Pseudo-Random Binary Sequences and Data Scramblers 

In this experiment you will be generating psuedo-random binary sequences using linear feedback shift registers. You will also learn about the self-synchronizing digital data scrambler and descrambler. These binary sequences will be used to simulate binary data sources for the remaining experiments.

You don't have to check out any equipment for this lab.

Deviations from the laboratory manual :

• Use benchmarking to find out the time it takes for generating one binary number.
• Write your program for implementing a scrambler and descrambler in assembly/C language. Use the primitive polynomial 1+D^2+D^5.

Tretter's lab manual asserts that the following polynomial is irreducible, i.e., cannot be factored into simpler polynomials over modulo-2 arithmetic:

     2    3    4
1 + x + x  + x  + x

In[6]:= Factor[ 1 + x + x^2 + x^3 + x^4, Modulus -> 2 ]

                 2    3    4
Out[6]= 1 + x + x  + x  + x

Treter's lab manual asserts that the same connection polynomial is not primitive. A polynomial of order m is primitive if the smallest value of N for which the polynomial x^N - 1 is divisible by the connection polynomial equals 2^m - 1. So, we can search over all N from 1 to 2^m - 1 inclusive. The connection polynomial above divides x⁵ - 1:

In[29]:= Factor[ x^5 - 1, Modulus -> 2 ]

                           2    3    4
Out[29]= (1 + x) (1 + x + x  + x  + x )

Presentation slides for Lab 4

Assignment

Submitting this assignment is optional, but doing it would be useful with your QUIZ preparations

Assignment 

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