Sequence detection by multi-valued coding and creation of multi-code sequences

1. A method of reversible coding a first sequence to a second sequence, the first sequence having n m-value symbols, each m-value symbol having one of m states with m≧2 and n>m, the first sequence having at least m m-value symbols with different states from each other and having an m-value symbol in a first state with α occurrences with α>1, comprising:

applying a coding rule to each symbol in the first sequence to generate the second sequence such that the second sequence has n different n-value symbols; and

each m-value symbol in a position in the first sequence being coded into an n-value symbol in a like position in the second sequence.

2. The method as claimed in claim 1 , further comprising the steps:

using a third sequence having r m-value symbols and r being greater than 1, each of the r m-value symbols having one of m states; and

coding the third sequence into a fourth sequence having r n-value symbols, each n-value symbol having one of n states, by using the method as claimed in claim 1 , and further including the step:

coding a k th occurrence with k≦α of an m-value symbol in the first of m states in the third sequence into an n-value symbol in the fourth sequence by selecting an n-value symbol in the second sequence occurring in a position in the second sequence identical to a position of the k th occurrence of the m-value symbol in the first state in the first sequence.

3. The method as claimed in claim 2 , an m-value symbol in the first of m states having k>α it occurrences in the third sequence, further comprising the steps:

calculating a k th occurrence of an m-value symbol in the first state in the third sequence as being equivalent to an m-value symbol in the first state in the first sequence in a position of a (k modulo-α) th occurrence in the first sequence whenever (k modulo-α) is not zero;

calculating the k th occurrence of an m-value symbol in the first state in the third sequence as being equivalent to an m-value symbol in the first state in the first sequence in a position of an α th occurrence in the first sequence whenever (k modulo-α) is zero; and

coding the k th occurrence of the m-value symbol in the first state in the third sequence into an n-value symbol in the fourth sequence in accordance with an equivalent position of an m-value symbol in the first sequence.

4. The method as claimed in claim 3 , further comprising evaluating s of the symbols in the third m-value sequence, wherein s≧2, and treating the first occurrence of each of the m possible m-value symbols after evaluating the s symbols as appearing for the first time.

5. A method for determining a correlation number between a first and a second sequence of m-value symbols, comprising the steps of:

coding the first and the second sequence into a third and fourth sequence of n-value symbols wherein n>m; and

determining a correlation number between the third and the fourth sequence by evaluating each symbol in the third sequence with a symbol in a like position in the fourth sequence.

6. The method as claimed in claim 5 , further comprising the steps:

initiating a sum;

evaluating a symbol in a first position of the third sequence and a symbol in a first position of the fourth sequence;

adding a number to the sum when the evaluated symbols are identical;

subtracting a number from the sum when the evaluated symbols are different;

evaluating a symbol in a next position of the third sequence and a symbol in a next position of the fourth sequence;

adding a number to the sum when the evaluated symbols in the next position of the third and fourth sequence are identical;

subtracting a number from the sum when the evaluated symbols in the next position of the third and fourth sequence are different; and

repeating the previous three steps until all symbols in the third and fourth sequence have been evaluated.

7. A method as claimed in claim 6 , further comprising subtracting the number 0 from the sum when a symbol in a position in the third sequence is different from a symbol in a like position in the fourth sequence.

8. A method for coding a first sequence of r m-value symbols into a second sequence of r n-value symbols with r≧2, n>m and m≧2, comprising the steps:

for each m-value symbol in the first sequence selecting a corresponding m-value symbol in a third sequence, wherein in the third sequence has n m-value symbols of which m m-value symbols have different states and one m-value symbol has a first state and appears p times with p>1;

selecting from a fourth sequence an n-value symbol corresponding to an m-value symbol in the third sequence, the fourth sequence having n n-value symbols, each n-value symbol having a different state, and wherein an m-value symbol in a position in the third sequence uniquely corresponds to an n-value symbol in the fourth sequence in a like position; and

generating in the second sequence an n-value symbol from an m-value symbol in the first sequence, by using an n-value symbol in the fourth sequence, generated from an m-value symbol in the third sequence which is the corresponding m-value symbol from the m-value symbol in the first sequence.

9. The method as claimed in claim 8 , further comprising

coding an m-value symbol in a position in the first sequence to an n-value symbol in the second sequence in a like position.

10. The method as claimed in claim 8 , further comprising

selecting for an m-value symbol in the first state in the first sequence occurring for a (p+1) th time a corresponding m-value symbol in the first state in the third sequence occurring for the first time in the third sequence.

11. The method as claimed in claim 8 , further comprising

selecting for an m-value symbol in the first state in the first sequence occurring for a (p+k) th time with 1<k<p a corresponding m-value symbol in the first state in the third sequence occurring for the k th time in the third sequence.

12. The method as claimed in claim 8 , further comprising

selecting for an m-value symbol in the first state in the first sequence occurring for a (t.p+1) th time with 1<k<p and t>1 a corresponding m-value symbol in the first state in the third sequence occurring for the first time in the third sequence.

13. The method as claimed in claim 8 , further comprising

selecting for an m-value symbol in the first state in the first sequence occurring for a (t.p+k) th time with 1<k<p and t>1 a corresponding m-value symbol in the first state in the third sequence occurring for the k th time in the third sequence.