How would one build an LFSR logical map, with a characteristic polynomial such as

$$P(x) = x^4 + x^3 + 1$$?

Also, how would you interpret it, and what would you do to do the reverse it in order to create a characteristic polynomial from an LFSR map?

  • $\begingroup$ Hint: calculate the reciprocal of $P(x)$ then use feedback polynomial as in here $\endgroup$
    – kelalaka
    Apr 8 '19 at 19:06
  • $\begingroup$ Thank you for the link, I am able to understand this much better, thanks kelalaka! $\endgroup$
    – Ayo -
    Apr 8 '19 at 19:32
  • $\begingroup$ Use sageMath . It has great functions to calculate characteristic polynomial. $\endgroup$ Apr 9 '19 at 9:56

The recipocal $P^*(x)$ of polynomial $$P(x)= a_0 + a_1x + a_2x^2 + \cdots + a_nx^n$$ of degree $n = deg(P(x))$ is given by;

$$P^*(x) = a_n + a_{n-1}x + \cdots + a_0x^n = x^n P(x^{-1})$$

The feedback polynomial defines the tap points of LFSR. The characteristic polynomial and is the reciprocal of feedback. Therefore;

Let $P^*(x)= x^4 \cdot P(1/x) = 1 + x + x^4 $ be the feedback polynomial LFSR calculated by the recipocal of characteristic polynomial $P(x)$. Then the taps of the LFSR as follows;

enter image description here

For further reading in this subject, Golomb's classic book is advised.

The image is produced with the LFSR drawing library.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.