Documentation

Convert mask vector to shift for shift register configuration

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 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].

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

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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 = 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.