shift2mask

Convert shift to mask vector for linear shift register

Syntax

mask = shift2mask(prpoly,shift)

Description

mask = shift2mask(prpoly,shift) returns the mask that is equivalent to the shift (or offset) specified by shift 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 Shift to Mask

Convert a shift in a linear feedback shift register into an equivalent mask.

Convert a shift of 5 into the equivalent mask $$x^3+x+1$$ for the linear feedback shift register with connections specified by the primitive polynomial $$x^4+x^3+1$$. The length of the mask is equal to the degree of the primitive polynomial, 4.

mk = shift2mask([1 1 0 0 1],5)

mk = 1×4

     1     0     1     1

Convert a shift of 7 to a mask of $$x^4+x^2$$ for the primitive polynomial $$x^5+x^2+1$$.

mk2 = shift2mask('x5+x2+1',7)

mk2 = 1×5

     1     0     1     0     0

Input Arguments

shift — Shift value

integer scalar

Shift value of a linear feedback shift register, specified as an integer scalar.

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: double | char | string

More About

Definition of Equivalent Mask

The equivalent mask for the shift s is the remainder after dividing the polynomial x^s by the primitive polynomial. The vector mask represents the remainder polynomial by listing the coefficients in order of descending powers.

Algorithms

Shifts, Masks, and Pseudo Noise Sequence Generators

Linear feedback shift registers are part of an implementation of a pseudo noise sequence generator. Below is a schematic diagram of a pseudo noise sequence generator. All adders perform addition modulo 2.

The primitive polynomial determines the state of each switch labeled g_k, and the mask determines the state of each switch labeled m_k. The lower half of the diagram shows the implementation of the shift, which delays the starting point of the output sequence. If the shift is zero, the m₀ switch is closed while all other m_k switches are open. The table below indicates how the shift affects the shift register's output.

	T = 0	T = 1	T = 2	...	T = s	T = s+1
Shift = 0	x0	x1	x2	...	xs	xs+1
Shift = s > 0	xs	xs+1	xs+2	...	x2s	x2s+1

To generate a pseudonoise sequence in a Simulink^® model, see the PN Sequence Generator block reference page.

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