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mask2shift

Convert mask vector to shift for shift register configuration

Syntax

shift = mask2shift(prpoly,mask)

Description

shift = mask2shift(prpoly,mask) returns the shift that is equivalent to a mask, for a linear feedback shift register whose connections are specified by the primitive polynomial prpoly. The prpoly input can have one of these formats:

  • A polynomial character vector

  • 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

The mask input is a binary vector whose length is the degree of the primitive polynomial.

    Note:   To save time, mask2shift does not check that prpoly is primitive. If it is not primitive, the output is not meaningful. To find primitive polynomials, use primpoly or see [2].

For more information about how masks and shifts are related to pseudonoise sequence generators, see shift2mask.

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 As = m(A). To interpret the vector mask as a polynomial, treat mask as a list of coefficients in order of descending powers.

Examples

collapse all

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

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.

Introduced before R2006a


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