary sequences.

Balance law: in each periodic period of these sequences, the number of zeros and the number of ones is almost equal. (More precisely, the mismatch is less than one.