Abstract: A system for communicating a sequence of information symbols using a chaotic sequence spread spectrum signal. The system includes a transmitter (402) for transmitting a signal including the information symbols, the information symbols encoded into the signal using a first chaotic sequence of chips generated at the transmitter. The system also includes a receiver (404) configure to receive the signal and extract the information symbols from the signal, the information symbols extracted using a second chaotic sequence of chips generated at the receiver. In the system, the first and the second chaotic sequences are identical and synchronized in time and frequency, each of the sequence of symbols is associated with a randomly generated threshold symbol energy value, and the portion of chips in the first and the second chaotic sequences associated with each of the plurality of information symbols is selected based on the associated threshold symbol energy value.

Abstract: Systems and methods for code-division multiplex communications. The methods involve forming orthogonal or statistically orthogonal chaotic spreading sequences (CSC1,1, CSCD,1), each comprising a different chaotic sequence. The methods also involve generating an offset chaotic spreading sequence (CSC1,2, CSC1,3, . . . , CSC1,K(1), CSCD,2, . . . , CSCD,K(D)) which is the same as a first one of the orthogonal or statistically orthogonal chaotic spreading sequences, but temporally offset. Spread spectrum communications signals (SSCs) are each respectively generated using one of the orthogonal or statistically orthogonal chaotic spreading sequences. Another SSC is generated using the offset chaotic spreading sequence. The SSCs are concurrently transmitted over a common RF frequency band.

Abstract: A semiconductor device includes a plurality of processing clusters that operate synchronously internally and arranged in a M×N matrix. Each processing cluster is formed as a plurality of processing elements and clocked buses that interconnect the processing elements within each processing cluster. A self-synchronous cluster wrapper is operative with the processing elements such that each processing cluster forms a programmable module. Self-synchronous global and local buses interconnect the processing clusters for communicating externally. An input/output circuit interconnects the global and local buses.

Abstract: A system for communicating includes a transmitter that has an encoder and baseband modulator that encodes and modulates a sequence of data symbols as a payload data constellation to be communicated. A PN sequence generator and baseband modulator form a pilot signal as a training sequence with a periodically repeating spread spectrum sequence. A circuit superimposes the pilot signal over the sequence of data symbols to form a composite communication signal that is transmitted. A receiver receives the composite communication signal and extracts the pilot signal from the composite communication signal.

Abstract: Methods for code-division multiplex communications. The method involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC1, . . . , CSCK) having different static offsets using a set of polynomial equations (f0(x(nT)), . . . , fN?1(x(nT)) and/or f0[x((n+v)T+t)], . . . , fN?1[x((n+v)T+t)]). The methods also involve forming spread spectrum communications signals respectively using the orthogonal or statistically orthogonal chaotic spreading codes. The methods further involve concurrently transmitting the spread spectrum communications signals over a common RF frequency band. The spreading codes are generated using different initial values for a variable “x” of a polynomial equation f(x(nT)) and/or different acc-dec values for a variable “v” of a polynomial equation f[x((n+v)T+t)]. The static offsets are defined by the different initial values for a variable “x” and/or different acc-dec values for a variable “v”.

Abstract: Methods for code-division multiplex communications. The methods involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC1, . . . , CSCK) using different sets of polynomial equations (f0(x(nT)), . . . , fN-1(x(nT))), different constant values (C0, C1, . . . , CN-1) for the polynomial equations, or different sets of relatively prime numbers (p0, p1, . . . , pN-1) as modulus (m0, m1, . . . , mN-1) in solving the polynomial equations. The methods also involve forming spread spectrum communications signals using the orthogonal or statistically orthogonal chaotic spreading codes, respectively. The method further involve concurrently transmitting the spread spectrum communications signals over a common RF frequency band.

Abstract: A system, method and apparatus includes a transmitter that has an encoder and baseband modulator that encodes and modulates a sequence of payload data symbols as a signal constellation to be communicated. An amble generator and baseband modulator generates amble symbols as a known sequence of M symbol times in length every N symbol times. A multiplexer multiplexes the data and amble symbols together to form a communications signal that is transmitted over a communications channel.

Abstract: A method for generating an accelerated and/or decelerated chaotic sequence. The method involves selecting a plurality of polynomial equations constructed from an acc-dec variable v. The method also involves selecting a value for the acc-dec variable v for advancing or stepping back a chaotic sequence generation by at least one cycle at a given time. The method further involves using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations using the acc-dec variable v. The solutions iteratively computed and expressed as RNS residue values. The method involves determining a series of digits in a weighted number system based on the RNS residue values.

Abstract: Systems (400, 500, 600) and methods (300) for generating a chaotic amplitude modulated signal absent of cyclostationary features by preserving a constant variance. The methods involve: generating a PAM signal including pulse amplitude modulation having a periodically changing amplitude; generating a first part of a constant power envelope signal (FPCPES) by dividing the PAM signal by a square root of a magnitude of the PAM signal; generating a second part of the constant power envelope signal (SPCPES) having a magnitude equal to a square root of one minus the magnitude of the PAM signal; and generating first and second spreading sequences (FSS and SSS). The methods also involve combining the FPCPES with the FSS to generate a first product signal (FPS) and combining the SPCPES with the SSS to generate a second product signal (SPS). A constant power envelope signal is generated using the FPS and SPS.

Abstract: A method is provided for correlating samples of a received signal and samples of an internally generated/stored sample sequence (“IGSSS”). The method involves performing a first iteration of a first-resolution correlation state. The first-resolution correlation state involves: selecting a first N sets of samples from the received signal; selecting a first set of samples from the IGSSS; and concurrently comparing each of the N sets of samples with the first set of samples to determine if a correlation exists between the same. If it is determined that a correlation does not exist between one of the N sets of samples and the first set of samples, then a second iteration of the first-resolution correlation state is performed. If it is determined that a correlation exists between one of the N sets of samples and the first set of samples, then a first iteration of a second-resolution correlation state is performed.

Abstract: A method (30°) for generating a sine and cosine of an input angle (Ø102). The method involves decomposing Ø102 to an octant or quadrant, a coarse angle (A), and a fine angle (B), determining cos(A), and determining sin(A). The method also involves decomposing cos(A) and sin(A) to a most significant word (MSW) and a least significant word (LSW). The method further involves computing an approximation of 1?cos(B), an approximation of sin(B), and a plurality of products (P1, . . . , P4) using the MSWs and approximations. The method involves computing approximations of cos(Ø?102) and sin(Ø?102) using the values for cos(A), sin(A), and P1, . . . , P4. The method involves scaling the approximations of cos(Ø?102) and sin(Ø?102) to a desired resolution.

Abstract: A cryptographic system (1000) is provided. The cryptographic system includes a data stream receiving means (DSRM), a number generator (NG), a mixed radix accumulator (MRA) and an encryptor. The DSRM (1002) receives a data stream (DS). The NG (702) generates a first number sequence (FNS) contained within a Galois Field GF[M]. The MRA (750) is configured to perform a first modification to a first number (FN) in FNS. The first modification involves summing the FN with a result of a modulo P operation performed on a second number in FNS that proceeds FN. The MRA is also configured to perform a second modification to FN utilizing a modulo P operation. The MRA is further configured to repeat the first and second modification for numbers in FNS to generate a second number sequence (SNS). The encryptor (1004) is configured to generate a modified data stream by combining SNS and DS.

Abstract: A cryptographic system (CS) comprised of generators (502), (504), (510), an encryption device (ED), and a decryption device (DD). The generator (502) generates a data sequence (DS) including payload data. The generator (504) generates an encryption sequence (ES) including random numbers. The ED (506) is configured to perform a CGFC arithmetic process. As such, the ED is comprised of a mapping device (MD) and an encryptor. The MD is configured to map the DS and ES from Galois field GF[pk] to Galois extension field GF[pk+1]. The encryptor is configured to generate an encrypted data sequence (EDS) by combining the DS and ES utilizing a Galois field multiplication operation in Galois extension field GF[pk+1]. The generator (510) is configured to generate a decryption sequence (DS). The DD (508) is configured to generate a decrypted data sequence by performing an inverse of the CGFC arithmetic process utilizing the EDS and DS.

Abstract: A cryptographic system (CS) is provided. The CS (800) comprises a data stream receiving means (DSRM), a generator (702), a mixed radix converter (MRC) and an encryptor (908). The DSRM (902) is configured to receive a data stream (DS). The generator is configured to selectively generate a random number sequence (RNS) utilizing a punctured ring structure. The MRC (704) is coupled to the generator and configured to perform a mixed radix conversion to convert the RNS from a first number base to a second number base. The encryptor is coupled to the DSRM and MRC. The encryptor is configured to generate an altered data stream by combining the RNS in the second number base with the DS. The punctured ring structure and the MRC are configured in combination to produce an RNS in the second number base which contains a priori defined statistical artifacts after the mixed radix conversion.

Abstract: A cryptographic system (CS) is provided. The CS (500) is comprised of a data stream receiving device (DSRD), a chaotic sequence generator (CSG) and an encryptor. The DSRD (602) is configured to receive an input data stream. The CSG (300) includes a computing means (3020, . . . , 302N-1) and a mapping means (304). The computing means is configured to use RNS arithmetic operations to respectively determine solutions for polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The mapping means is configured to determine a series of digits in the weighted number system based on the RNS residue values. The encryptor is coupled to the DSRD and CSG. The encryptor is configured to generate a modified data stream by incorporating or combining the series of digits with the input data stream.

Abstract: A method is provided for combining two or more input sequences in a communications system to increase a repetition period of the input sequences in a resource-efficient manner. The method includes a receiving step, a mapping step, and a generating step. The receiving step involves receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk]. The mapping step involves mapping the first and second number sequences to a Galois extension field GF[pk+1]. The generating step involves generating an output sequence by combining the first number sequence with the second number sequence utilizing a Galois field multiplication operation in the Galois extension field GF[pk+1]. p is a prime number. k is an integer. pk+1 defines a finite field size of the Galois extension field GF[pk+1].

Abstract: A method is provided for coherently demodulating a chaotic sequence spread spectrum signal at a receiver (104). The method includes receiving a chaotic sequence spread spectrum signal including a plurality of information symbols. The method also includes generating a first string of discrete time chaotic samples. The first string of discrete time chaotic samples is identical to a second string of discrete time chaotic samples generated at a transmitter. The method further includes processing the chaotic sequence spread spectrum signal at the receiver to identify a time offset and a frequency offset relative to the first string of discrete time chaotic samples. Each of the discrete time chaotic samples of the first string of discrete time chaotic samples has a shorter sample time interval than the duration of the information symbols.

Abstract: A method is presided for masking a process used in generating a random number sequence. The method includes generating a random number sequence. This step involves selectively generating the random number sequence utilizing a ring structure which has been punctured. The method also includes performing a mixed radix conversion to convert the random number sequence from a first number base to a second number base. The method further includes puncturing the ring structure by removing at least one element therefrom to eliminate a statistical artifact in the random number sequence expressed in the second number base. The first number base and second number base are selected so that they are respectively defined by a first Galois field characteristic and a second Galois field characteristic.

Abstract: A method is provided for generating a coherent chaotic sequence spread spectrum communications system. The method includes phase modulating a carrier with information symbols. The method also includes generating a string of discrete time chaotic samples. The method further includes modulating the carrier in a chaotic manner using the string of discrete time chaotic samples. Each of the discrete time chaotic samples has a shorter sample time interval than the duration of the information symbols. The generating step includes selecting a plurality of polynomial equations. The generating step also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The generating step further includes determining a series of digits in the weighted number system based on the RNS residue values.

Abstract: A method is provided for masking a process used in generating a number sequence. The method includes generating a first sequence of numbers contained within a Galois field GF[M]. The method also includes performing a first modification to a first number in the first sequence of numbers. The first modification includes summing the first number with a result of a modulo P operation performed on a second number of the first sequence that proceeds the first number. M is relatively prime with respect to P. The method further includes performing a second modification to the first random number. The second modification is comprised of a modulo P operation. This second modification is performed subsequent to the first modification. The method includes repeating the first and second modification for a plurality of numbers comprising the first sequence of numbers to generate a second sequence of numbers.