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mask2shift

Convert mask vector to shift for linear shift register

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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].

example

Examples

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Open Live Script

Convert masks into shifts for a linear feedback shift register.

Convert a mask of x3+1 into an equivalent shift for the linear feedback shift register whose connections are specified by the primitive polynomial x4+x3+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 x2 into an equivalent shift for the primitive polynomial x3+x+1.

s3 = mask2shift('x3+x+1','x2')
s3 = 
2

Input Arguments

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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

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

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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.

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

See Also

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