Spread-spectrum codes generation
A method for communicating comprises generating at least one spreading code from a preferred Golay generator and/or a preferred generalized Golay generator. The preferred generalized Golay generator may comprise a plurality of preferred Golay generators. The outputs of the preferred Golay generator are logic 0 and 1. Each stage of the preferred Golay generator may comprise a single basic storage unit, such as a Flip-Flop. Generalized Golay codes comprise pseudo-complementary sequences having code lengths that differ from Golay complementary sequences and are characterized by low autocorrelation sidelobes relative to the autocorrelation peak.
1. A method for communication, comprising:
generating at least one spreading code using at least one Golay generator comprising M stages, each stage comprising a memory component, a first multiplier that multiplies the output of the memory component with an m th seed element of a seed vector, a second multiplier that multiplies the output signal of the first multiplier with an m th gating signal, an adder and a subtractor spreading at least a portion of a data stream with the at least one spreading code; and
transmitting the spread data stream.
2. The method of claim 1 , wherein the at least one spreading code is a generalized Golay code formed of K constituent Golay codes and having a length N determined by
N
=
∑
k
=
1
K
2
M
k
where K≧2, and where a k th constituent Golay code has length 2 M k .
3. The method of claim 1 , wherein each memory component comprises a number of delay elements, and wherein the total number of delay elements in the Golay generator is less than N−1, where N is the Golay code length.
4. The method of claim 3 , wherein the total number of delay elements is M, wherein the seed vector is of length M, and wherein N=2 M .
5. The method of claim 1 , wherein the Golay generator further comprises an M-bit counter and an M-bit control unit, and wherein an m th bit of the counter provides a clock signal or an enable signal of a corresponding m th stage, and wherein an m th bit output by the control unit provides the m th gating signal.
6. A method for communication, comprising:
receiving a spread data stream;
generating at least one spreading code using at least one Golay generator comprising M stages, each stage comprising a memory component, a first multiplier that multiplies the output of the memory component with an m th seed element of a seed vector, a second multiplier that multiplies the output signal of the first multiplier with an m th gating signal, an adder and a subtractor; and
despreading at least a portion of the received data stream with the at least one spreading code.
7. The method in claim 6 , wherein the at least one spreading code is a generalized Golay code formed of K constituent Golay codes and having a length N determined by
N
=
∑
k
=
1
K
2
M
k
where K≧2, and where k th constituent Golay code has length 2 M k .
8. The method of claim 6 , wherein each memory component comprises a number of delay elements, and wherein the total number of delay elements in the Golay generator is less than N−1, where N is the Golay code length.
9. The method of claim 8 , wherein the total number of delay elements is M, wherein the seed vector is of length M, and wherein N=2 M .
10. The method of claim 6 , wherein the Golay generator further comprises an M-bit counter and an M-bit control unit, and wherein an m th bit of the counter provides a clock signal or an enable signal of a corresponding m th stage, and wherein an m th bit output by the control unit provides the m th gating signal.
11. An apparatus for communications, comprising:
a generator for generating at least one spreading code using at least one Golay generator comprising M stages, each stage comprising a memory component, a first multiplier that multiplies the output of the memory component with an m th seed element of a seed vector, a second multiplier that multiplies the output signal of the first multiplier with an m th gating signal, an adder and a subtractor;
a spreader for spreading at least a portion of a data stream with the at least one spreading code; and
a transmitter for transmitting the spread data stream.
12. The apparatus of claim 11 , wherein the at least one spreading code comprises is a generalized Golay code formed of K constituent Golay codes and having a length N determined by
N
=
∑
k
=
1
K
2
M
k
where K≧2, and where a k th constituent Golay code has length 2 M k .
13. The apparatus of claim 11 , wherein the each memory component comprises a number of delay elements, and wherein the total number of delay elements in the Golay generator is less than N−1, where N is the Golay code length.
14. The apparatus of claim 13 , wherein the total number of delay elements is M, where N=2 M is the Golay code length.
15. The apparatus of claim 11 , wherein the Golay generator further comprises an M-bit counter and an M-bit control unit, and wherein an m th bit of the counter provides a clock signal or an enable signal of a corresponding m th stage, and wherein an m th bit output by the control unit provides the m th gating signal.
16. The apparatus of claim 11 , wherein the first multiplier is implemented using an XOR logic gate, and wherein the second multiplier is implemented using an AND logic gate.
17. An apparatus for communication, comprising:
a receiver for receiving a spread data stream;
a generator for generating at least one spreading code using at least one Golay generator comprising M stages, each stage comprising a memory component, a first multiplier that multiplies the output of the memory component with an m th seed element of a seed vector, a second multiplier that multiplies the output signal of the first multiplier with an m th gating signal, an adder and a subtractor; and
a despreader for despreading at least a portion of a received data stream with the at least one spreading code.
18. The apparatus of claim 17 , wherein the spreading code comprises a generalized Golay code formed of K constituent Golay codes and having a length N determined by
N
=
∑
k
=
1
K
2
M
k
where K≧2, and where a k th constituent Golay code has length 2 M k .
19. The apparatus of claim 17 , wherein each memory component comprises a number of delay elements, and wherein the total number of delay elements in the Golay generator is less than N−1, where N is the Golay code length.
20. The apparatus of claim 17 , wherein the total number of delay elements is M, where N=2 M is the Golay code length.
21. The apparatus of claim 17 , wherein the Golay generator further comprises an M-bit counter and an M-bit control unit, and wherein an m th bit of the counter provides a clock signal or an enable signal of a corresponding m th stage, and wherein an m th bit output by the control unit provides the m th gating signal.
22. The apparatus of claim 17 , wherein the first multiplier is implemented using an XOR logic gate, and wherein the second multiplier is implemented using an AND logic gate.
23. A method for communication, comprising:
generating at least one generalized Golay code by concatenating constituent Golay codes, the generalized Golay code having a length N determined by
N
=
∑
k
=
1
K
2
M
k
,
where K≧2, the number of constituent Golay codes, each k th constituent Golay code has length 2 M k , and N does not equal any Golay complementary sequence length; and
spreading at least a portion of a data stream with the at least one generalized Golay code; and
transmitting the spread data stream.
24. A method for communication, comprising:
receiving a spread data stream;
generating at least one generalized Golay code by concatenating constituent Golay codes, the at least one generalized Golay code having a length N determined by
N
=
∑
k
=
1
K
2
M
k
,
where K≧2, is the number of constituent Golay codes, each k th constituent Golay code has length 2 M k , and N does not equal any Golay complementary sequence length; and
despreading at least a portion of the received data stream with the at least one generalized Golay code.
25. An apparatus for communications, comprising:
a generator for generating at least one generalized Golay code formed of concatenated constituent Golay codes and having a length N determined by
N
=
∑
k
=
1
K
2
M
k
,
where K≧2,is the number of constituent Golay codes, each k th constituent Golay code has length 2 M k , and N does not equal any Golay complementary sequence length;
a spreader for spreading at least a portion of a data stream with the at least one generalized Golay code; and
a transmitter for transmitting the spread data stream.
26. An apparatus for communication, comprising:
a receiver for receiving a spread data stream;
a generator for generating at least one generalized Golay code formed of concatenated constituent Golay codes and having a length N determined by
N
=
∑
k
=
1
K
2
M
k
,
where K≧2, is the number of constituent Golay codes, each k th constituent Golay code has length 2 M k , and N does not equal any Golay complementary sequence length; and
a despreader for despreading at least a portion of the received data stream with the at least one generalized Golay code.
27. The apparatus of claim 25 , wherein the generator comprises K Golay generators, each Golay generator comprising M k stages, each stage comprising a memory component, a first multiplier that multiplies the output of the memory component with an m th seed element of a seed vector, a second multiplier that multiplies the output signal of the first multiplier with an m th gating signal, an adder, and a subtractor.
28. The apparatus of claim 26 , wherein the generator comprises K Golay generators, each Golay generator comprising M k stages, each stage comprising a memory component, a first multiplier that multiplies the output of the memory component with an m th seed element of a seed vector, a second multiplier that multiplies the output signal of the first multiplier with an m th gating signal, an adder, and a subtractor.