shift2mask

Convert shift to mask vector for shift register configuration

Syntax

mask = shift2mask(prpoly,shift)

Description

mask = shift2mask(prpoly,shift)returns the mask that is equivalent to the shift (or offset) specified byshift, for a linear feedback shift register whose connections are specified by the primitive polynomialprpoly. Theprpolyinput can have one of these formats:

Apolynomial 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

Theshiftinput is an integer scalar.

Note

To save time,shift2maskdoes not check thatprpolyis primitive. If it is not primitive, the output is not meaningful. To find primitive polynomials, useprimpolyor see[2].

Definition of Equivalent Mask

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

Shifts, Masks, and Pseudonoise Sequence Generators

Linear feedback shift registers are part of an implementation of a pseudonoise sequence generator. Below is a schematic diagram of a pseudonoise 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 m₀switch is closed while all other m_kswitches 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	...	x_s	x_s+1
Shift = s > 0	x_s	x_s+1	x_s+2	...	x_2s	x_2s+1

If you have Communications Toolbox™ software and want to generate a pseudonoise sequence in a Simulink^®模型中,看到PN Sequence Generatorblock reference page.

Examples

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Convert Shift to Mask

Open Live Script

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

Convert a shift of 5 into the equivalent mask $x^{3} + x + 1$ conne的线性反馈移位寄存器ctions are 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 =1×41 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 =1×51 0 1 0 0

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