Ternary and higher multi-value digital scramblers/descramblers
Ternary (3-value) and higher, multi-value digital scramblers/descramblers in digital communications. The method and apparatus of the present invention includes the creation of ternary (3-value) and higher value truth tables that establish ternary and higher value scrambling functions which are its own descrambling functions. The invention directly codes by scrambling ternary and higher-value digital signals and directly decodes by descrambling with the same function. A disclosed application of the invention is the creation of composite ternary and higher-value scrambling devices and methods consisting of single scrambling devices or functions combined with ternary or higher value shift registers. Another disclosed application is the creation of ternary and higher-value spread spectrum digital signals. Another disclosed application is a composite ternary or higher value scrambling system, comprising an odd number of scrambling functions and the ability to be its own descrambler.
1. A method of descrambling a sequence of p scrambled n-state symbols with n>2 and p>1 into a sequence of p descrambled n-state symbols, an n-state symbol being able to assume one of n states, comprising:
inputting a first scrambled n-state symbol of the sequence of p scrambled n-state symbols on a first input of a descrambling n-state function;
inputting a second n-state symbol on a second input of the descrambling n-state function;
generating by a processor of a descrambled n-state symbol in accordance with the descrambling n-state function, wherein a truth table representing the descrambling n-state function is implemented in a memory that is accessed by the processor;
wherein a relationship between the first scrambled n-state symbol which may be called A, the second n-state symbol which may be called B and the descrambled n-state symbol which may be called C is defined by the n-state truth table that is commutative and self reversing and that satisfies the following equations for all possible states of A and B:
A sc B=C; (1)
C sc B=A; and (2)
A sc C=B; and (3)
repeating the previous steps until all symbols of the sequence of p scrambled n-state symbols have been descrambled by the processor.
2. The method of claim 1 , further comprising:
generating the second n-state symbol on an output of an n-state Linear Feedback Shift Register.
3. The method of claim 1 , wherein a lowest of n states is a first state and the descrambled n-state symbol does not have the first state when first scrambled n-state symbol and the second n-state symbol have a same state.
4. The method of claim 1 , wherein the sequence of p scrambled n-state symbols has been created by scrambling a sequence of p n-state symbols by a scrambling method that applies the descrambling n-state logic function.
5. The method of claim 1 , wherein n is an odd integer.
6. The method of claim 1 , wherein the processor is part of a communication system.
7. An apparatus for descrambling a plurality of scrambled n-state symbols including a first scrambled n-state symbol, each n-state symbol enabled to assume one of n states with n>2, comprising:
a descrambling device having a first and a second input and an output, the first input enabled to receive a signal representing the first scrambled n-state symbol, the second input enabled to receive a signal representing a second n-state symbol and the output providing a signal representing a descrambled n-state symbol;
wherein a relationship between the first scrambled n-state symbol which may be called A, the second n-state symbol which may be called B and the descrambled n-state symbol which may be called C is determined by a commutative self reversing n-state logic function sc, that satisfies the following equations for all possible states of A and B:
A sc B=C; (1)
C sc B=A; and (2)
A sc C=B: and (3)
wherein the descrambling device includes a memory that implements a truth table that defines the commutative self reversing n-state logic function sc.
8. The apparatus as claimed in claim 7 , further comprising:
an n-state Linear Feedback Shift Register (LFSR) including an output that provides the signal representing the second n-state symbol.
9. The apparatus as claimed in claim 7 , wherein the first scrambled n-state symbol and the second n-state symbol are represented by a first and a second plurality of binary signals.
10. The apparatus as claimed in claim 7 , wherein the commutative self reversing n-state logic function is realized by implementing its truth table in a memory.
11. The apparatus as claimed in claim 7 , further comprising a corresponding scrambling apparatus, including:
a scrambling device, having a first input enabled to receive a signal representing a first n-state symbol, a second input enabled to receive a signal representing the second symbol, and an output enabled to provide the first scrambled n-state symbol;
wherein the scrambling device implements the commutative self reversing n-state logic function sc.
12. The apparatus of claim 11 , wherein the corresponding scrambler has an identical structure as the descrambler.
13. The apparatus of claim 7 , wherein the descrambler is part of a communication system.
14. The apparatus of claim 7 , wherein a signal representing the first scrambled n-state symbol is part of a spread spectrum signal.
15. A method for scrambling a sequence of p n-state symbols with p>1, including a first n-state symbol, each n-state symbol enabled to assume one of n states with n>2, each n-state symbol being represented by a signal, comprising:
inputting the first n-state symbol of the sequence of p n-state symbols on a first input of a scrambling n-state function;
inputting a second n-state symbol on a second input of the scrambling n-state function;
generating by a processor of a scrambled n-state symbol in accordance with the scrambling n-state function, wherein a truth table representing the scrambling n-state function is implemented in a memory that is accessed by the processor;
wherein a relationship between the first n-state symbol which may be called A, the second n-state symbol which may be called B and the scrambled n-state symbol which may be called C is defined by the n-state truth table that is commutative and self reversing and that satisfies the following equations for all possible states of A and B:
A sc B=C; (1)
C sc B=A; and (2)
A sc C=B; and (3)
repeating the previous steps until all symbols of the sequence of p n-state symbols have been scrambled by the processor.
16. The method of claim 15 , further comprising:
inputting the scrambled n-state symbol on an input of an n-state Linear Feedback Shift Register.
17. The method of claim 15 , wherein a lowest of n states is a first state and the scrambled n-state symbol does not have the first state when first scrambled n-state symbol and the second n-state symbol have a same state.
18. The method of claim 15 , wherein the processor is part of a communication system.
19. The method of claim 15 , wherein a signal representing the scrambled n-state symbol is part of a spread spectrum signal.