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# Generating Pseudo Noise Sequences

IP.com Disclosure Number: IPCOM000092116D
Original Publication Date: 1968-Sep-01
Included in the Prior Art Database: 2005-Mar-05
Document File: 2 page(s) / 46K

IBM

## Related People

Hsiao, MY: AUTHOR

## Abstract

This method generates pseudo noise sequences of length 2/k/-1 by k-stage feedback shift registers with a speed k-times faster than existing methods. A pseudo noise sequence is defined as a maximum-length linear recurring sequence modulo-2. Thus, a sequence is a pseudo noise sequence if, and only it, it is a binary sequence which satisfies a linear recurrence and has a period 2/k/-1.

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Generating Pseudo Noise Sequences

This method generates pseudo noise sequences of length 2/k/-1 by k-stage feedback shift registers with a speed k-times faster than existing methods. A pseudo noise sequence is defined as a maximum-length linear recurring sequence modulo-2. Thus, a sequence is a pseudo noise sequence if, and only it, it is a binary sequence which satisfies a linear recurrence and has a period 2/k/-1.

Selecting, as an example, the polynomial 1+x+x/4/ associated with the shift register generator in drawing A, the various successions of the states starting from the initial state 0001 are listed in Table I. This shows that the output sequence, considered four bits at a time, is the same as the state transitions of S1, S5, S9 and S13 respectively, with the states of the shift register labeled x/3/ x/2/ x/1/ x/0/. Thus, a circuit which has the state transitions of S1, S5, S9, and S13 generates the complete pseudo noise sequence obtainable with the shift register of drawing A starting with the initial state 1000 within four shifting clock times. The speed of generating a pseudo noise sequence is thus improved by a multiple of four. The circuit can be implemented for T/4/ instead of T, where T is the companion matrix of the chosen polynomial. For the polynomial of the example 1+x+x/4/, 0 1 0 0 1 1 0 0

0 0 1 0 0 1 1 0

T= 0 0 0 1 and by direct multiplication T/4/= 0 0 1 1 1 1 0 0 1 1 0 1. The equations for implementing the circuit are obtained from each row...