The Creation and Detection of Binary and Non-Binary Pseudo-Noise Sequences Not Using LFSR Circuits
The invention discloses methods to create binary and non-binary sequences of a pseudo-random nature such that possible symbols occur at or almost at the same rate. The invention also discloses methods using symbol words of fixed lengths to generate unique sequences. These methods do not apply Linear Feedback Shift Registers (LFSRs). Methods to detect the presence of a pre-defined sequence are also disclosed. These methods do not apply LFSRs.
1 . A method for generating a sequence having k n-valued symbols from k different words of p n-valued symbols with k, p and n being integers 2 or greater, comprising:
a) selecting a first word from the k different words;
b) selecting a second word from the k different words that have not been selected in such a manner that the first (p−1) symbols of the second word are identical to the last (p−1) symbols of the first word;
c) assigning a first symbol of the first word as a next symbol in the sequence;
d) assigning the second word to be the first word; and
e) repeating step b) to d) until all k words have been selected once;
f) wherein an LFSR is not used.
2 . The method as claimed in claim 1 , wherein the steps are executed by a computer program.
3 . The method as claimed in claim 1 , wherein n=2 and k=(2 p −1).
4 . The method as claimed in claim 1 , wherein n=2 and k=(2 p ).
5 . The method as claimed in claim 1 , wherein n≠2 and k=(n p −1).
6 . The method as claimed in claim 1 , wherein n≠2 and k=(n p ).
7 . The method as claimed in claim 1 , wherein the sequence is a pseudo-noise sequence.
8 . A method for comparing a first sequence having k n-valued symbols and which can be decomposed into k different words of p n-valued symbols, with a second sequence having not more than k symbols comprising:
selecting m words of p symbols from the second sequence and determining an order of the m words;
determining whether the m words are present in the first sequence;
determining an order of the m words in the first sequence if they are present; and
deciding that the second sequence is identical to the first sequence when the m words appear in the first and the second sequence in an identical order.
9 . The method as claimed in claim 8 , wherein the m words are a sample of the second sequence.
10 . The method as claimed in claim 8 , wherein the second sequence is from a plurality of different sequences each having k n-valued symbols wherein each sequence can be decomposed into k different words of p n-valued symbols.
11 . The method as clamed in claim 8 , wherein errors may have occurred in the second sequence and a measure of similarity between the first sequence and the second sequence is provided by a probability number.
12 . The method as claimed in claim 8 , wherein the steps of the method are executed by a computer program.
13 . An apparatus for comparing a first sequence having k n-valued symbols and which can be decomposed into a plurality of k different words of p n-valued symbols with a second sequence having not more than k symbols comprising:
a processor;
a device that outputs a representation of the first sequence to the processor;
an input for inputting the second sequence to the processor;
application software operable on the processor to process data representing the first and the second sequence, including:
selecting m words of p symbols from the second sequence and
determining a relative order of the m words in the second sequence;
determining whether the m words are present in the first sequence;
determining an order of the m words in the first sequence if they are present; and
deciding that the second sequence is identical to the first sequence when the m words appear in the first and the second sequence in an identical order.
14 . The apparatus as claimed in claim 13 , wherein the m words are a sample of the second sequence.
15 . The apparatus as claimed in claim 13 , wherein the second sequence is from a plurality of different sequences having k n-valued symbols wherein each sequence can be decomposed into k different words of p n-valued symbols.
16 . The apparatus as claimed in claim 13 , wherein errors may have occurred in the second sequence and a measure of similarity between the first sequence and the second sequence is provided by a probability number.
17 . The apparatus as claimed in claim 13 , wherein the apparatus is part of a wireless device.
18 . The apparatus as claimed in claim 13 , wherein the apparatus is part of a device connected to a communication line.
19 . The apparatus as claimed in claim 13 , wherein the apparatus is part of a UWB device.