mask2shift

Convert mask vector to shift for linear shift register

Syntax

shift = mask2shift(prpoly,mask)

Description

shift = mask2shift(prpoly,mask) returns the shift that is equivalent to a mask vector for a linear feedback shift register with connections specified by the primitive polynomial prpoly.

Note

The input prpoly must be primitive to produce a meaningful output. Use the isprimitive function to check if prpoly is primitive. For more information, see primpoly or [2].

Examples

Convert Mask to Shift

Convert masks into shifts for a linear feedback shift register.

Convert a mask of $$x^3+1$$ into an equivalent shift for the linear feedback shift register whose connections are specified by the primitive polynomial $$x^4+x^3+1$$.

s1 = mask2shift([1 1 0 0 1],[1 0 0 1])

s1 = 
4

Convert a mask of 1 to a shift. The mask is equivalent to a shift of 0.

s2 = mask2shift([1 1 0 0 1],[0 0 0 1])

s2 = 
0

Convert a mask of $$x^2$$ into an equivalent shift for the primitive polynomial $$x^3+x+1$$.

s3 = mask2shift('x3+x+1','x2')

s3 = 
2

Input Arguments

mask — Polynomial input

binary vector

Polynomial input, specified as a binary vector. The length of the mask is equal to the degree of the primitive polynomial and defined in the descending order.

Data Types: double

prpoly — Primitive polynomial

polynomial character vector | binary vector | integer scalar

Primitive polynomial, specified as one of the following:

• A character vector or string scalar of a polynomial. For more information, see Representation of Polynomials in Communications Toolbox.

• A binary vector that lists the coefficients of the primitive polynomial in order of descending powers.

• An integer scalar whose binary representation gives the coefficients of the primitive polynomial, where the least significant bit is the constant term.

Data Types: string | char

More About

Definition of Equivalent Shift

If A is a root of the primitive polynomial and m(A) is the mask polynomial evaluated at A, the equivalent shift s solves the equation A^s = m(A). To interpret the vector mask as a polynomial, treat mask as a list of coefficients in order of descending powers.

References

[1] Lee, J. S., and L. E. Miller, CDMA Systems Engineering Handbook, Boston, Artech House, 1998.

[2] Simon, Marvin K., Jim K. Omura, et al., Spread Spectrum Communications Handbook, New York, McGraw-Hill, 1994.

Version History

Introduced before R2006a